UserDataOperators.hpp

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/** \file UserDataOperators.hpp
 * \brief User data operators for finite element computations
 *
 * This file contains a comprehensive collection of user data operators used in
 * MoFEM finite element computations. These operators provide functionality for
 * calculating, transforming, and manipulating field values at integration points.
 *
 * ## Main Categories of Operators:
 *
 * ### Field Value Calculation Operators
 * - **Scalar Field Operators**: Calculate scalar field values at integration points
 *   - OpCalculateScalarFieldValues: General scalar field value calculation
 *   - OpCalculateScalarFieldValuesFromPetscVecImpl: PETSc vector-based scalar values
 * - **Vector Field Operators**: Calculate vector field values at integration points
 *   - OpCalculateVectorFieldValues: General vector field value calculation
 *   - OpCalculateDivergenceVectorFieldValues: Divergence calculation for vector fields
 * - **Tensor Field Operators**: Calculate tensor field values at integration points
 *   - OpCalculateTensor2FieldValues: Second-rank tensor field calculations
 *   - OpCalculateTensor2SymmetricFieldValues: Symmetric tensor field calculations
 *
 * ### Field Gradient Calculation Operators
 * - **Scalar Gradient Operators**:
 *   - OpCalculateScalarFieldGradient: Gradient of scalar fields
 *   - OpCalculateScalarFieldHessian: Hessian (second derivatives) of scalar fields
 * - **Vector Gradient Operators**:
 *   - OpCalculateVectorFieldGradient: Gradient of vector fields
 *
 * ### Matrix and Tensor Operations
 * - **Matrix Manipulation**:
 *   - OpInvertMatrix: Matrix inversion at integration points
 *   - OpScaleMatrix: Element-wise matrix scaling operations
 *   - OpCalculateTraceFromMat: Trace calculation for matrices
 * - **Tensor Operations**:
 *   - OpSymmetrizeTensor: Tensor symmetrization operations
 *   - OpTensorTimesSymmetricTensor: Tensor multiplication operations
 *
 * ### Coordinate and Geometry Operations
 * - **Transformation Operators**: Handle coordinate transformations and geometric operations
 * - **Integration Point Operations**: Manage data at Gauss integration points
 *
 * ## Key Features:
 *
 * ### Template-Based Design
 * Most operators are implemented as template structures allowing:
 * - Flexible data types (double, float, etc.)
 * - Various tensor dimensions and field dimensions
 * - Different storage layouts and allocators
 * - Compile-time optimization for specific use cases
 *
 * ### PETSc Integration
 * Many operators provide seamless integration with PETSc:
 * - Direct access to PETSc vectors and matrices
 * - Efficient data exchange between MoFEM and PETSc
 * - Support for distributed computing environments
 *
 * ### Field Space Support
 * Operators support various finite element field spaces:
 * - H1 (continuous) spaces for scalar and vector fields
 * - Hdiv spaces for flux-like vector fields
 * - Hcurl spaces for curl-conforming vector fields
 * - L2 spaces for discontinuous fields
 *
 * ### Memory Management
 * Robust memory management through:
 * - Smart pointer usage (boost::shared_ptr)
 * - RAII principles for resource management
 * - Exception safety and error handling
 *
 * ## Usage Patterns:
 *
 * 1. **Field Evaluation**: Calculate field values at integration points for
 *    post-processing, visualization, or coupling with other physics
 *
 * 2. **Gradient Calculations**: Compute spatial derivatives for stress analysis,
 *    heat conduction, fluid dynamics, and other gradient-dependent phenomena
 *
 * 3. **Matrix Operations**: Perform linear algebra operations needed in
 *    constitutive relations, coordinate transformations, and iterative solvers
 *
 * 4. **Data Extraction**: Extract computed results from finite element solutions
 *    for analysis, visualization, or coupling with external codes
 *
 * ## Thread Safety and Performance:
 * - Operators are designed to be thread-safe when used properly
 * - Optimized for performance in parallel finite element computations
 * - Minimal memory allocations during computation loops
 *
 * @note These operators are typically used within the MoFEM pipeline system
 *       and are automatically integrated into finite element assembly processes.
 *
 * @see ForcesAndSourcesCore::UserDataOperator for base class documentation
 * @see EntitiesFieldData for field data management
 * @see PipelineManager for operator pipeline management
 */
 
#ifndef __USER_DATA_OPERATORS_HPP__
  #define __USER_DATA_OPERATORS_HPP__
 
namespace MoFEM {
 
/** \name Get values at Gauss pts */
 
/**@{*/
 
/** \name Scalar values */
 
/**@{*/
 
/** \brief Scalar field values at integration points
 *
 */
 
/**
 * @brief Operator for calculating scalar field values at integration points
 *
 * This template structure calculates scalar field values at integration points
 * and stores them in a provided data container. It supports different storage
 * types through template parameters and can optionally work with PETSc vectors.
 *
 * @tparam T Data type for the scalar field values (e.g., double, float)
 * @tparam A Allocator type for the ublas vector storage
 */
template <class T, class A>
struct OpCalculateScalarFieldValues_General
    : public ForcesAndSourcesCore::UserDataOperator {
 
  /**
   * @brief Constructor for scalar field values calculation operator
   *
   * @param field_name Name of the scalar field to calculate values for
   * @param data_ptr Shared pointer to ublas vector for storing calculated values
   * @param zero_type Entity type for zero-level entities (default: MBVERTEX)
   */
  OpCalculateScalarFieldValues_General(
      const std::string field_name,
      boost::shared_ptr<ublas::vector<T, A>> data_ptr,
      const EntityType zero_type = MBVERTEX)
      : ForcesAndSourcesCore::UserDataOperator(field_name, OPROW),
        dataPtr(data_ptr), zeroType(zero_type) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  /**
   * @brief Constructor with PETSc vector support
   *
   * @param field_name Name of the scalar field to calculate values for
   * @param data_ptr Shared pointer to ublas vector for storing calculated values
   * @param data_vec Smart PETSc vector object for additional data storage
   * @param zero_type Entity type for zero-level entities (default: MBVERTEX)
   */
  OpCalculateScalarFieldValues_General(
      const std::string field_name,
      boost::shared_ptr<ublas::vector<T, A>> data_ptr,
      SmartPetscObj<Vec> data_vec, const EntityType zero_type = MBVERTEX)
      : ForcesAndSourcesCore::UserDataOperator(field_name, OPROW),
        dataPtr(data_ptr), zeroType(zero_type), dataVec(data_vec) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  /**
   * \brief calculate values of scalar field at integration points
   * @param  side side entity number
   * @param  type side entity type
   * @param  data entity data
   * @return      error code
   */
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
protected:
  boost::shared_ptr<ublas::vector<T, A>> dataPtr;
  const EntityHandle zeroType;
  SmartPetscObj<Vec> dataVec;
  VectorDouble dotVector;
};
 
/**
 * \brief Specialization of member function
 *
 */
template <class T, class A>
MoFEMErrorCode OpCalculateScalarFieldValues_General<T, A>::doWork(
    int side, EntityType type, EntitiesFieldData::EntData &data) {
  MoFEMFunctionBegin;
  SETERRQ(PETSC_COMM_SELF, MOFEM_NOT_IMPLEMENTED, "Not implemented for T = %s",
           typeid(T).name() // boost::core::demangle(typeid(T).name()).c_str()
  );
  MoFEMFunctionReturn(0);
}
 
/**
 * @brief Specialization for double precision scalar field values calculation
 *
 * This structure is a specialization of OpCalculateScalarFieldValues_General
 * for double precision scalar fields using DoubleAllocator. It provides
 * concrete implementation for calculating scalar field values at integration
 * points and storing them in double precision format.
 *
 * @ingroup mofem_forces_and_sources_user_data_operators
 */
struct OpCalculateScalarFieldValues
    : public OpCalculateScalarFieldValues_General<double, DoubleAllocator> {
 
  using OpCalculateScalarFieldValues_General<
      double, DoubleAllocator>::OpCalculateScalarFieldValues_General;
 
  /**
   * \brief calculate values of scalar field at integration points
   * @param  side side entity number
   * @param  type side entity type
   * @param  data entity data
   * @return      error code
   */
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
    VectorDouble &vec = *dataPtr;
    const size_t nb_gauss_pts = getGaussPts().size2();
    if (type == zeroType || vec.size() != nb_gauss_pts) {
      vec.resize(nb_gauss_pts, false);
      vec.clear();
    }
 
    const size_t nb_dofs = data.getFieldData().size();
 
    if (nb_dofs) {
 
      if (dataVec.use_count()) {
        dotVector.resize(nb_dofs, false);
        const double *array;
        CHKERR VecGetArrayRead(dataVec, &array);
        const auto &local_indices = data.getLocalIndices();
        for (int i = 0; i != local_indices.size(); ++i)
          if (local_indices[i] != -1)
            dotVector[i] = array[local_indices[i]];
          else
            dotVector[i] = 0;
        CHKERR VecRestoreArrayRead(dataVec, &array);
        data.getFieldData().swap(dotVector);
      }
 
      const size_t nb_base_functions = data.getN().size2();
      auto base_function = data.getFTensor0N();
      auto values_at_gauss_pts = getFTensor0FromVec(vec);
      for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
        auto field_data = data.getFTensor0FieldData();
        size_t bb = 0;
        for (; bb != nb_dofs; ++bb) {
          values_at_gauss_pts += field_data * base_function;
          ++field_data;
          ++base_function;
        }
        // It is possible to have more base functions than dofs
        for (; bb < nb_base_functions; ++bb)
          ++base_function;
        ++values_at_gauss_pts;
      }
 
      if (dataVec.use_count()) {
        data.getFieldData().swap(dotVector);
      }
    }
 
    MoFEMFunctionReturn(0);
  }
};
 
/**
 * @brief Calculate scalar field values from PETSc vector at integration points
 *
 * This template structure extracts scalar field values from a PETSc vector
 * and calculates them at integration points. It supports different data contexts
 * through the template parameter and can handle various entity types.
 *
 * @tparam CTX PETSc data context type specifying how data is accessed
 *
 * @ingroup mofem_forces_and_sources_user_data_operators
 */
template <PetscData::DataContext CTX>
struct OpCalculateScalarFieldValuesFromPetscVecImpl
    : public ForcesAndSourcesCore::UserDataOperator {
 
  /**
   * @brief Constructor for PETSc vector-based scalar field calculation
   *
   * @param field_name Name of the scalar field to extract values from
   * @param data_ptr Shared pointer to VectorDouble for storing calculated values
   * @param zero_at_type Entity type where values should be zeroed (default: MBVERTEX)
   */
  OpCalculateScalarFieldValuesFromPetscVecImpl(
      const std::string field_name, boost::shared_ptr<VectorDouble> data_ptr,
      const EntityType zero_at_type = MBVERTEX)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroAtType(zero_at_type) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
 
    const size_t nb_gauss_pts = getGaussPts().size2();
 
    VectorDouble &vec = *dataPtr;
    if (type == zeroAtType || vec.size() != nb_gauss_pts) {
      vec.resize(nb_gauss_pts, false);
      vec.clear();
    }
 
    auto &local_indices = data.getLocalIndices();
    const size_t nb_dofs = local_indices.size();
    if (nb_dofs) {
 
      const double *array;
 
      auto get_array = [&](const auto ctx, auto vec) {
        MoFEMFunctionBegin;
  #ifndef NDEBUG
        if ((getFEMethod()->data_ctx & ctx).none()) {
          MOFEM_LOG_CHANNEL("SELF");
          MOFEM_LOG("SELF", Sev::error)
              << "In this case field degrees of freedom are read from vector.  "
                 "That usually happens when time solver is used, and acces to "
                 "first or second rates is needed. You probably not set ts_u, "
                 "ts_u_t, or ts_u_tt and associated data structure, i.e. "
                 "data_ctx to CTX_SET_X, CTX_SET_X_T, or CTX_SET_X_TT "
                 "respectively";
          SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY, "Vector not set!");
        }
  #endif
        CHKERR VecGetArrayRead(vec, &array);
        MoFEMFunctionReturn(0);
      };
 
      auto restore_array = [&](auto vec) {
        return VecRestoreArrayRead(vec, &array);
      };
 
      switch (CTX) {
      case PetscData::CTX_SET_X:
        CHKERR get_array(PetscData::CtxSetX, getFEMethod()->ts_u);
        break;
      case PetscData::CTX_SET_X_T:
        CHKERR get_array(PetscData::CtxSetX_T, getFEMethod()->ts_u_t);
        break;
      case PetscData::CTX_SET_X_TT:
        CHKERR get_array(PetscData::CtxSetX_TT, getFEMethod()->ts_u_tt);
        break;
      default:
        SETERRQ(PETSC_COMM_SELF, MOFEM_NOT_IMPLEMENTED,
                "That case is not implemented");
      }
 
      std::array<double, MAX_DOFS_ON_ENTITY> dot_dofs_vector;
      for (int i = 0; i != local_indices.size(); ++i)
        if (local_indices[i] != -1)
          dot_dofs_vector[i] = array[local_indices[i]];
        else
          dot_dofs_vector[i] = 0;
 
      switch (CTX) {
      case PetscData::CTX_SET_X:
        CHKERR restore_array(getFEMethod()->ts_u);
        break;
      case PetscData::CTX_SET_X_T:
        CHKERR restore_array(getFEMethod()->ts_u_t);
        break;
      case PetscData::CTX_SET_X_TT:
        CHKERR restore_array(getFEMethod()->ts_u_tt);
        break;
      default:
        SETERRQ(PETSC_COMM_SELF, MOFEM_NOT_IMPLEMENTED,
                "That case is not implemented");
      }
 
      const size_t nb_base_functions = data.getN().size2();
      auto base_function = data.getFTensor0N();
      auto values_at_gauss_pts = getFTensor0FromVec(vec);
 
      for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
        size_t bb = 0;
        for (; bb != nb_dofs; ++bb) {
          values_at_gauss_pts += dot_dofs_vector[bb] * base_function;
          ++base_function;
        }
        // Number of dofs can be smaller than number of Tensor_Dim x base
        // functions
        for (; bb < nb_base_functions; ++bb)
          ++base_function;
        ++values_at_gauss_pts;
      }
    }
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<VectorDouble> dataPtr;
  const EntityHandle zeroAtType;
};
 
using OpCalculateScalarFieldValuesDot =
    OpCalculateScalarFieldValuesFromPetscVecImpl<PetscData::CTX_SET_X_T>;
using OpCalculateScalarFieldValuesDotDot =
    OpCalculateScalarFieldValuesFromPetscVecImpl<PetscData::CTX_SET_X_TT>;
 
/**
 * \deprecated Name inconsistent with other operators
 *
 */
using OpCalculateScalarValuesDot = OpCalculateScalarFieldValuesDot;
 
/**@}*/
 
/** \name Vector field values at integration points */
 
/**@{*/
 
/**
 * @brief Calculate field values for tensor field rank 1, i.e. vector field
 *
 * This template structure calculates vector field values at integration points
 * and stores them in a matrix container. It supports various tensor dimensions,
 * data types, and storage layouts through template parameters.
 *
 * @tparam Tensor_Dim Dimension of the vector field (e.g., 2 for 2D, 3 for 3D)
 * @tparam T Data type for the field values (e.g., double, float)
 * @tparam L Layout type for the ublas matrix storage
 * @tparam A Allocator type for the ublas matrix storage
 */
template <int Tensor_Dim, class T, class L, class A>
struct OpCalculateVectorFieldValues_General
    : public ForcesAndSourcesCore::UserDataOperator {
 
  /**
   * @brief Constructor for vector field values calculation operator
   *
   * @param field_name Name of the vector field to calculate values for
   * @param data_ptr Shared pointer to ublas matrix for storing calculated values
   * @param zero_type Entity type for zero-level entities (default: MBVERTEX)
   */
  OpCalculateVectorFieldValues_General(
      const std::string field_name,
      boost::shared_ptr<ublas::matrix<T, L, A>> data_ptr,
      const EntityType zero_type = MBVERTEX)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroType(zero_type) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  /**
   * \brief calculate values of vector field at integration points
   * @param  side side entity number
   * @param  type side entity type
   * @param  data entity data
   * @return      error code
   */
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
protected:
  boost::shared_ptr<ublas::matrix<T, L, A>> dataPtr;
  const EntityHandle zeroType;
};
 
template <int Tensor_Dim, class T, class L, class A>
MoFEMErrorCode
OpCalculateVectorFieldValues_General<Tensor_Dim, T, L, A>::doWork(
    int side, EntityType type, EntitiesFieldData::EntData &data) {
  MoFEMFunctionBeginHot;
  SETERRQ(PETSC_COMM_SELF, MOFEM_NOT_IMPLEMENTED,
           "Not implemented for T = %s and dim = %d",
           typeid(T).name(), // boost::core::demangle(typeid(T).name()),
           Tensor_Dim);
  MoFEMFunctionReturnHot(0);
}
 
/** \brief Calculate field values (template specialization) for tensor field
 * rank 1, i.e. vector field
 *
 */
template <int Tensor_Dim>
struct OpCalculateVectorFieldValues_General<Tensor_Dim, double,
                                            ublas::row_major, DoubleAllocator>
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateVectorFieldValues_General(const std::string field_name,
                                       boost::shared_ptr<MatrixDouble> data_ptr,
                                       const EntityType zero_type = MBVERTEX)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroType(zero_type) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  OpCalculateVectorFieldValues_General(const std::string field_name,
                                       boost::shared_ptr<MatrixDouble> data_ptr,
                                       SmartPetscObj<Vec> data_vec,
                                       const EntityType zero_type = MBVERTEX)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), dataVec(data_vec), zeroType(zero_type) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
protected:
  boost::shared_ptr<MatrixDouble> dataPtr;
  SmartPetscObj<Vec> dataVec;
  const EntityHandle zeroType;
  VectorDouble dotVector;
};
 
/**
 * \brief Member function specialization calculating values for tenor field rank
 *
 */
template <int Tensor_Dim>
MoFEMErrorCode OpCalculateVectorFieldValues_General<
    Tensor_Dim, double, ublas::row_major,
    DoubleAllocator>::doWork(int side, EntityType type,
                             EntitiesFieldData::EntData &data) {
  MoFEMFunctionBegin;
 
  const size_t nb_gauss_pts = getGaussPts().size2();
  auto &mat = *dataPtr;
  if (type == zeroType || mat.size2() != nb_gauss_pts) {
    mat.resize(Tensor_Dim, nb_gauss_pts, false);
    mat.clear();
  }
 
  const size_t nb_dofs = data.getFieldData().size();
  if (nb_dofs) {
 
    if (dataVec.use_count()) {
      dotVector.resize(nb_dofs, false);
      const double *array;
      CHKERR VecGetArrayRead(dataVec, &array);
      const auto &local_indices = data.getLocalIndices();
      for (int i = 0; i != local_indices.size(); ++i)
        if (local_indices[i] != -1)
          dotVector[i] = array[local_indices[i]];
        else
          dotVector[i] = 0;
      CHKERR VecRestoreArrayRead(dataVec, &array);
      data.getFieldData().swap(dotVector);
    }
 
    if (nb_gauss_pts) {
      const size_t nb_base_functions = data.getN().size2();
      auto base_function = data.getFTensor0N();
      auto values_at_gauss_pts = getFTensor1FromMat<Tensor_Dim>(mat);
      FTensor::Index<'I', Tensor_Dim> I;
      const size_t size = nb_dofs / Tensor_Dim;
      if (nb_dofs % Tensor_Dim) {
        SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                "Nb. of DOFs is inconsistent with Tensor_Dim");
      }
      for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
        auto field_data = data.getFTensor1FieldData<Tensor_Dim>();
 
  #ifndef NDEBUG
        if (field_data.l2() != field_data.l2()) {
          MOFEM_LOG("SELF", Sev::error) << "field data: " << field_data;
          SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                  "Wrong number in coefficients");
        }
  #endif
 
        size_t bb = 0;
        for (; bb != size; ++bb) {
 
  #ifndef SINGULARITY
    #ifndef NDEBUG
          if (base_function != base_function) {
            MOFEM_LOG("SELF", Sev::error) << "base function: " << base_function;
            SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                    "Wrong number number in base functions");
          }
    #endif
  #endif
 
          values_at_gauss_pts(I) += field_data(I) * base_function;
          ++field_data;
          ++base_function;
        }
        // Number of dofs can be smaller than number of Tensor_Dim x base
        // functions
        for (; bb < nb_base_functions; ++bb)
          ++base_function;
        ++values_at_gauss_pts;
      }
    }
 
    if (dataVec.use_count()) {
      data.getFieldData().swap(dotVector);
    }
  }
  MoFEMFunctionReturn(0);
}
 
/**
 * @brief Specialization for double precision vector field values calculation
 *
 * This structure is a specialization of OpCalculateVectorFieldValues_General
 * for double precision vector fields using row_major layout and DoubleAllocator.
 * It provides a convenient interface for calculating vector field values at
 * integration points.
 *
 * @tparam Tensor_Dim Dimension of the vector field (e.g., 2 for 2D, 3 for 3D)
 *
 * @ingroup mofem_forces_and_sources_user_data_operators
 */
template <int Tensor_Dim>
struct OpCalculateVectorFieldValues
    : public OpCalculateVectorFieldValues_General<
          Tensor_Dim, double, ublas::row_major, DoubleAllocator> {
 
  using OpCalculateVectorFieldValues_General<
      Tensor_Dim, double, ublas::row_major,
      DoubleAllocator>::OpCalculateVectorFieldValues_General;
};
 
/**@}*/
 
/** \name Vector field values at integration points */
 
/**@{*/
 
/**
 * @brief Calculate divergence of vector field at integration points
 *
 * This template structure calculates the divergence of a vector field at
 * integration points. It supports different coordinate systems and tensor
 * dimensions, making it suitable for various physical applications.
 *
 * @tparam Tensor_Dim Dimension of the vector field (e.g., 2 for 2D, 3 for 3D)
 * @tparam COORDINATE_SYSTEM Coordinate system type (default: CARTESIAN)
 */
template <int Tensor_Dim, CoordinateTypes COORDINATE_SYSTEM = CARTESIAN>
struct OpCalculateDivergenceVectorFieldValues
    : public ForcesAndSourcesCore::UserDataOperator {
 
  /**
   * @brief Constructor for vector field divergence calculation operator
   *
   * @param field_name Name of the vector field to calculate divergence for
   * @param data_ptr Shared pointer to VectorDouble for storing calculated divergence values
   * @param zero_type Entity type for zero-level entities (default: MBVERTEX)
   */
  OpCalculateDivergenceVectorFieldValues(
      const std::string field_name, boost::shared_ptr<VectorDouble> data_ptr,
      const EntityType zero_type = MBVERTEX)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroType(zero_type) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
 
    // When we move to C++17 add if constexpr()
    if constexpr (COORDINATE_SYSTEM == POLAR || COORDINATE_SYSTEM == SPHERICAL)
      SETERRQ(PETSC_COMM_SELF, MOFEM_NOT_IMPLEMENTED,
               "%s coordiante not implemented",
               CoordinateTypesNames[COORDINATE_SYSTEM]);
 
    const size_t nb_gauss_pts = getGaussPts().size2();
    auto &vec = *dataPtr;
    if (type == zeroType) {
      vec.resize(nb_gauss_pts, false);
      vec.clear();
    }
 
    const size_t nb_dofs = data.getFieldData().size();
    if (nb_dofs) {
 
      if (nb_gauss_pts) {
        const size_t nb_base_functions = data.getN().size2();
        auto values_at_gauss_pts = getFTensor0FromVec(vec);
        FTensor::Index<'I', Tensor_Dim> I;
        const size_t size = nb_dofs / Tensor_Dim;
  #ifndef NDEBUG
        if (nb_dofs % Tensor_Dim) {
          SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                  "Number of dofs should multiple of dimensions");
        }
  #endif
 
        // When we move to C++17 add if constexpr()
        if constexpr (COORDINATE_SYSTEM == CARTESIAN) {
          auto diff_base_function = data.getFTensor1DiffN<Tensor_Dim>();
          for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
            auto field_data = data.getFTensor1FieldData<Tensor_Dim>();
            size_t bb = 0;
            for (; bb != size; ++bb) {
              values_at_gauss_pts += field_data(I) * diff_base_function(I);
              ++field_data;
              ++diff_base_function;
            }
            // Number of dofs can be smaller than number of Tensor_Dim x base
            // functions
            for (; bb < nb_base_functions; ++bb)
              ++diff_base_function;
            ++values_at_gauss_pts;
          }
        }
 
        // When we move to C++17 add if constexpr()
        if constexpr (COORDINATE_SYSTEM == CYLINDRICAL) {
          auto t_coords = getFTensor1CoordsAtGaussPts();
          auto values_at_gauss_pts = getFTensor0FromVec(vec);
          auto base_function = data.getFTensor0N();
          auto diff_base_function = data.getFTensor1DiffN<Tensor_Dim>();
          for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
            auto field_data = data.getFTensor1FieldData<Tensor_Dim>();
            size_t bb = 0;
            for (; bb != size; ++bb) {
              values_at_gauss_pts += field_data(I) * diff_base_function(I);
              values_at_gauss_pts +=
                  base_function * (field_data(0) / t_coords(0));
              ++field_data;
              ++base_function;
              ++diff_base_function;
            }
            // Number of dofs can be smaller than number of Tensor_Dim x base
            // functions
            for (; bb < nb_base_functions; ++bb) {
              ++base_function;
              ++diff_base_function;
            }
            ++values_at_gauss_pts;
            ++t_coords;
          }
        }
      }
    }
    MoFEMFunctionReturn(0);
  }
 
protected:
  boost::shared_ptr<VectorDouble> dataPtr;
  const EntityHandle zeroType;
};
 
/** \brief Approximate field values for given petsc vector
 *
 * \note Look at PetscData to see what vectors could be extracted with that user
 * data operator.
 *
 * \ingroup mofem_forces_and_sources_user_data_operators
 */
template <int Tensor_Dim, PetscData::DataContext CTX>
struct OpCalculateVectorFieldValuesFromPetscVecImpl
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateVectorFieldValuesFromPetscVecImpl(
      const std::string field_name, boost::shared_ptr<MatrixDouble> data_ptr,
      const EntityType zero_at_type = MBVERTEX, bool throw_error = true)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroAtType(zero_at_type), throwError(throw_error) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
 
    auto &local_indices = data.getLocalIndices();
    const size_t nb_dofs = local_indices.size();
    const size_t nb_gauss_pts = getGaussPts().size2();
 
    MatrixDouble &mat = *dataPtr;
    if (type == zeroAtType) {
      mat.resize(Tensor_Dim, nb_gauss_pts, false);
      mat.clear();
    }
    if (!nb_dofs)
      MoFEMFunctionReturnHot(0);
 
    if (!throwError) {
      if ((getFEMethod()->data_ctx & PetscData::Switches(CTX)).none()) {
        MoFEMFunctionReturnHot(0);
      }
    }
 
    const double *array;
 
    auto get_array = [&](const auto ctx, auto vec) {
      MoFEMFunctionBegin;
  #ifndef NDEBUG
      if ((getFEMethod()->data_ctx & ctx).none()) {
        MOFEM_LOG_CHANNEL("SELF");
        MOFEM_LOG("SELF", Sev::error)
            << "In this case field degrees of freedom are read from vector.  "
               "That usually happens when time solver is used, and access to "
               "first or second rates is needed. You probably not set ts_u, "
               "ts_u_t, or ts_u_tt and associated data structure, i.e. "
               "data_ctx to CTX_SET_X, CTX_SET_DX, CTX_SET_X_T, or "
               "CTX_SET_X_TT respectively";
        SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY, "Vector not set");
      }
  #endif
      CHKERR VecGetArrayRead(vec, &array);
      MoFEMFunctionReturn(0);
    };
 
    auto restore_array = [&](auto vec) {
      return VecRestoreArrayRead(vec, &array);
    };
 
    switch (CTX) {
    case PetscData::CTX_SET_X:
      CHKERR get_array(PetscData::CtxSetX, getFEMethod()->ts_u);
      break;
    case PetscData::CTX_SET_DX:
      CHKERR get_array(PetscData::CtxSetX, getFEMethod()->dx);
      break;
    case PetscData::CTX_SET_X_T:
      CHKERR get_array(PetscData::CtxSetX_T, getFEMethod()->ts_u_t);
      break;
    case PetscData::CTX_SET_X_TT:
      CHKERR get_array(PetscData::CtxSetX_TT, getFEMethod()->ts_u_tt);
      break;
    default:
      SETERRQ(PETSC_COMM_SELF, MOFEM_NOT_IMPLEMENTED,
              "That case is not implemented");
    }
 
    dotVector.resize(local_indices.size());
    for (int i = 0; i != local_indices.size(); ++i)
      if (local_indices[i] != -1)
        dotVector[i] = array[local_indices[i]];
      else
        dotVector[i] = 0;
 
    switch (CTX) {
    case PetscData::CTX_SET_X:
      CHKERR restore_array(getFEMethod()->ts_u);
      break;
    case PetscData::CTX_SET_DX:
      CHKERR restore_array(getFEMethod()->dx);
      break;
    case PetscData::CTX_SET_X_T:
      CHKERR restore_array(getFEMethod()->ts_u_t);
      break;
    case PetscData::CTX_SET_X_TT:
      CHKERR restore_array(getFEMethod()->ts_u_tt);
      break;
    default:
      SETERRQ(PETSC_COMM_SELF, MOFEM_NOT_IMPLEMENTED,
              "That case is not implemented");
    }
 
    const size_t nb_base_functions = data.getN().size2();
    auto base_function = data.getFTensor0N();
    auto values_at_gauss_pts = getFTensor1FromMat<Tensor_Dim>(mat);
 
    FTensor::Index<'I', Tensor_Dim> I;
    const size_t size = nb_dofs / Tensor_Dim;
    if (nb_dofs % Tensor_Dim) {
      SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY, "Data inconsistency");
    }
    for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
      auto field_data = getFTensor1FromArray<Tensor_Dim, Tensor_Dim>(dotVector);
      size_t bb = 0;
      for (; bb != size; ++bb) {
        values_at_gauss_pts(I) += field_data(I) * base_function;
        ++field_data;
        ++base_function;
      }
      // Number of dofs can be smaller than number of Tensor_Dim x base
      // functions
      for (; bb < nb_base_functions; ++bb)
        ++base_function;
      ++values_at_gauss_pts;
    }
    MoFEMFunctionReturn(0);
  }
 
protected:
  boost::shared_ptr<MatrixDouble> dataPtr;
  const EntityHandle zeroAtType;
  VectorDouble dotVector;
  bool throwError;
};
 
/** \brief Get rate of values at integration pts for tensor field
 * rank 1, i.e. vector field
 *
 * \ingroup mofem_forces_and_sources_user_data_operators
 */
template <int Tensor_Dim>
using OpCalculateVectorFieldValuesDot =
    OpCalculateVectorFieldValuesFromPetscVecImpl<Tensor_Dim,
                                                 PetscData::CTX_SET_X_T>;
 
/** \brief Get second rate of values at integration pts for tensor
 * field rank 1, i.e. vector field
 *
 * \ingroup mofem_forces_and_sources_user_data_operators
 */
template <int Tensor_Dim>
using OpCalculateVectorFieldValuesDotDot =
    OpCalculateVectorFieldValuesFromPetscVecImpl<Tensor_Dim,
                                                 PetscData::CTX_SET_X_TT>;
 
/** \brief Get second time second update vector at integration pts for tensor
 * field rank 1, i.e. vector field
 *
 * \ingroup mofem_forces_and_sources_user_data_operators
 */
template <int Tensor_Dim>
using OpCalculateVectorFieldSNESUpdateValues =
    OpCalculateVectorFieldValuesFromPetscVecImpl<Tensor_Dim,
                                                 PetscData::CTX_SET_DX>;
 
/**@}*/
 
/** \name Tensor field values at integration points */
 
/**@{*/
 
/** \brief Calculate field values for tenor field rank 2.
 *
 */
template <int Tensor_Dim0, int Tensor_Dim1, class T, class L, class A>
struct OpCalculateTensor2FieldValues_General
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateTensor2FieldValues_General(
      const std::string field_name,
      boost::shared_ptr<ublas::matrix<T, L, A>> data_ptr,
      const EntityType zero_type = MBVERTEX)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroType(zero_type) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
protected:
  boost::shared_ptr<ublas::matrix<T, L, A>> dataPtr;
  const EntityHandle zeroType;
};
 
template <int Tensor_Dim0, int Tensor_Dim1, class T, class L, class A>
MoFEMErrorCode
OpCalculateTensor2FieldValues_General<Tensor_Dim0, Tensor_Dim1, T, L, A>::
    doWork(int side, EntityType type, EntitiesFieldData::EntData &data) {
  MoFEMFunctionBeginHot;
  SETERRQ(PETSC_COMM_SELF, MOFEM_NOT_IMPLEMENTED,
           "Not implemented for T = %s, dim0 = %d and dim1 = %d",
           typeid(T).name(), // boost::core::demangle(typeid(T).name()),
           Tensor_Dim0, Tensor_Dim1);
  MoFEMFunctionReturnHot(0);
}
 
template <int Tensor_Dim0, int Tensor_Dim1>
struct OpCalculateTensor2FieldValues_General<Tensor_Dim0, Tensor_Dim1, double,
                                             ublas::row_major, DoubleAllocator>
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateTensor2FieldValues_General(
      const std::string field_name,
      boost::shared_ptr<
          ublas::matrix<double, ublas::row_major, DoubleAllocator>>
          data_ptr,
      const EntityType zero_type = MBVERTEX)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroType(zero_type) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  OpCalculateTensor2FieldValues_General(
      const std::string field_name,
      boost::shared_ptr<
          ublas::matrix<double, ublas::row_major, DoubleAllocator>>
          data_ptr,
      SmartPetscObj<Vec> data_vec, const EntityType zero_type = MBVERTEX)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroType(zero_type), dataVec(data_vec) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
protected:
  boost::shared_ptr<ublas::matrix<double, ublas::row_major, DoubleAllocator>>
      dataPtr;
  const EntityHandle zeroType;
  SmartPetscObj<Vec> dataVec;
  VectorDouble dotVector;
};
 
template <int Tensor_Dim0, int Tensor_Dim1>
MoFEMErrorCode OpCalculateTensor2FieldValues_General<
    Tensor_Dim0, Tensor_Dim1, double, ublas::row_major,
    DoubleAllocator>::doWork(int side, EntityType type,
                             EntitiesFieldData::EntData &data) {
  MoFEMFunctionBegin;
 
  MatrixDouble &mat = *dataPtr;
  const size_t nb_gauss_pts = data.getN().size1();
  if (type == zeroType) {
    mat.resize(Tensor_Dim0 * Tensor_Dim1, nb_gauss_pts, false);
    mat.clear();
  }
 
  const size_t nb_dofs = data.getFieldData().size();
 
  if (dataVec.use_count()) {
    dotVector.resize(nb_dofs, false);
    const double *array;
    CHKERR VecGetArrayRead(dataVec, &array);
    const auto &local_indices = data.getLocalIndices();
    for (int i = 0; i != local_indices.size(); ++i)
      if (local_indices[i] != -1)
        dotVector[i] = array[local_indices[i]];
      else
        dotVector[i] = 0;
    CHKERR VecRestoreArrayRead(dataVec, &array);
    data.getFieldData().swap(dotVector);
  }
 
  if (nb_dofs) {
    const size_t nb_base_functions = data.getN().size2();
    auto base_function = data.getFTensor0N();
    auto values_at_gauss_pts =
        getFTensor2FromMat<Tensor_Dim0, Tensor_Dim1>(mat);
    FTensor::Index<'i', Tensor_Dim0> i;
    FTensor::Index<'j', Tensor_Dim1> j;
    const size_t size = nb_dofs / (Tensor_Dim0 * Tensor_Dim1);
    for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
      auto field_data = data.getFTensor2FieldData<Tensor_Dim0, Tensor_Dim1>();
      size_t bb = 0;
      for (; bb != size; ++bb) {
        values_at_gauss_pts(i, j) += field_data(i, j) * base_function;
        ++field_data;
        ++base_function;
      }
      for (; bb < nb_base_functions; ++bb)
        ++base_function;
      ++values_at_gauss_pts;
    }
 
    if (dataVec.use_count()) {
      data.getFieldData().swap(dotVector);
    }
  }
  MoFEMFunctionReturn(0);
}
 
/** \brief Get values at integration pts for tensor field rank 2, i.e. matrix
 * field
 *
 * \ingroup mofem_forces_and_sources_user_data_operators
 */
template <int Tensor_Dim0, int Tensor_Dim1>
struct OpCalculateTensor2FieldValues
    : public OpCalculateTensor2FieldValues_General<
          Tensor_Dim0, Tensor_Dim1, double, ublas::row_major, DoubleAllocator> {
 
  using OpCalculateTensor2FieldValues_General<
      Tensor_Dim0, Tensor_Dim1, double, ublas::row_major,
      DoubleAllocator>::OpCalculateTensor2FieldValues_General;
};
 
/** \brief Get time direvarive values at integration pts for tensor field rank
 * 2, i.e. matrix field
 *
 * \ingroup mofem_forces_and_sources_user_data_operators
 */
template <int Tensor_Dim0, int Tensor_Dim1>
struct OpCalculateTensor2FieldValuesDot
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateTensor2FieldValuesDot(const std::string field_name,
                                   boost::shared_ptr<MatrixDouble> data_ptr,
                                   const EntityType zero_at_type = MBVERTEX)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroAtType(zero_at_type) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
 
    const size_t nb_gauss_pts = getGaussPts().size2();
    MatrixDouble &mat = *dataPtr;
    if (type == zeroAtType) {
      mat.resize(Tensor_Dim0 * Tensor_Dim1, nb_gauss_pts, false);
      mat.clear();
    }
    const auto &local_indices = data.getLocalIndices();
    const size_t nb_dofs = local_indices.size();
    if (nb_dofs) {
      dotVector.resize(nb_dofs, false);
      const double *array;
      CHKERR VecGetArrayRead(getFEMethod()->ts_u_t, &array);
      for (size_t i = 0; i != local_indices.size(); ++i)
        if (local_indices[i] != -1)
          dotVector[i] = array[local_indices[i]];
        else
          dotVector[i] = 0;
      CHKERR VecRestoreArrayRead(getFEMethod()->ts_u_t, &array);
 
      const size_t nb_base_functions = data.getN().size2();
 
      auto base_function = data.getFTensor0N();
      auto values_at_gauss_pts =
          getFTensor2FromMat<Tensor_Dim0, Tensor_Dim1>(mat);
      FTensor::Index<'i', Tensor_Dim0> i;
      FTensor::Index<'j', Tensor_Dim1> j;
      const size_t size = nb_dofs / (Tensor_Dim0 * Tensor_Dim1);
      for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
        auto field_data =
            getFTensor2FromPtr<Tensor_Dim0, Tensor_Dim1>(&*dotVector.begin());
        size_t bb = 0;
        for (; bb != size; ++bb) {
          values_at_gauss_pts(i, j) += field_data(i, j) * base_function;
          ++field_data;
          ++base_function;
        }
        for (; bb < nb_base_functions; ++bb)
          ++base_function;
        ++values_at_gauss_pts;
      }
    }
    MoFEMFunctionReturn(0);
  }
 
protected:
  boost::shared_ptr<MatrixDouble> dataPtr; ///< Data computed into this matrix
  EntityType zeroAtType;  ///< Zero values at Gauss point at this type
  VectorDouble dotVector; ///< Keeps temporary values of time derivatives
};
 
/**
 * @brief Calculate symmetric tensor field values at integration pts.
 *
 * @tparam Tensor_Dim
 
 * \ingroup mofem_forces_and_sources_user_data_operators
 */
template <int Tensor_Dim>
struct OpCalculateTensor2SymmetricFieldValues
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateTensor2SymmetricFieldValues(
      const std::string field_name, boost::shared_ptr<MatrixDouble> data_ptr,
      const EntityType zero_type = MBEDGE, const int zero_side = 0)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroType(zero_type), zeroSide(zero_side) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  OpCalculateTensor2SymmetricFieldValues(
      const std::string field_name, boost::shared_ptr<MatrixDouble> data_ptr,
      SmartPetscObj<Vec> data_vec, const EntityType zero_type = MBEDGE,
      const int zero_side = 0)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroType(zero_type), zeroSide(zero_side),
        dataVec(data_vec) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
    MatrixDouble &mat = *dataPtr;
    const int nb_gauss_pts = getGaussPts().size2();
    if (type == this->zeroType && side == zeroSide) {
      mat.resize((Tensor_Dim * (Tensor_Dim + 1)) / 2, nb_gauss_pts, false);
      mat.clear();
    }
    const int nb_dofs = data.getFieldData().size();
    if (!nb_dofs)
      MoFEMFunctionReturnHot(0);
 
    if (dataVec.use_count()) {
      dotVector.resize(nb_dofs, false);
      const double *array;
      CHKERR VecGetArrayRead(dataVec, &array);
      const auto &local_indices = data.getLocalIndices();
      for (int i = 0; i != local_indices.size(); ++i)
        if (local_indices[i] != -1)
          dotVector[i] = array[local_indices[i]];
        else
          dotVector[i] = 0;
      CHKERR VecRestoreArrayRead(dataVec, &array);
      data.getFieldData().swap(dotVector);
    }
 
    const int nb_base_functions = data.getN().size2();
    auto base_function = data.getFTensor0N();
    auto values_at_gauss_pts = getFTensor2SymmetricFromMat<Tensor_Dim>(mat);
    FTensor::Index<'i', Tensor_Dim> i;
    FTensor::Index<'j', Tensor_Dim> j;
    const int size = nb_dofs / ((Tensor_Dim * (Tensor_Dim + 1)) / 2);
    for (int gg = 0; gg != nb_gauss_pts; ++gg) {
      auto field_data = data.getFTensor2SymmetricFieldData<Tensor_Dim>();
      int bb = 0;
      for (; bb != size; ++bb) {
        values_at_gauss_pts(i, j) += field_data(i, j) * base_function;
        ++field_data;
        ++base_function;
      }
      for (; bb < nb_base_functions; ++bb)
        ++base_function;
      ++values_at_gauss_pts;
    }
 
    if (dataVec.use_count()) {
      data.getFieldData().swap(dotVector);
    }
 
    MoFEMFunctionReturn(0);
  }
 
protected:
  boost::shared_ptr<MatrixDouble> dataPtr;
  const EntityHandle zeroType;
  const int zeroSide;
  SmartPetscObj<Vec> dataVec;
  VectorDouble dotVector;
};
 
/**
 * @brief Calculate symmetric tensor field rates ant integratio pts.
 *
 * @tparam Tensor_Dim
 *
 * \ingroup mofem_forces_and_sources_user_data_operators
 */
template <int Tensor_Dim>
struct OpCalculateTensor2SymmetricFieldValuesDot
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateTensor2SymmetricFieldValuesDot(
      const std::string field_name, boost::shared_ptr<MatrixDouble> data_ptr,
      const EntityType zero_type = MBEDGE, const int zero_side = 0)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroType(zero_type), zeroSide(zero_side) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
    const int nb_gauss_pts = getGaussPts().size2();
    MatrixDouble &mat = *dataPtr;
    constexpr auto symm_size = (Tensor_Dim * (Tensor_Dim + 1)) / 2;
    if (type == zeroType && side == zeroSide) {
      mat.resize(symm_size, nb_gauss_pts, false);
      mat.clear();
    }
    auto &local_indices = data.getLocalIndices();
    const int nb_dofs = local_indices.size();
    if (!nb_dofs)
      MoFEMFunctionReturnHot(0);
 
  #ifndef NDEBUG
    if ((getFEMethod()->data_ctx & PetscData::CtxSetX_T).none()) {
      MOFEM_LOG_CHANNEL("SELF");
      MOFEM_LOG("SELF", Sev::error)
          << "In this case field degrees of freedom are read from vector.  "
             "That usually happens when time solver is used, and acces to "
             "first rates is needed. You probably not set "
             "ts_u_t and associated data structure data_ctx to CTX_SET_X_T "
             "respectively";
      SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY, "Vector not set!");
    }
  #endif
 
    dotVector.resize(nb_dofs, false);
    const double *array;
    CHKERR VecGetArrayRead(getFEMethod()->ts_u_t, &array);
    for (int i = 0; i != local_indices.size(); ++i)
      if (local_indices[i] != -1)
        dotVector[i] = array[local_indices[i]];
      else
        dotVector[i] = 0;
    CHKERR VecRestoreArrayRead(getFEMethod()->ts_u_t, &array);
 
    const int nb_base_functions = data.getN().size2();
 
    auto base_function = data.getFTensor0N();
    auto values_at_gauss_pts = getFTensor2SymmetricFromMat<Tensor_Dim>(mat);
    FTensor::Index<'i', Tensor_Dim> i;
    FTensor::Index<'j', Tensor_Dim> j;
    const int size = nb_dofs / symm_size;
    for (int gg = 0; gg != nb_gauss_pts; ++gg) {
      auto field_data = getFTensorDotData<Tensor_Dim>();
      int bb = 0;
      for (; bb != size; ++bb) {
        values_at_gauss_pts(i, j) += field_data(i, j) * base_function;
        ++field_data;
        ++base_function;
      }
      for (; bb < nb_base_functions; ++bb)
        ++base_function;
      ++values_at_gauss_pts;
    }
 
    MoFEMFunctionReturn(0);
  }
 
protected:
  boost::shared_ptr<MatrixDouble> dataPtr;
  const EntityHandle zeroType;
  const int zeroSide;
  VectorDouble dotVector;
 
  template <int Dim> inline auto getFTensorDotData() {
    static_assert(Dim || !Dim, "not implemented");
  }
};
 
template <>
template <>
inline auto
OpCalculateTensor2SymmetricFieldValuesDot<3>::getFTensorDotData<3>() {
  return FTensor::Tensor2_symmetric<FTensor::PackPtr<double *, 6>, 3>(
      &dotVector[0], &dotVector[1], &dotVector[2], &dotVector[3], &dotVector[4],
      &dotVector[5]);
}
 
template <>
template <>
inline auto
OpCalculateTensor2SymmetricFieldValuesDot<2>::getFTensorDotData<2>() {
  return FTensor::Tensor2_symmetric<FTensor::PackPtr<double *, 3>, 2>(
      &dotVector[0], &dotVector[1], &dotVector[2]);
}
 
/**@}*/
 
/** \name Gradients and Hessian of scalar fields at integration points */
 
/**@{*/
 
/**
 * \brief Evaluate field gradient values for scalar field, i.e. gradient is
 * tensor rank 1 (vector)
 *
 */
template <int Tensor_Dim, class T, class L, class A>
struct OpCalculateScalarFieldGradient_General
    : public OpCalculateVectorFieldValues_General<Tensor_Dim, T, L, A> {
 
  using OpCalculateVectorFieldValues_General<
      Tensor_Dim, T, L, A>::OpCalculateVectorFieldValues_General;
};
 
/** \brief Evaluate field gradient values for scalar field, i.e. gradient is
 * tensor rank 1 (vector), specialization
 *
 */
template <int Tensor_Dim>
struct OpCalculateScalarFieldGradient_General<Tensor_Dim, double,
                                              ublas::row_major, DoubleAllocator>
    : public OpCalculateVectorFieldValues_General<
          Tensor_Dim, double, ublas::row_major, DoubleAllocator> {
 
  using OpCalculateVectorFieldValues_General<
      Tensor_Dim, double, ublas::row_major,
      DoubleAllocator>::OpCalculateVectorFieldValues_General;
 
  /**
   * \brief calculate gradient values of scalar field at integration points
   * @param  side side entity number
   * @param  type side entity type
   * @param  data entity data
   * @return      error code
   */
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
};
 
/**
 * \brief Member function specialization calculating scalar field gradients for
 * tenor field rank 1
 *
 */
template <int Tensor_Dim>
MoFEMErrorCode OpCalculateScalarFieldGradient_General<
    Tensor_Dim, double, ublas::row_major,
    DoubleAllocator>::doWork(int side, EntityType type,
                             EntitiesFieldData::EntData &data) {
  MoFEMFunctionBegin;
 
  const size_t nb_gauss_pts = this->getGaussPts().size2();
  auto &mat = *this->dataPtr;
  if (type == this->zeroType) {
    mat.resize(Tensor_Dim, nb_gauss_pts, false);
    mat.clear();
  }
 
  const int nb_dofs = data.getFieldData().size();
  if (nb_dofs) {
 
    if (nb_gauss_pts) {
      const int nb_base_functions = data.getN().size2();
      auto diff_base_function = data.getFTensor1DiffN<Tensor_Dim>();
      auto gradients_at_gauss_pts = getFTensor1FromMat<Tensor_Dim>(mat);
 
  #ifndef NDEBUG
      if (nb_dofs > nb_base_functions)
        SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                 "Number of base functions inconsistent with number of DOFs "
                 "(%d > %d)",
                 nb_dofs, nb_base_functions);
 
      if (data.getDiffN().size2() != nb_base_functions * Tensor_Dim)
        SETERRQ(
            PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
            "Number of base functions inconsistent with number of derivatives "
            "(%lu != %d)",
            data.getDiffN().size2(), nb_base_functions);
 
      if (data.getDiffN().size1() != nb_gauss_pts)
        SETERRQ(
            PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
            "Number of base functions inconsistent with number of integration "
            "pts (%lu != %lu)",
            data.getDiffN().size2(), nb_gauss_pts);
 
  #endif
 
      FTensor::Index<'I', Tensor_Dim> I;
      for (int gg = 0; gg < nb_gauss_pts; ++gg) {
        auto field_data = data.getFTensor0FieldData();
        int bb = 0;
        for (; bb != nb_dofs; ++bb) {
          gradients_at_gauss_pts(I) += field_data * diff_base_function(I);
          ++field_data;
          ++diff_base_function;
        }
        // Number of dofs can be smaller than number of base functions
        for (; bb < nb_base_functions; ++bb)
          ++diff_base_function;
        ++gradients_at_gauss_pts;
      }
    }
  }
 
  MoFEMFunctionReturn(0);
}
 
/** \brief Get field gradients at integration pts for scalar field rank 0, i.e.
 * vector field
 *
 * \ingroup mofem_forces_and_sources_user_data_operators
 */
template <int Tensor_Dim>
struct OpCalculateScalarFieldGradient
    : public OpCalculateScalarFieldGradient_General<
          Tensor_Dim, double, ublas::row_major, DoubleAllocator> {
  using OpCalculateScalarFieldGradient_General<
      Tensor_Dim, double, ublas::row_major,
      DoubleAllocator>::OpCalculateScalarFieldGradient_General;
};
 
/** \brief Evaluate field gradient values for scalar field, i.e. gradient is
 * tensor rank 1 (vector), specialization
 *
 */
template <int Tensor_Dim>
struct OpCalculateScalarFieldHessian
    : public OpCalculateVectorFieldValues_General<
          Tensor_Dim, double, ublas::row_major, DoubleAllocator> {
 
  using OpCalculateVectorFieldValues_General<
      Tensor_Dim, double, ublas::row_major,
      DoubleAllocator>::OpCalculateVectorFieldValues_General;
 
  /**
   * \brief calculate gradient values of scalar field at integration points
   * @param  side side entity number
   * @param  type side entity type
   * @param  data entity data
   * @return      error code
   */
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
};
 
template <int Tensor_Dim>
MoFEMErrorCode OpCalculateScalarFieldHessian<Tensor_Dim>::doWork(
    int side, EntityType type, EntitiesFieldData::EntData &data) {
  MoFEMFunctionBegin;
 
  const size_t nb_gauss_pts = this->getGaussPts().size2();
  auto &mat = *this->dataPtr;
  if (type == this->zeroType) {
    mat.resize(Tensor_Dim * Tensor_Dim, nb_gauss_pts, false);
    mat.clear();
  }
 
  const int nb_dofs = data.getFieldData().size();
  if (nb_dofs) {
 
    if (nb_gauss_pts) {
      const int nb_base_functions = data.getN().size2();
 
      auto &hessian_base = data.getN(BaseDerivatives::SecondDerivative);
  #ifndef NDEBUG
      if (hessian_base.size1() != nb_gauss_pts) {
        SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                 "Wrong number of integration pts (%ld != %d)",
                 hessian_base.size1(), nb_gauss_pts);
      }
      if (hessian_base.size2() != nb_base_functions * Tensor_Dim * Tensor_Dim) {
        SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                 "Wrong number of base functions (%ld != %d)",
                 hessian_base.size2() / (Tensor_Dim * Tensor_Dim),
                 nb_base_functions);
      }
      if (hessian_base.size2() < nb_dofs * Tensor_Dim * Tensor_Dim) {
        SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                 "Wrong number of base functions (%ld < %d)",
                 hessian_base.size2(), nb_dofs * Tensor_Dim * Tensor_Dim);
      }
  #endif
 
      auto t_diff2_base_function = getFTensor2FromPtr<Tensor_Dim, Tensor_Dim>(
          &*hessian_base.data().begin());
 
      auto hessian_at_gauss_pts =
          getFTensor2FromMat<Tensor_Dim, Tensor_Dim>(mat);
 
      FTensor::Index<'I', Tensor_Dim> I;
      FTensor::Index<'J', Tensor_Dim> J;
      for (int gg = 0; gg != nb_gauss_pts; ++gg) {
        auto field_data = data.getFTensor0FieldData();
        int bb = 0;
        for (; bb != nb_dofs; ++bb) {
          hessian_at_gauss_pts(I, J) +=
              field_data * t_diff2_base_function(I, J);
          ++field_data;
          ++t_diff2_base_function;
        }
        // Number of dofs can be smaller than number of base functions
        for (; bb < nb_base_functions; ++bb) {
          ++t_diff2_base_function;
        }
 
        ++hessian_at_gauss_pts;
      }
    }
  }
 
  MoFEMFunctionReturn(0);
}
 
/**}*/
 
/** \name Gradients and hessian of tensor fields at integration points */
 
/**@{*/
 
/**
 * \brief Evaluate field gradient values for vector field, i.e. gradient is
 * tensor rank 2
 * 
 * \tparam Tensor_Dim0 Dimension of the vector field
 * \tparam Tensor_Dim1 Dimension of the gradient (usually spatial dimension)
 * \tparam S Storage order for the field data
 * \tparam T Data type
 * \tparam L Layout type
 * \tparam A Allocator type
 *
 */
template <int Tensor_Dim0, int Tensor_Dim1, int S, class T, class L, class A>
struct OpCalculateVectorFieldGradient_General
    : public OpCalculateTensor2FieldValues_General<Tensor_Dim0, Tensor_Dim1, T,
                                                   L, A> {
 
  using OpCalculateTensor2FieldValues_General<
      Tensor_Dim0, Tensor_Dim1, T, L, A>::OpCalculateTensor2FieldValues_General;
};
 
template <int Tensor_Dim0, int Tensor_Dim1, int S>
struct OpCalculateVectorFieldGradient_General<
    Tensor_Dim0, Tensor_Dim1, S, double, ublas::row_major, DoubleAllocator>
    : public OpCalculateTensor2FieldValues_General<
          Tensor_Dim0, Tensor_Dim1, double, ublas::row_major, DoubleAllocator> {
 
  using OpCalculateTensor2FieldValues_General<
      Tensor_Dim0, Tensor_Dim1, double, ublas::row_major,
      DoubleAllocator>::OpCalculateTensor2FieldValues_General;
 
  /**
   * \brief calculate values of vector field at integration points
   * @param  side side entity number
   * @param  type side entity type
   * @param  data entity data
   * @return      error code
   */
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
};
 
/**
 * \brief Member function specialization calculating vector field gradients for
 * tenor field rank 2
 *
 */
template <int Tensor_Dim0, int Tensor_Dim1, int S>
MoFEMErrorCode OpCalculateVectorFieldGradient_General<
    Tensor_Dim0, Tensor_Dim1, S, double, ublas::row_major,
    DoubleAllocator>::doWork(int side, EntityType type,
                             EntitiesFieldData::EntData &data) {
  MoFEMFunctionBegin;
  if (!this->dataPtr)
    SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
            "Data pointer not allocated");
 
  const size_t nb_gauss_pts = this->getGaussPts().size2();
  auto &mat = *this->dataPtr;
  if (type == this->zeroType) {
    mat.resize(Tensor_Dim0 * Tensor_Dim1, nb_gauss_pts, false);
    mat.clear();
  }
 
  if (nb_gauss_pts) {
    const size_t nb_dofs = data.getFieldData().size();
 
    if (nb_dofs) {
 
      if (this->dataVec.use_count()) {
        this->dotVector.resize(nb_dofs, false);
        const double *array;
        CHKERR VecGetArrayRead(this->dataVec, &array);
        const auto &local_indices = data.getLocalIndices();
        for (int i = 0; i != local_indices.size(); ++i)
          if (local_indices[i] != -1)
            this->dotVector[i] = array[local_indices[i]];
          else
            this->dotVector[i] = 0;
        CHKERR VecRestoreArrayRead(this->dataVec, &array);
        data.getFieldData().swap(this->dotVector);
      }
 
      const int nb_base_functions = data.getN().size2();
      auto diff_base_function = data.getFTensor1DiffN<Tensor_Dim1>();
      auto gradients_at_gauss_pts =
          getFTensor2FromMat<Tensor_Dim0, Tensor_Dim1>(mat);
      FTensor::Index<'I', Tensor_Dim0> I;
      FTensor::Index<'J', Tensor_Dim1> J;
      int size = nb_dofs / Tensor_Dim0;
      if (nb_dofs % Tensor_Dim0) {
        SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                "Data inconsistency");
      }
      for (int gg = 0; gg < nb_gauss_pts; ++gg) {
        auto field_data = getFTensor1FromPtr<Tensor_Dim0, S>(
            data.getFieldData().data().data());
 
  #ifndef NDEBUG
                if (field_data.l2() != field_data.l2()) {
          MOFEM_LOG("SELF", Sev::error) << "field data " << field_data;
          SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                  "Wrong number in coefficients");
        }
  #endif
 
        int bb = 0;
        for (; bb < size; ++bb) {
  #ifndef SINGULARITY
    #ifndef NDEBUG
          if (diff_base_function.l2() != diff_base_function.l2()) {
            MOFEM_LOG("SELF", Sev::error)
                << "diff_base_function: " << diff_base_function;
            SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                    "Wrong number number in base functions");
          }
    #endif
  #endif
 
          gradients_at_gauss_pts(I, J) += field_data(I) * diff_base_function(J);
          ++field_data;
          ++diff_base_function;
        }
        // Number of dofs can be smaller than number of Tensor_Dim0 x base
        // functions
        for (; bb != nb_base_functions; ++bb)
          ++diff_base_function;
        ++gradients_at_gauss_pts;
      }
 
      if (this->dataVec.use_count()) {
        data.getFieldData().swap(this->dotVector);
      }
    }
  }
  MoFEMFunctionReturn(0);
}
 
/** \brief Get field gradients at integration pts for scalar field rank 0, i.e.
 * vector field
 * 
 * \tparam Tensor_Dim0 Dimension of the vector field
 * \tparam Tensor_Dim1 Dimension of the gradient (usually spatial dimension)
 * \tparam S Stride in the storage of the vector field, default is Tensor_Dim0
 *
 * \ingroup mofem_forces_and_sources_user_data_operators
 */
template <int Tensor_Dim0, int Tensor_Dim1, int S = Tensor_Dim0>
struct OpCalculateVectorFieldGradient
    : public OpCalculateVectorFieldGradient_General<Tensor_Dim0, Tensor_Dim1, S,
                                                    double, ublas::row_major,
                                                    DoubleAllocator> {
 
  using OpCalculateVectorFieldGradient_General<
      Tensor_Dim0, Tensor_Dim1, S, double, ublas::row_major,
      DoubleAllocator>::OpCalculateVectorFieldGradient_General;
};
 
/** \brief Get field gradients time derivative at integration pts for scalar
 * field rank 0, i.e. vector field
 *
 * \ingroup mofem_forces_and_sources_user_data_operators
 */
template <int Tensor_Dim0, int Tensor_Dim1>
struct OpCalculateVectorFieldGradientDot
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateVectorFieldGradientDot(const std::string field_name,
                                    boost::shared_ptr<MatrixDouble> data_ptr,
                                    const EntityType zero_at_type = MBVERTEX)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroAtType(zero_at_type) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
 
    const auto &local_indices = data.getLocalIndices();
    const int nb_dofs = local_indices.size();
    const int nb_gauss_pts = this->getGaussPts().size2();
 
    auto &mat = *this->dataPtr;
    if (type == this->zeroAtType) {
      mat.resize(Tensor_Dim0 * Tensor_Dim1, nb_gauss_pts, false);
      mat.clear();
    }
    if (!nb_dofs)
      MoFEMFunctionReturnHot(0);
 
    dotVector.resize(nb_dofs, false);
    const double *array;
    CHKERR VecGetArrayRead(getFEMethod()->ts_u_t, &array);
    for (int i = 0; i != local_indices.size(); ++i)
      if (local_indices[i] != -1)
        dotVector[i] = array[local_indices[i]];
      else
        dotVector[i] = 0;
    CHKERR VecRestoreArrayRead(getFEMethod()->ts_u_t, &array);
 
    const int nb_base_functions = data.getN().size2();
    auto diff_base_function = data.getFTensor1DiffN<Tensor_Dim1>();
    auto gradients_at_gauss_pts =
        getFTensor2FromMat<Tensor_Dim0, Tensor_Dim1>(mat);
    FTensor::Index<'I', Tensor_Dim0> I;
    FTensor::Index<'J', Tensor_Dim1> J;
    int size = nb_dofs / Tensor_Dim0;
    if (nb_dofs % Tensor_Dim0) {
      SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY, "Data inconsistency");
    }
 
    for (int gg = 0; gg < nb_gauss_pts; ++gg) {
      auto field_data = getFTensor1FromPtr<Tensor_Dim0>(&*dotVector.begin());
      int bb = 0;
      for (; bb < size; ++bb) {
        gradients_at_gauss_pts(I, J) += field_data(I) * diff_base_function(J);
        ++field_data;
        ++diff_base_function;
      }
      // Number of dofs can be smaller than number of Tensor_Dim0 x base
      // functions
      for (; bb != nb_base_functions; ++bb)
        ++diff_base_function;
      ++gradients_at_gauss_pts;
    }
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<MatrixDouble> dataPtr; ///< Data computed into this matrix
  EntityType zeroAtType;  ///< Zero values at Gauss point at this type
  VectorDouble dotVector; ///< Keeps temporary values of time derivatives
};
 
/**
 * \brief Evaluate field gradient values for symmetric 2nd order tensor field,
 * i.e. gradient is tensor rank 3
 *
 */
template <int Tensor_Dim0, int Tensor_Dim1, class T, class L, class A>
struct OpCalculateTensor2SymmetricFieldGradient_General
    : public OpCalculateTensor2FieldValues_General<Tensor_Dim0, Tensor_Dim1, T,
                                                   L, A> {
 
  OpCalculateTensor2SymmetricFieldGradient_General(
      const std::string field_name, boost::shared_ptr<MatrixDouble> data_ptr,
      const EntityType zero_type = MBVERTEX)
      : OpCalculateTensor2FieldValues_General<Tensor_Dim0, Tensor_Dim1, T, L,
                                              A>(field_name, data_ptr,
                                                 zero_type) {}
};
 
template <int Tensor_Dim0, int Tensor_Dim1>
struct OpCalculateTensor2SymmetricFieldGradient_General<
    Tensor_Dim0, Tensor_Dim1, double, ublas::row_major, DoubleAllocator>
    : public OpCalculateTensor2FieldValues_General<
          Tensor_Dim0, Tensor_Dim1, double, ublas::row_major, DoubleAllocator> {
 
  OpCalculateTensor2SymmetricFieldGradient_General(
      const std::string field_name, boost::shared_ptr<MatrixDouble> data_ptr,
      const EntityType zero_type = MBVERTEX)
      : OpCalculateTensor2FieldValues_General<Tensor_Dim0, Tensor_Dim1, double,
                                              ublas::row_major,
                                              DoubleAllocator>(
            field_name, data_ptr, zero_type) {}
 
  /**
   * \brief calculate values of vector field at integration points
   * @param  side side entity number
   * @param  type side entity type
   * @param  data entity data
   * @return      error code
   */
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
};
 
/**
 * \brief Member function specialization calculating tensor field gradients for
 * symmetric tensor field rank 2
 *
 */
template <int Tensor_Dim0, int Tensor_Dim1>
MoFEMErrorCode OpCalculateTensor2SymmetricFieldGradient_General<
    Tensor_Dim0, Tensor_Dim1, double, ublas::row_major,
    DoubleAllocator>::doWork(int side, EntityType type,
                             EntitiesFieldData::EntData &data) {
  MoFEMFunctionBegin;
  if (!this->dataPtr)
    SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
            "Data pointer not allocated");
 
  const size_t nb_gauss_pts = this->getGaussPts().size2();
  constexpr size_t msize = (Tensor_Dim0 * (Tensor_Dim0 + 1)) / 2;
  auto &mat = *this->dataPtr;
  if (type == this->zeroType) {
    mat.resize(msize * Tensor_Dim1, nb_gauss_pts, false);
    mat.clear();
  }
 
  if (nb_gauss_pts) {
    const size_t nb_dofs = data.getFieldData().size();
 
    if (nb_dofs) {
 
      const int nb_base_functions = data.getN().size2();
      auto diff_base_function = data.getFTensor1DiffN<Tensor_Dim1>();
      auto gradients_at_gauss_pts =
          getFTensor3DgFromMat<Tensor_Dim0, Tensor_Dim1>(mat);
      FTensor::Index<'I', Tensor_Dim0> I;
      FTensor::Index<'J', Tensor_Dim0> J;
      FTensor::Index<'K', Tensor_Dim1> K;
      int size = nb_dofs / msize;
      if (nb_dofs % msize) {
        SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                "Data inconsistency");
      }
      for (int gg = 0; gg < nb_gauss_pts; ++gg) {
        auto field_data = data.getFTensor2SymmetricFieldData<Tensor_Dim0>();
        int bb = 0;
        for (; bb < size; ++bb) {
          gradients_at_gauss_pts(I, J, K) +=
              field_data(I, J) * diff_base_function(K);
          ++field_data;
          ++diff_base_function;
        }
        // Number of dofs can be smaller than number of Tensor_Dim0 x base
        // functions
        for (; bb != nb_base_functions; ++bb)
          ++diff_base_function;
        ++gradients_at_gauss_pts;
      }
    }
  }
  MoFEMFunctionReturn(0);
}
 
/** \brief Get field gradients at integration pts for symmetric tensorial field
 * rank 2
 *
 * \ingroup mofem_forces_and_sources_user_data_operators
 */
template <int Tensor_Dim0, int Tensor_Dim1>
struct OpCalculateTensor2SymmetricFieldGradient
    : public OpCalculateTensor2SymmetricFieldGradient_General<
          Tensor_Dim0, Tensor_Dim1, double, ublas::row_major, DoubleAllocator> {
 
  OpCalculateTensor2SymmetricFieldGradient(
      const std::string field_name, boost::shared_ptr<MatrixDouble> data_ptr,
      const EntityType zero_type = MBVERTEX)
      : OpCalculateTensor2SymmetricFieldGradient_General<
            Tensor_Dim0, Tensor_Dim1, double, ublas::row_major,
            DoubleAllocator>(field_name, data_ptr, zero_type) {}
};
 
template <int Tensor_Dim0, int Tensor_Dim1>
struct OpCalculateVectorFieldHessian
    : public OpCalculateTensor2FieldValues_General<
          Tensor_Dim0, Tensor_Dim1, double, ublas::row_major, DoubleAllocator> {
 
  using OpCalculateTensor2FieldValues_General<
      Tensor_Dim0, Tensor_Dim1, double, ublas::row_major,
      DoubleAllocator>::OpCalculateTensor2FieldValues_General;
 
  /**
   * \brief calculate values of vector field at integration points
   * @param  side side entity number
   * @param  type side entity type
   * @param  data entity data
   * @return      error code
   */
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
};
 
/**
 * \brief Member function specialization calculating vector field gradients for
 * tenor field rank 2
 *
 */
template <int Tensor_Dim0, int Tensor_Dim1>
MoFEMErrorCode OpCalculateVectorFieldHessian<Tensor_Dim0, Tensor_Dim1>::doWork(
    int side, EntityType type, EntitiesFieldData::EntData &data) {
  MoFEMFunctionBegin;
  if (!this->dataPtr)
    SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
            "Data pointer not allocated");
 
  const size_t nb_gauss_pts = this->getGaussPts().size2();
  auto &mat = *this->dataPtr;
  if (type == this->zeroType) {
    mat.resize(Tensor_Dim0 * Tensor_Dim1 * Tensor_Dim1, nb_gauss_pts, false);
    mat.clear();
  }
 
  if (nb_gauss_pts) {
    const size_t nb_dofs = data.getFieldData().size();
 
    if (nb_dofs) {
 
      if (this->dataVec.use_count()) {
        this->dotVector.resize(nb_dofs, false);
        const double *array;
        CHKERR VecGetArrayRead(this->dataVec, &array);
        const auto &local_indices = data.getLocalIndices();
        for (int i = 0; i != local_indices.size(); ++i)
          if (local_indices[i] != -1)
            this->dotVector[i] = array[local_indices[i]];
          else
            this->dotVector[i] = 0;
        CHKERR VecRestoreArrayRead(this->dataVec, &array);
        data.getFieldData().swap(this->dotVector);
      }
 
      const int nb_base_functions = data.getN().size2();
 
      auto &hessian_base = data.getN(BaseDerivatives::SecondDerivative);
  #ifndef NDEBUG
      if (hessian_base.size1() != nb_gauss_pts) {
        SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                 "Wrong number of integration pts (%d != %d)",
                 hessian_base.size1(), nb_gauss_pts);
      }
      if (hessian_base.size2() !=
          nb_base_functions * Tensor_Dim1 * Tensor_Dim1) {
        SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                 "Wrong number of base functions (%d != %d)",
                 hessian_base.size2() / (Tensor_Dim1 * Tensor_Dim1),
                 nb_base_functions);
      }
      if (hessian_base.size2() < nb_dofs * Tensor_Dim1 * Tensor_Dim1) {
        SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                 "Wrong number of base functions (%d < %d)",
                 hessian_base.size2(), nb_dofs * Tensor_Dim1 * Tensor_Dim1);
      }
  #endif
 
      auto t_diff2_base_function = getFTensor2FromPtr<Tensor_Dim1, Tensor_Dim1>(
          &*hessian_base.data().begin());
 
      auto t_hessian_at_gauss_pts =
          getFTensor3FromMat<Tensor_Dim0, Tensor_Dim1, Tensor_Dim1>(mat);
 
      FTensor::Index<'I', Tensor_Dim0> I;
      FTensor::Index<'J', Tensor_Dim1> J;
      FTensor::Index<'K', Tensor_Dim1> K;
 
      int size = nb_dofs / Tensor_Dim0;
  #ifndef NDEBUG
      if (nb_dofs % Tensor_Dim0) {
        SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                "Data inconsistency");
      }
  #endif
 
      for (int gg = 0; gg < nb_gauss_pts; ++gg) {
        auto field_data = data.getFTensor1FieldData<Tensor_Dim0>();
        int bb = 0;
        for (; bb < size; ++bb) {
          t_hessian_at_gauss_pts(I, J, K) +=
              field_data(I) * t_diff2_base_function(J, K);
          ++field_data;
          ++t_diff2_base_function;
        }
        // Number of dofs can be smaller than number of Tensor_Dim0 x base
        // functions
        for (; bb != nb_base_functions; ++bb)
          ++t_diff2_base_function;
        ++t_hessian_at_gauss_pts;
      }
 
      if (this->dataVec.use_count()) {
        data.getFieldData().swap(this->dotVector);
      }
    }
  }
  MoFEMFunctionReturn(0);
}
 
/**@}*/
 
/** \name Transform tensors and vectors */
 
/**@{*/
 
/**
 * @brief Calculate \f$ \pmb\sigma_{ij} = \mathbf{D}_{ijkl} \pmb\varepsilon_{kl}
 * \f$
 *
 * @tparam DIM
 *
 * \ingroup mofem_forces_and_sources_user_data_operators
 */
template <int DIM_01, int DIM_23, int S = 0>
struct OpTensorTimesSymmetricTensor
    : public ForcesAndSourcesCore::UserDataOperator {
 
  using EntData = EntitiesFieldData::EntData;
  using UserOp = ForcesAndSourcesCore::UserDataOperator;
 
  /**
   * @deprecated Do not use this constructor
   */
  DEPRECATED
  OpTensorTimesSymmetricTensor(const std::string field_name,
                               boost::shared_ptr<MatrixDouble> in_mat,
                               boost::shared_ptr<MatrixDouble> out_mat,
                               boost::shared_ptr<MatrixDouble> d_mat)
      : UserOp(field_name, OPROW), inMat(in_mat), outMat(out_mat), dMat(d_mat) {
    // Only is run for vertices
    std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
    if (!inMat)
      THROW_MESSAGE("Pointer for in mat is null");
    if (!outMat)
      THROW_MESSAGE("Pointer for out mat is null");
    if (!dMat)
      THROW_MESSAGE("Pointer for tensor mat is null");
  }
 
  OpTensorTimesSymmetricTensor(boost::shared_ptr<MatrixDouble> in_mat,
                               boost::shared_ptr<MatrixDouble> out_mat,
                               boost::shared_ptr<MatrixDouble> d_mat)
      : UserOp(NOSPACE, OPSPACE), inMat(in_mat), outMat(out_mat), dMat(d_mat) {
    // Only is run for vertices
    if (!inMat)
      THROW_MESSAGE("Pointer for in mat is null");
    if (!outMat)
      THROW_MESSAGE("Pointer for out mat is null");
    if (!dMat)
      THROW_MESSAGE("Pointer for tensor mat is null");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type, EntData &data) {
    MoFEMFunctionBegin;
    const size_t nb_gauss_pts = getGaussPts().size2();
    auto t_D = getFTensor4DdgFromMat<DIM_01, DIM_23, S>(*(dMat));
    auto t_in = getFTensor2SymmetricFromMat<DIM_01>(*(inMat));
    outMat->resize((DIM_23 * (DIM_23 + 1)) / 2, nb_gauss_pts, false);
    auto t_out = getFTensor2SymmetricFromMat<DIM_23>(*(outMat));
    for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
      t_out(i, j) = t_D(i, j, k, l) * t_in(k, l);
      ++t_in;
      ++t_out;
    }
    MoFEMFunctionReturn(0);
  }
 
private:
  FTensor::Index<'i', DIM_01> i;
  FTensor::Index<'j', DIM_01> j;
  FTensor::Index<'k', DIM_23> k;
  FTensor::Index<'l', DIM_23> l;
 
  boost::shared_ptr<MatrixDouble> inMat;
  boost::shared_ptr<MatrixDouble> outMat;
  boost::shared_ptr<MatrixDouble> dMat;
};
 
/**
 * @brief Operator for symmetrizing tensor fields
 *
 * This template structure symmetrizes tensor fields by computing the symmetric
 * part of an input tensor and storing the result in an output matrix. It's
 * commonly used in mechanics where symmetric tensors (like stress and strain)
 * are required.
 *
 * @tparam DIM Dimension of the tensor field
 */
template <int DIM>
struct OpSymmetrizeTensor : public ForcesAndSourcesCore::UserDataOperator {
 
  using EntData = EntitiesFieldData::EntData;
  using UserOp = ForcesAndSourcesCore::UserDataOperator;
 
  /**
   * @deprecated Do not use this constructor
   */
  DEPRECATED OpSymmetrizeTensor(const std::string field_name,
                                boost::shared_ptr<MatrixDouble> in_mat,
                                boost::shared_ptr<MatrixDouble> out_mat)
      : UserOp(field_name, OPROW), inMat(in_mat), outMat(out_mat) {
    // Only is run for vertices
    std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
    if (!inMat)
      THROW_MESSAGE("Pointer not set for in matrix");
    if (!outMat)
      THROW_MESSAGE("Pointer not set for in matrix");
  }
 
  /**
   * @brief Constructor for tensor symmetrization operator
   *
   * @param in_mat Shared pointer to input matrix containing asymmetric tensor
   * @param out_mat Shared pointer to output matrix for storing symmetric tensor
   */
  OpSymmetrizeTensor(boost::shared_ptr<MatrixDouble> in_mat,
                     boost::shared_ptr<MatrixDouble> out_mat)
      : UserOp(NOSPACE, OPSPACE), inMat(in_mat), outMat(out_mat) {
    // Only is run for vertices
    if (!inMat)
      THROW_MESSAGE("Pointer not set for in matrix");
    if (!outMat)
      THROW_MESSAGE("Pointer not set for in matrix");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type, EntData &data) {
    MoFEMFunctionBegin;
    const size_t nb_gauss_pts = getGaussPts().size2();
    auto t_in = getFTensor2FromMat<DIM, DIM>(*(inMat));
    outMat->resize((DIM * (DIM + 1)) / 2, nb_gauss_pts, false);
    auto t_out = getFTensor2SymmetricFromMat<DIM>(*(outMat));
    for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
      t_out(i, j) = (t_in(i, j) || t_in(j, i)) / 2;
      ++t_in;
      ++t_out;
    }
    MoFEMFunctionReturn(0);
  }
 
private:
  FTensor::Index<'i', DIM> i;
  FTensor::Index<'j', DIM> j;
  boost::shared_ptr<MatrixDouble> inMat;
  boost::shared_ptr<MatrixDouble> outMat;
};
 
/**
 * @brief Operator for scaling matrix values by a scalar factor
 *
 * This structure performs element-wise scaling of matrix data by multiplying
 * all elements by a scalar value. It's useful for applying material properties,
 * coordinate transformations, or other scaling operations in finite element
 * computations.
 */
struct OpScaleMatrix : public ForcesAndSourcesCore::UserDataOperator {
 
  using EntData = EntitiesFieldData::EntData;
  using UserOp = ForcesAndSourcesCore::UserDataOperator;
 
  /**
   * @deprecated Do not use this constructor
   */
  DEPRECATED OpScaleMatrix(const std::string field_name, const double scale,
                           boost::shared_ptr<MatrixDouble> in_mat,
                           boost::shared_ptr<MatrixDouble> out_mat)
      : UserOp(field_name, OPROW), inMat(in_mat), outMat(out_mat) {
    scalePtr = boost::make_shared<double>(scale);
    // Only is run for vertices
    std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
    if (!inMat)
      THROW_MESSAGE("Pointer not set for in matrix");
    if (!outMat)
      THROW_MESSAGE("Pointer not set for in matrix");
  }
 
  /**
   * @brief Constructor for matrix scaling operator
   *
   * @param scale_ptr Shared pointer to scalar value for scaling matrix elements
   * @param in_mat Shared pointer to input matrix to be scaled
   * @param out_mat Shared pointer to output matrix for storing scaled results
   */
  OpScaleMatrix(boost::shared_ptr<double> scale_ptr,
                boost::shared_ptr<MatrixDouble> in_mat,
                boost::shared_ptr<MatrixDouble> out_mat)
      : UserOp(NOSPACE, OPSPACE), scalePtr(scale_ptr), inMat(in_mat),
        outMat(out_mat) {
    if (!scalePtr)
      THROW_MESSAGE("Pointer not set for scale");
    if (!inMat)
      THROW_MESSAGE("Pointer not set for in matrix");
    if (!outMat)
      THROW_MESSAGE("Pointer not set for in matrix");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type, EntData &data) {
    MoFEMFunctionBegin;
    outMat->resize(inMat->size1(), inMat->size2(), false);
    noalias(*outMat) = (*scalePtr) * (*inMat);
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<double> scalePtr;
  boost::shared_ptr<MatrixDouble> inMat;
  boost::shared_ptr<MatrixDouble> outMat;
};
 
/**@}*/
 
/** \name H-div/H-curls (Vectorial bases) values at integration points */
 
/**@{*/
 
/** \brief Get vector field for H-div approximation
 * \ingroup mofem_forces_and_sources_user_data_operators
 */
template <int Base_Dim, int Field_Dim, class T, class L, class A>
struct OpCalculateHVecVectorField_General;
 
/** \brief Get vector field for H-div approximation
 * \ingroup mofem_forces_and_sources_user_data_operators
 */
template <int Field_Dim>
struct OpCalculateHVecVectorField_General<3, Field_Dim, double,
                                          ublas::row_major, DoubleAllocator>
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateHVecVectorField_General(const std::string field_name,
                                     boost::shared_ptr<MatrixDouble> data_ptr,
                                     SmartPetscObj<Vec> data_vec,
                                     const EntityType zero_type = MBEDGE,
                                     const int zero_side = 0)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), dataVec(data_vec), zeroType(zero_type),
        zeroSide(zero_side) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  OpCalculateHVecVectorField_General(const std::string field_name,
                                     boost::shared_ptr<MatrixDouble> data_ptr,
                                     const EntityType zero_type = MBEDGE,
                                     const int zero_side = 0)
      : OpCalculateHVecVectorField_General(
            field_name, data_ptr, SmartPetscObj<Vec>(), zero_type, zero_side) {}
 
  /**
   * \brief Calculate values of vector field at integration points
   * @param  side side entity number
   * @param  type side entity type
   * @param  data entity data
   * @return      error code
   */
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
private:
  boost::shared_ptr<MatrixDouble> dataPtr;
  SmartPetscObj<Vec> dataVec;
  const EntityHandle zeroType;
  const int zeroSide;
  VectorDouble dotVector;
};
 
template <int Field_Dim>
MoFEMErrorCode OpCalculateHVecVectorField_General<
    3, Field_Dim, double, ublas::row_major,
    DoubleAllocator>::doWork(int side, EntityType type,
                             EntitiesFieldData::EntData &data) {
  MoFEMFunctionBegin;
  const size_t nb_integration_points = this->getGaussPts().size2();
  if (type == zeroType && side == zeroSide) {
    dataPtr->resize(Field_Dim, nb_integration_points, false);
    dataPtr->clear();
  }
  const size_t nb_dofs = data.getFieldData().size();
  if (!nb_dofs)
    MoFEMFunctionReturnHot(0);
 
  if (dataVec.use_count()) {
    dotVector.resize(nb_dofs, false);
    const double *array;
    CHKERR VecGetArrayRead(dataVec, &array);
    const auto &local_indices = data.getLocalIndices();
    for (int i = 0; i != local_indices.size(); ++i)
      if (local_indices[i] != -1)
        dotVector[i] = array[local_indices[i]];
      else
        dotVector[i] = 0;
    CHKERR VecRestoreArrayRead(dataVec, &array);
    data.getFieldData().swap(dotVector);
  }
 
  const size_t nb_base_functions = data.getN().size2() / 3;
  FTensor::Index<'i', Field_Dim> i;
  auto t_n_hdiv = data.getFTensor1N<3>();
  auto t_data = getFTensor1FromMat<Field_Dim>(*dataPtr);
  for (size_t gg = 0; gg != nb_integration_points; ++gg) {
    auto t_dof = data.getFTensor0FieldData();
    int bb = 0;
    for (; bb != nb_dofs; ++bb) {
      t_data(i) += t_n_hdiv(i) * t_dof;
      ++t_n_hdiv;
      ++t_dof;
    }
    for (; bb != nb_base_functions; ++bb)
      ++t_n_hdiv;
    ++t_data;
  }
 
  if (dataVec.use_count()) {
    data.getFieldData().swap(dotVector);
  }
  MoFEMFunctionReturn(0);
}
 
/** \brief Get vector field for H-div approximation
 *
 * \ingroup mofem_forces_and_sources_user_data_operators
 */
template <int Base_Dim, int Field_Dim = Base_Dim>
struct OpCalculateHVecVectorField
    : public OpCalculateHVecVectorField_General<
          Base_Dim, Field_Dim, double, ublas::row_major, DoubleAllocator> {
  using OpCalculateHVecVectorField_General<
      Base_Dim, Field_Dim, double, ublas::row_major,
      DoubleAllocator>::OpCalculateHVecVectorField_General;
};
 
/** \brief Get vector field for H-div approximation
 * \ingroup mofem_forces_and_sources_user_data_operators
 */
template <int Base_Dim, int Field_Dim = Base_Dim>
struct OpCalculateHVecVectorFieldDot;
 
template <int Field_Dim>
struct OpCalculateHVecVectorFieldDot<3, Field_Dim>
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateHVecVectorFieldDot(const std::string field_name,
                                boost::shared_ptr<MatrixDouble> data_ptr,
                                const EntityType zero_type = MBEDGE,
                                const int zero_side = 0)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroType(zero_type), zeroSide(zero_side) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  /**
   * \brief Calculate values of vector field at integration points
   * @param  side side entity number
   * @param  type side entity type
   * @param  data entity data
   * @return      error code
   */
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
private:
  boost::shared_ptr<MatrixDouble> dataPtr;
  const EntityHandle zeroType;
  const int zeroSide;
};
 
template <int Field_Dim>
MoFEMErrorCode OpCalculateHVecVectorFieldDot<3, Field_Dim>::doWork(
    int side, EntityType type, EntitiesFieldData::EntData &data) {
  MoFEMFunctionBegin;
 
  const size_t nb_integration_points = this->getGaussPts().size2();
  if (type == zeroType && side == zeroSide) {
    dataPtr->resize(Field_Dim, nb_integration_points, false);
    dataPtr->clear();
  }
 
  auto &local_indices = data.getIndices();
  const size_t nb_dofs = local_indices.size();
  if (nb_dofs) {
 
    std::array<double, MAX_DOFS_ON_ENTITY> dot_dofs_vector;
    const double *array;
    CHKERR VecGetArrayRead(getFEMethod()->ts_u_t, &array);
    for (size_t i = 0; i != nb_dofs; ++i)
      if (local_indices[i] != -1)
        dot_dofs_vector[i] = array[local_indices[i]];
      else
        dot_dofs_vector[i] = 0;
    CHKERR VecRestoreArrayRead(getFEMethod()->ts_u_t, &array);
 
    const size_t nb_base_functions = data.getN().size2() / 3;
    FTensor::Index<'i', Field_Dim> i;
    auto t_n_hdiv = data.getFTensor1N<3>();
    auto t_data = getFTensor1FromMat<Field_Dim>(*dataPtr);
    for (size_t gg = 0; gg != nb_integration_points; ++gg) {
      int bb = 0;
      for (; bb != nb_dofs; ++bb) {
        t_data(i) += t_n_hdiv(i) * dot_dofs_vector[bb];
        ++t_n_hdiv;
      }
      for (; bb != nb_base_functions; ++bb)
        ++t_n_hdiv;
      ++t_data;
    }
  }
 
  MoFEMFunctionReturn(0);
}
 
/**
 * @brief Calculate divergence of vector field
 * @ingroup mofem_forces_and_sources_user_data_operators
 *
 * @tparam BASE_DIM
 * @tparam SPACE_DIM
 */
template <int BASE_DIM, int SPACE_DIM>
struct OpCalculateHdivVectorDivergence
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateHdivVectorDivergence(const std::string field_name,
                                  boost::shared_ptr<VectorDouble> data_ptr,
                                  const EntityType zero_type = MBEDGE,
                                  const int zero_side = 0)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroType(zero_type), zeroSide(zero_side) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
    const size_t nb_integration_points = getGaussPts().size2();
    if (type == zeroType && side == zeroSide) {
      dataPtr->resize(nb_integration_points, false);
      dataPtr->clear();
    }
    const size_t nb_dofs = data.getFieldData().size();
    if (!nb_dofs)
      MoFEMFunctionReturnHot(0);
    const size_t nb_base_functions = data.getN().size2() / BASE_DIM;
    FTensor::Index<'i', BASE_DIM> i;
    FTensor::Index<'j', SPACE_DIM> j;
    auto t_n_diff_hdiv = data.getFTensor2DiffN<BASE_DIM, SPACE_DIM>();
    auto t_data = getFTensor0FromVec(*dataPtr);
    for (size_t gg = 0; gg != nb_integration_points; ++gg) {
      auto t_dof = data.getFTensor0FieldData();
      int bb = 0;
      for (; bb != nb_dofs; ++bb) {
        t_data += t_dof * t_n_diff_hdiv(j, j);
        ++t_n_diff_hdiv;
        ++t_dof;
      }
      for (; bb != nb_base_functions; ++bb)
        ++t_n_diff_hdiv;
      ++t_data;
    }
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<VectorDouble> dataPtr;
  const EntityHandle zeroType;
  const int zeroSide;
};
 
/**
 * @brief Calculate gradient of vector field
 * @ingroup mofem_forces_and_sources_user_data_operators
 *
 * @tparam BASE_DIM
 * @tparam SPACE_DIM
 */
template <int BASE_DIM, int SPACE_DIM>
struct OpCalculateHVecVectorGradient
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateHVecVectorGradient(const std::string field_name,
                                boost::shared_ptr<MatrixDouble> data_ptr,
                                const EntityType zero_type = MBEDGE,
                                const int zero_side = 0)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroType(zero_type), zeroSide(zero_side) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
    const size_t nb_integration_points = getGaussPts().size2();
    if (type == zeroType && side == zeroSide) {
      dataPtr->resize(BASE_DIM * SPACE_DIM, nb_integration_points, false);
      dataPtr->clear();
    }
    const size_t nb_dofs = data.getFieldData().size();
    if (!nb_dofs)
      MoFEMFunctionReturnHot(0);
    const size_t nb_base_functions = data.getN().size2() / BASE_DIM;
    FTensor::Index<'i', BASE_DIM> i;
    FTensor::Index<'j', SPACE_DIM> j;
    auto t_base_diff = data.getFTensor2DiffN<BASE_DIM, SPACE_DIM>();
    auto t_data = getFTensor2FromMat<BASE_DIM, SPACE_DIM>(*dataPtr);
    for (size_t gg = 0; gg != nb_integration_points; ++gg) {
      auto t_dof = data.getFTensor0FieldData();
      int bb = 0;
      for (; bb != nb_dofs; ++bb) {
        t_data(i, j) += t_dof * t_base_diff(i, j);
        ++t_base_diff;
        ++t_dof;
      }
      for (; bb != nb_base_functions; ++bb)
        ++t_base_diff;
      ++t_data;
    }
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<MatrixDouble> dataPtr;
  const EntityHandle zeroType;
  const int zeroSide;
};
 
/**
 * @brief Calculate gradient of tensor field
 * @ingroup mofem_forces_and_sources_user_data_operators
 *
 * @tparam BASE_DIM
 * @tparam FIELD_DIM
 * @tparam SPACE_DIM
 */
template <int BASE_DIM, int FIELD_DIM, int SPACE_DIM>
struct OpCalculateHVecTensorGradient;
 
/**
 * @brief Specialisation for 3D tensor field gradient calculation
 * @ingroup mofem_forces_and_sources_user_data_operators
 *
 */
template <>
struct OpCalculateHVecTensorGradient<3, 9, 3>
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateHVecTensorGradient(const std::string field_name,
                                boost::shared_ptr<MatrixDouble> data_ptr,
                                const EntityType zero_type = MBEDGE,
                                const int zero_side = 0)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroType(zero_type), zeroSide(zero_side) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
 
    const size_t nb_integration_points = getGaussPts().size2();
    if (type == zeroType && side == zeroSide) {
      dataPtr->resize(27, nb_integration_points,
                      false);
      dataPtr->clear();
    }
 
  #ifndef NDEBUG
    if (data.getFieldData().size() % 3) {
      SETERRQ(
          PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
          "Data inconsistency, nb_dofs %% COEFF_DIM != 0, that is %ld %% %d "
          "!= 0",
          data.getFieldData().size(), 3);
    }
  #endif
 
    const auto nb_dofs = data.getFieldData().size() / 3;
    if (!nb_dofs)
      MoFEMFunctionReturnHot(0);
      
    const size_t nb_base_functions = data.getN().size2() / 3;
    FTensor::Index<'i', 3> i;
    FTensor::Index<'j', 3> j;
    FTensor::Index<'k', 3> k;
 
    auto t_base_diff = data.getFTensor2DiffN<3, 3>();
    auto t_data = getFTensor3FromMat<3, 3, 3>(*dataPtr);
    for (size_t gg = 0; gg != nb_integration_points; ++gg) {
      auto t_dof = data.getFTensor1FieldData<3>();
      int bb = 0;
      for (; bb != nb_dofs; ++bb) {
        t_data(k, i, j) += t_base_diff(i, j) * t_dof(k);
        ++t_base_diff;
        ++t_dof;
      }
      for (; bb != nb_base_functions; ++bb)
        ++t_base_diff;
      ++t_data;
    }
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<MatrixDouble> dataPtr;
  const EntityHandle zeroType;
  const int zeroSide;
};
 
template <>
struct OpCalculateHVecTensorGradient<9, 9, 3>
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateHVecTensorGradient(const std::string field_name,
                                boost::shared_ptr<MatrixDouble> data_ptr,
                                const EntityType zero_type = MBEDGE,
                                const int zero_side = 0)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroType(zero_type), zeroSide(zero_side) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
 
    const size_t nb_integration_points = getGaussPts().size2();
    if (type == zeroType && side == zeroSide) {
      dataPtr->resize(27, nb_integration_points, false);
      dataPtr->clear();
    }
 
    const auto nb_dofs = data.getFieldData().size();
    if (!nb_dofs)
      MoFEMFunctionReturnHot(0);
      
    const size_t nb_base_functions = data.getN().size2() / 9;
 
  #ifndef NDEBUG
    if (data.getDiffN().size1() != nb_integration_points) {
      SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
              "Wrong number of integration pts (%ld != %ld)",
              data.getDiffN().size1(), nb_integration_points);
    }
    if (data.getDiffN().size2() != nb_base_functions * 27) {
      SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
              "Wrong number of base functions (%ld != %ld)",
              data.getDiffN().size2() / 27, nb_base_functions);
    }
    if (nb_base_functions < nb_dofs) {
      SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
              "Wrong number of base functions (%ld < %ld)", nb_base_functions,
              nb_dofs);
    }
  #endif
 
    FTensor::Index<'i', 3> i;
    FTensor::Index<'j', 3> j;
    FTensor::Index<'k', 3> k;
 
    auto t_base_diff = data.getFTensor3DiffN<3, 3, 3>();
    auto t_data = getFTensor3FromMat<3, 3, 3>(*dataPtr);
    for (size_t gg = 0; gg != nb_integration_points; ++gg) {
      auto t_dof = data.getFTensor0FieldData();
      int bb = 0;
      for (; bb != nb_dofs; ++bb) {
        t_data(k, i, j) += t_base_diff(k, i, j) * t_dof;
        ++t_base_diff;
        ++t_dof;
      }
      for (; bb != nb_base_functions; ++bb)
        ++t_base_diff;
      ++t_data;
    }
 
 
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<MatrixDouble> dataPtr;
  const EntityHandle zeroType;
  const int zeroSide;
};
 
/**
 * @brief Calculate gradient of vector field
 * @ingroup mofem_forces_and_sources_user_data_operators
 *
 * @tparam BASE_DIM
 * @tparam SPACE_DIM
 */
template <int BASE_DIM, int SPACE_DIM>
struct OpCalculateHVecVectorHessian
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateHVecVectorHessian(const std::string field_name,
                               boost::shared_ptr<MatrixDouble> data_ptr,
                               const EntityType zero_type = MBEDGE,
                               const int zero_side = 0)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroType(zero_type), zeroSide(zero_side) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
    const size_t nb_integration_points = getGaussPts().size2();
    if (type == zeroType && side == zeroSide) {
      dataPtr->resize(BASE_DIM * SPACE_DIM * SPACE_DIM, nb_integration_points,
                      false);
      dataPtr->clear();
    }
    const size_t nb_dofs = data.getFieldData().size();
    if (!nb_dofs)
      MoFEMFunctionReturnHot(0);
 
    const int nb_base_functions = data.getN().size2() / BASE_DIM;
 
  #ifndef NDEBUG
    auto &hessian_base = data.getN(BaseDerivatives::SecondDerivative);
    if (hessian_base.size1() != nb_integration_points) {
      SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
               "Wrong number of integration pts (%d != %d)",
               hessian_base.size1(), nb_integration_points);
    }
    if (hessian_base.size2() !=
        BASE_DIM * nb_base_functions * SPACE_DIM * SPACE_DIM) {
      SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
               "Wrong number of base functions (%d != %d)",
               hessian_base.size2() / (BASE_DIM * SPACE_DIM * SPACE_DIM),
               nb_base_functions);
    }
    if (hessian_base.size2() < BASE_DIM * nb_dofs * SPACE_DIM * SPACE_DIM) {
      SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
               "Wrong number of base functions (%d < %d)", hessian_base.size2(),
               BASE_DIM * nb_dofs * SPACE_DIM * SPACE_DIM);
    }
  #endif
 
    FTensor::Index<'i', BASE_DIM> i;
    FTensor::Index<'j', SPACE_DIM> j;
    FTensor::Index<'k', SPACE_DIM> k;
 
    auto t_base_diff2 =
        data.getFTensor3Diff2N<BASE_DIM, SPACE_DIM, SPACE_DIM>();
    auto t_data = getFTensor3FromMat<BASE_DIM, SPACE_DIM, SPACE_DIM>(*dataPtr);
    for (size_t gg = 0; gg != nb_integration_points; ++gg) {
      auto t_dof = data.getFTensor0FieldData();
      int bb = 0;
      for (; bb != nb_dofs; ++bb) {
        t_data(i, j, k) += t_dof * t_base_diff2(i, j, k);
 
        ++t_base_diff2;
        ++t_dof;
      }
      for (; bb != nb_base_functions; ++bb)
        ++t_base_diff2;
      ++t_data;
    }
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<MatrixDouble> dataPtr;
  const EntityHandle zeroType;
  const int zeroSide;
};
 
/**
 * @brief Calculate divergence of vector field dot
 * @ingroup mofem_forces_and_sources_user_data_operators
 *
 * @tparam Tensor_Dim dimension of space
 */
template <int Tensor_Dim1, int Tensor_Dim2>
struct OpCalculateHdivVectorDivergenceDot
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateHdivVectorDivergenceDot(const std::string field_name,
                                     boost::shared_ptr<VectorDouble> data_ptr,
                                     const EntityType zero_type = MBEDGE,
                                     const int zero_side = 0)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), zeroType(zero_type), zeroSide(zero_side) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
    const size_t nb_integration_points = getGaussPts().size2();
    if (type == zeroType && side == zeroSide) {
      dataPtr->resize(nb_integration_points, false);
      dataPtr->clear();
    }
 
    const auto &local_indices = data.getLocalIndices();
    const int nb_dofs = local_indices.size();
    if (nb_dofs) {
 
      std::array<double, MAX_DOFS_ON_ENTITY> dot_dofs_vector;
      const double *array;
      CHKERR VecGetArrayRead(getFEMethod()->ts_u_t, &array);
      for (size_t i = 0; i != local_indices.size(); ++i)
        if (local_indices[i] != -1)
          dot_dofs_vector[i] = array[local_indices[i]];
        else
          dot_dofs_vector[i] = 0;
      CHKERR VecRestoreArrayRead(getFEMethod()->ts_u_t, &array);
 
      const size_t nb_base_functions = data.getN().size2() / Tensor_Dim1;
      FTensor::Index<'i', Tensor_Dim1> i;
      auto t_n_diff_hdiv = data.getFTensor2DiffN<Tensor_Dim1, Tensor_Dim2>();
      auto t_data = getFTensor0FromVec(*dataPtr);
      for (size_t gg = 0; gg != nb_integration_points; ++gg) {
        int bb = 0;
        for (; bb != nb_dofs; ++bb) {
          double div = 0;
          for (auto ii = 0; ii != Tensor_Dim2; ++ii)
            div += t_n_diff_hdiv(ii, ii);
          t_data += dot_dofs_vector[bb] * div;
          ++t_n_diff_hdiv;
        }
        for (; bb != nb_base_functions; ++bb)
          ++t_n_diff_hdiv;
        ++t_data;
      }
    }
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<VectorDouble> dataPtr;
  const EntityHandle zeroType;
  const int zeroSide;
};
 
/**
 * @brief Calculate curl   of vector field
 * @ingroup mofem_forces_and_sources_user_data_operators
 *
 * @tparam Base_Dim base function dimension
 * @tparam Space_Dim dimension of space
 * @tparam Hcurl field dimension
 */
template <int Base_Dim, int Space_Dim> struct OpCalculateHcurlVectorCurl;
 
/**
 * @brief Calculate curl of vector field
 * @ingroup mofem_forces_and_sources_user_data_operators
 *
 * @tparam Base_Dim base function dimension
 * @tparam Space_Dim dimension of space
 * @tparam Hcurl field dimension
 */
template <>
struct OpCalculateHcurlVectorCurl<3, 3>
    : public ForcesAndSourcesCore::UserDataOperator {
  OpCalculateHcurlVectorCurl(const std::string field_name,
                             boost::shared_ptr<MatrixDouble> data_ptr,
                             const EntityType zero_type = MBEDGE,
                             const int zero_side = 0);
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
private:
  boost::shared_ptr<MatrixDouble> dataPtr;
  const EntityHandle zeroType;
  const int zeroSide;
};
 
/**
 * @brief Calculate curl of vector field
 * @ingroup mofem_forces_and_sources_user_data_operators
 *
 * @tparam Field_Dim dimension of field
 * @tparam Space_Dim dimension of space
 */
template <>
struct OpCalculateHcurlVectorCurl<1, 2>
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateHcurlVectorCurl(const std::string field_name,
                             boost::shared_ptr<MatrixDouble> data_ptr,
                             const EntityType zero_type = MBVERTEX,
                             const int zero_side = 0);
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
private:
  boost::shared_ptr<MatrixDouble> dataPtr;
  const EntityHandle zeroType;
  const int zeroSide;
};
 
/**
 * @brief Calculate curl of vector field
 * @ingroup mofem_forces_and_sources_user_data_operators
 *
 * @tparam Field_Dim dimension of field
 * @tparam Space_Dim dimension of space
 */
template <>
struct OpCalculateHcurlVectorCurl<1, 3>
    : public FaceElementForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateHcurlVectorCurl(const std::string field_name,
                             boost::shared_ptr<MatrixDouble> data_ptr,
                             const EntityType zero_type = MBVERTEX,
                             const int zero_side = 0);
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
private:
  boost::shared_ptr<MatrixDouble> dataPtr;
  const EntityHandle zeroType;
  const int zeroSide;
};
 
/**
 * @brief Calculate tenor field using vectorial base, i.e. Hdiv/Hcurl
 * \ingroup mofem_forces_and_sources_user_data_operators
 *
 * @tparam Tensor_Dim0 rank of the field
 * @tparam Tensor_Dim1 dimension of space
 */
template <int Tensor_Dim0, int Tensor_Dim1>
struct OpCalculateHVecTensorField
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateHVecTensorField(const std::string field_name,
                             boost::shared_ptr<MatrixDouble> data_ptr,
                             boost::shared_ptr<double> scale_ptr,
                             SmartPetscObj<Vec> data_vec = SmartPetscObj<Vec>(),
                             const EntityType zero_type = MBEDGE,
                             const int zero_side = 0)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), scalePtr(scale_ptr), dataVec(data_vec),
        zeroType(zero_type), zeroSide(zero_side) {
    if (!dataPtr)
      CHK_THROW_MESSAGE(MOFEM_DATA_INCONSISTENCY, "Pointer is not set");
  }
 
  OpCalculateHVecTensorField(const std::string field_name,
                             boost::shared_ptr<MatrixDouble> data_ptr,
                             const EntityType zero_type = MBEDGE,
                             const int zero_side = 0)
      : OpCalculateHVecTensorField(field_name, data_ptr, nullptr,
                                   SmartPetscObj<Vec>(), zero_type, zero_side) {
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
    const size_t nb_integration_points = getGaussPts().size2();
    if (type == zeroType && side == zeroSide) {
      dataPtr->resize(Tensor_Dim0 * Tensor_Dim1, nb_integration_points, false);
      dataPtr->clear();
    }
    const size_t nb_dofs = data.getFieldData().size();
    if (nb_dofs) {
 
      if (dataVec.use_count()) {
        dotVector.resize(nb_dofs, false);
        const double *array;
        CHKERR VecGetArrayRead(dataVec, &array);
        const auto &local_indices = data.getLocalIndices();
        for (int i = 0; i != local_indices.size(); ++i)
          if (local_indices[i] != -1)
            dotVector[i] = array[local_indices[i]];
          else
            dotVector[i] = 0;
        CHKERR VecRestoreArrayRead(dataVec, &array);
        data.getFieldData().swap(dotVector);
      }
 
      double scale = (scalePtr) ? *scalePtr : 1.0;
      const size_t nb_base_functions = data.getN().size2() / 3;
      FTensor::Index<'i', Tensor_Dim0> i;
      FTensor::Index<'j', Tensor_Dim1> j;
      auto t_n_hvec = data.getFTensor1N<3>();
      auto t_data = getFTensor2FromMat<Tensor_Dim0, Tensor_Dim1>(*dataPtr);
      for (size_t gg = 0; gg != nb_integration_points; ++gg) {
        auto t_dof = data.getFTensor1FieldData<Tensor_Dim0>();
        size_t bb = 0;
        for (; bb != nb_dofs / Tensor_Dim0; ++bb) {
          t_data(i, j) += (scale * t_dof(i)) * t_n_hvec(j);
          ++t_n_hvec;
          ++t_dof;
        }
        for (; bb < nb_base_functions; ++bb)
          ++t_n_hvec;
        ++t_data;
      }
 
      if (dataVec.use_count()) {
        data.getFieldData().swap(dotVector);
      }
    }
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<MatrixDouble> dataPtr;
  boost::shared_ptr<double> scalePtr;
  SmartPetscObj<Vec> dataVec;
  const EntityHandle zeroType;
  const int zeroSide;
  VectorDouble dotVector; ///< Keeps temporary values of time derivatives
};
 
/** \brief Get tensor field for H-div approximation
 * \ingroup mofem_forces_and_sources_user_data_operators
 *
 * \warning This operator is not tested
 */
template <int Tensor_Dim0, int Tensor_Dim1>
struct OpCalculateBrokenHVecTensorField
    : public ForcesAndSourcesCore::UserDataOperator {
 
  using OP = ForcesAndSourcesCore::UserDataOperator;
 
  OpCalculateBrokenHVecTensorField(
      const std::string field_name, boost::shared_ptr<MatrixDouble> data_ptr,
      SmartPetscObj<Vec> data_vec, EntityType broken_type,
      boost::shared_ptr<Range> broken_range_ptr = nullptr,
      boost::shared_ptr<double> scale_ptr = nullptr,
      const EntityType zero_type = MBEDGE, const int zero_side = 0)
      : OP(field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), dataVec(data_vec), brokenType(broken_type),
        brokenRangePtr(broken_range_ptr), zeroType(zero_type) {
    if (!dataPtr)
      CHK_THROW_MESSAGE(MOFEM_DATA_INCONSISTENCY, "Pointer is not set");
  }
 
  /**
   * \brief Calculate values of vector field at integration points
   * @param  side side entity number
   * @param  type side entity type
   * @param  data entity data
   * @return      error code
   */
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
private:
  boost::shared_ptr<MatrixDouble> dataPtr;
  SmartPetscObj<Vec> dataVec;
  EntityType brokenType;
  boost::shared_ptr<Range> brokenRangePtr;
  boost::shared_ptr<double> scalePtr;
  const EntityHandle zeroType;
  VectorDouble dotVector;
};
 
template <int Tensor_Dim0, int Tensor_Dim1>
MoFEMErrorCode
OpCalculateBrokenHVecTensorField<Tensor_Dim0, Tensor_Dim1>::doWork(
    int side, EntityType type, EntitiesFieldData::EntData &data) {
  MoFEMFunctionBegin;
  const size_t nb_integration_points = OP::getGaussPts().size2();
  if (type == zeroType) {
    dataPtr->resize(Tensor_Dim0 * Tensor_Dim1, nb_integration_points, false);
    dataPtr->clear();
  }
  const size_t nb_dofs = data.getFieldData().size();
  if (!nb_dofs)
    MoFEMFunctionReturnHot(0);
 
  if (dataVec.use_count()) {
    dotVector.resize(nb_dofs, false);
    const double *array;
    CHKERR VecGetArrayRead(dataVec, &array);
    const auto &local_indices = data.getLocalIndices();
    for (int i = 0; i != local_indices.size(); ++i)
      if (local_indices[i] != -1)
        dotVector[i] = array[local_indices[i]];
      else
        dotVector[i] = 0;
    CHKERR VecRestoreArrayRead(dataVec, &array);
    data.getFieldData().swap(dotVector);
  }
 
  /**
   * @brief Get side face dofs
   *
   * Find which base functions on borken space have adjacent given entity type
   * and are in the range ptr if given.
   *
   */
  auto get_get_side_face_dofs = [&]() {
    auto fe_type = OP::getFEType();
 
    BaseFunction::DofsSideMap &side_dof_map =
        data.getFieldEntities()[0]->getDofSideMap().at(fe_type);
    std::vector<int> side_face_dofs;
    side_face_dofs.reserve(data.getIndices().size() / Tensor_Dim0);
 
    for (
 
        auto it = side_dof_map.get<1>().begin();
        it != side_dof_map.get<1>().end(); ++it
 
    ) {
      if ((Tensor_Dim0 * it->dof) >= data.getIndices().size()) {
        break;
      }
      if (it->type == brokenType) {
        if (brokenRangePtr) {
          auto ent = OP::getSideEntity(it->side, brokenType);
          if (brokenRangePtr->find(ent) != brokenRangePtr->end()) {
            side_face_dofs.push_back(it->dof);
          }
        } else {
          side_face_dofs.push_back(it->dof);
        }
      }
    }
 
    return side_face_dofs;
  };
 
  auto side_face_dofs = get_get_side_face_dofs();
 
  FTensor::Index<'i', Tensor_Dim0> i;
  FTensor::Index<'j', Tensor_Dim1> j;
  auto t_data = getFTensor2FromMat<Tensor_Dim0, Tensor_Dim1>(*dataPtr);
  for (size_t gg = 0; gg != nb_integration_points; ++gg) {
    for (auto b : side_face_dofs) {
      auto t_row_base = data.getFTensor1N<3>(gg, b);
      auto t_dof = getFTensor1FromPtr<Tensor_Dim0>(data.getFieldData().data() +
                                                   b * Tensor_Dim0);
      t_data(i, j) += t_dof(i) * t_row_base(j);
    }
    ++t_data;
  }
  *dataPtr *= (scalePtr) ? *scalePtr : 1.0;
 
  if (dataVec.use_count()) {
    data.getFieldData().swap(dotVector);
  }
 
  MoFEMFunctionReturn(0);
}
 
/**
 * @brief Calculate tenor field using tensor base, i.e. Hdiv/Hcurl
 * \ingroup mofem_forces_and_sources_user_data_operators
 *
 * @tparam Tensor_Dim0 rank of the field
 * @tparam Tensor_Dim1 dimension of space
 */
template <int Tensor_Dim0, int Tensor_Dim1>
struct OpCalculateHTensorTensorField
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateHTensorTensorField(
      const std::string field_name, boost::shared_ptr<MatrixDouble> data_ptr,
      boost::shared_ptr<double> scale_ptr,
      SmartPetscObj<Vec> data_vec = SmartPetscObj<Vec>(),
      const EntityType zero_type = MBEDGE, const int zero_side = 0)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), scalePtr(scale_ptr), dataVec(data_vec),
        zeroType(zero_type), zeroSide(zero_side) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  OpCalculateHTensorTensorField(const std::string field_name,
                                boost::shared_ptr<MatrixDouble> data_ptr,
                                const EntityType zero_type = MBEDGE,
                                const int zero_side = 0)
      : OpCalculateHTensorTensorField(field_name, data_ptr, nullptr,
                                      SmartPetscObj<Vec>(), zero_type,
                                      zero_side) {}
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
    const size_t nb_integration_points = getGaussPts().size2();
    if (type == zeroType && side == zeroSide) {
      dataPtr->resize(Tensor_Dim0 * Tensor_Dim1, nb_integration_points, false);
      dataPtr->clear();
    }
    const size_t nb_dofs = data.getFieldData().size();
    if (!nb_dofs)
      MoFEMFunctionReturnHot(0);
 
    if (dataVec.use_count()) {
      dotVector.resize(nb_dofs, false);
      const double *array;
      CHKERR VecGetArrayRead(dataVec, &array);
      const auto &local_indices = data.getLocalIndices();
      for (int i = 0; i != local_indices.size(); ++i)
        if (local_indices[i] != -1)
          dotVector[i] = array[local_indices[i]];
        else
          dotVector[i] = 0;
      CHKERR VecRestoreArrayRead(dataVec, &array);
      data.getFieldData().swap(dotVector);
    }
 
    double scale = (scalePtr) ? *scalePtr : 1.0;
    const size_t nb_base_functions =
        data.getN().size2() / (Tensor_Dim0 * Tensor_Dim1);
    FTensor::Index<'i', Tensor_Dim0> i;
    FTensor::Index<'j', Tensor_Dim1> j;
    auto t_n_hten = data.getFTensor2N<Tensor_Dim0, Tensor_Dim1>();
    auto t_data = getFTensor2FromMat<Tensor_Dim0, Tensor_Dim1>(*dataPtr);
    for (size_t gg = 0; gg != nb_integration_points; ++gg) {
      auto t_dof = data.getFTensor0FieldData();
      size_t bb = 0;
      for (; bb != nb_dofs; ++bb) {
        t_data(i, j) += (scale * t_dof) * t_n_hten(i, j);
        ++t_n_hten;
        ++t_dof;
      }
      for (; bb < nb_base_functions; ++bb)
        ++t_n_hten;
      ++t_data;
    }
 
    if (dataVec.use_count()) {
      data.getFieldData().swap(dotVector);
    }
 
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<MatrixDouble> dataPtr;
  boost::shared_ptr<double> scalePtr;
  SmartPetscObj<Vec> dataVec;
  const EntityHandle zeroType;
  const int zeroSide;
  VectorDouble dotVector; ///< Keeps temporary values of time derivatives
};
 
/**
 * @brief Calculate divergence of tonsorial field using vectorial base
 * \ingroup mofem_forces_and_sources_user_data_operators
 *
 * @tparam Tensor_Dim0 rank of the field
 * @tparam Tensor_Dim1 dimension of space
 */
template <int Tensor_Dim0, int Tensor_Dim1,
          CoordinateTypes CoordSys = CARTESIAN>
struct OpCalculateHVecTensorDivergence
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateHVecTensorDivergence(const std::string field_name,
                                  boost::shared_ptr<MatrixDouble> data_ptr,
                                  SmartPetscObj<Vec> data_vec,
                                  const EntityType zero_type = MBEDGE,
                                  const int zero_side = 0)
      : ForcesAndSourcesCore::UserDataOperator(
            field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), dataVec(data_vec), zeroType(zero_type),
        zeroSide(zero_side) {
    if (!dataPtr)
      CHK_THROW_MESSAGE(MOFEM_DATA_INCONSISTENCY, "Pointer is not set");
  }
 
  OpCalculateHVecTensorDivergence(const std::string field_name,
                                  boost::shared_ptr<MatrixDouble> data_ptr,
                                  const EntityType zero_type = MBEDGE,
                                  const int zero_side = 0)
      : OpCalculateHVecTensorDivergence(
            field_name, data_ptr, SmartPetscObj<Vec>(), zero_type, zero_side) {}
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
    const size_t nb_integration_points = getGaussPts().size2();
    if (type == zeroType && side == zeroSide) {
      dataPtr->resize(Tensor_Dim0, nb_integration_points, false);
      dataPtr->clear();
    }
    const size_t nb_dofs = data.getFieldData().size();
    if (nb_dofs) {
 
      if (dataVec.use_count()) {
        dotVector.resize(nb_dofs, false);
        const double *array;
        CHKERR VecGetArrayRead(dataVec, &array);
        const auto &local_indices = data.getLocalIndices();
        for (int i = 0; i != local_indices.size(); ++i)
          if (local_indices[i] != -1)
            dotVector[i] = array[local_indices[i]];
          else
            dotVector[i] = 0;
        CHKERR VecRestoreArrayRead(dataVec, &array);
        data.getFieldData().swap(dotVector);
      }
 
      const size_t nb_base_functions = data.getN().size2() / 3;
      FTensor::Index<'i', Tensor_Dim0> i;
      FTensor::Index<'j', Tensor_Dim1> j;
      auto t_n_diff_hvec = data.getFTensor2DiffN<3, Tensor_Dim1>();
      auto t_data = getFTensor1FromMat<Tensor_Dim0>(*dataPtr);
      auto t_base = data.getFTensor1N<3>();
      auto t_coords = getFTensor1CoordsAtGaussPts();
      for (size_t gg = 0; gg != nb_integration_points; ++gg) {
        auto t_dof = data.getFTensor1FieldData<Tensor_Dim0>();
        size_t bb = 0;
        for (; bb != nb_dofs / Tensor_Dim0; ++bb) {
          double div = t_n_diff_hvec(j, j);
          t_data(i) += t_dof(i) * div;
          if constexpr (CoordSys == CYLINDRICAL) {
            t_data(i) += t_base(0) * (t_dof(i) / t_coords(0));
          }
          ++t_n_diff_hvec;
          ++t_dof;
          ++t_base;
        }
        for (; bb < nb_base_functions; ++bb) {
          ++t_base;
          ++t_n_diff_hvec;
        }
        ++t_data;
        ++t_coords;
      }
 
      if (dataVec.use_count()) {
        data.getFieldData().swap(dotVector);
      }
    }
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<MatrixDouble> dataPtr;
  SmartPetscObj<Vec> dataVec;
  const EntityHandle zeroType;
  const int zeroSide;
 
  VectorDouble dotVector; ///< Keeps temporary values of time derivatives
};
 
/**
 * @brief Calculate divergence of tonsorial field using vectorial base
 * \ingroup mofem_forces_and_sources_user_data_operators
 *
 * \warning This operator is not tested
 *
 * @tparam Tensor_Dim0 rank of the field
 * @tparam Tensor_Dim1 dimension of space
 */
template <int Tensor_Dim0, int Tensor_Dim1,
          CoordinateTypes CoordSys = CARTESIAN>
struct OpCalculateBrokenHVecTensorDivergence
    : public ForcesAndSourcesCore::UserDataOperator {
 
  using OP = ForcesAndSourcesCore::UserDataOperator;
 
  OpCalculateBrokenHVecTensorDivergence(
      const std::string field_name, boost::shared_ptr<MatrixDouble> data_ptr,
      SmartPetscObj<Vec> data_vec, EntityType broken_type,
      boost::shared_ptr<Range> broken_range_ptr = nullptr,
      boost::shared_ptr<double> scale_ptr = nullptr,
      const EntityType zero_type = MBEDGE)
      : OP(field_name, ForcesAndSourcesCore::UserDataOperator::OPROW),
        dataPtr(data_ptr), dataVec(data_vec), brokenType(broken_type),
        brokenRangePtr(broken_range_ptr), scalePtr(scale_ptr),
        zeroType(zero_type) {
    if (!dataPtr)
      CHK_THROW_MESSAGE(MOFEM_DATA_INCONSISTENCY, "Pointer is not set");
  }
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
    const size_t nb_integration_points = getGaussPts().size2();
    if (type == zeroType && side == 0) {
      dataPtr->resize(Tensor_Dim0, nb_integration_points, false);
      dataPtr->clear();
    }
 
    const size_t nb_dofs = data.getFieldData().size();
    if (nb_dofs) {
 
      if (dataVec.use_count()) {
        dotVector.resize(nb_dofs, false);
        const double *array;
        CHKERR VecGetArrayRead(dataVec, &array);
        const auto &local_indices = data.getLocalIndices();
        for (int i = 0; i != local_indices.size(); ++i)
          if (local_indices[i] != -1)
            dotVector[i] = array[local_indices[i]];
          else
            dotVector[i] = 0;
        CHKERR VecRestoreArrayRead(dataVec, &array);
        data.getFieldData().swap(dotVector);
      }
 
      /**
       * @brief Get side face dofs
       *
       * Find which base functions on borken space have adjacent given entity
       * type and are in the range ptr if given.
       *
       */
      auto get_get_side_face_dofs = [&]() {
        auto fe_type = OP::getFEType();
 
        BaseFunction::DofsSideMap &side_dof_map =
            data.getFieldEntities()[0]->getDofSideMap().at(fe_type);
        std::vector<int> side_face_dofs;
        side_face_dofs.reserve(data.getIndices().size() / Tensor_Dim0);
 
        for (
 
            auto it = side_dof_map.get<1>().begin();
            it != side_dof_map.get<1>().end(); ++it
 
        ) {
          if ((Tensor_Dim0 * it->dof) >= data.getIndices().size()) {
            break;
          }
          if (it->type == brokenType) {
            if (brokenRangePtr) {
              auto ent = OP::getSideEntity(it->side, brokenType);
              if (brokenRangePtr->find(ent) != brokenRangePtr->end()) {
                side_face_dofs.push_back(it->dof);
              }
            } else {
              side_face_dofs.push_back(it->dof);
            }
          }
        }
 
        return side_face_dofs;
      };
 
      auto side_face_dofs = get_get_side_face_dofs();
 
      FTensor::Index<'i', Tensor_Dim0> i;
      FTensor::Index<'j', Tensor_Dim1> j;
      auto t_data = getFTensor1FromMat<Tensor_Dim0>(*dataPtr);
      auto t_coords = getFTensor1CoordsAtGaussPts();
      for (size_t gg = 0; gg != nb_integration_points; ++gg) {
        for (auto b : side_face_dofs) {
          auto t_dof = getFTensor1FromPtr<Tensor_Dim0>(
              data.getFieldData().data() + b * Tensor_Dim0);
          auto t_base = data.getFTensor1N<3>(gg, b);
          auto t_diff_base = data.getFTensor2DiffN<3, Tensor_Dim1>(gg, b);
          double div = t_diff_base(j, j);
          t_data(i) += t_dof(i) * div;
          if constexpr (CoordSys == CYLINDRICAL) {
            t_data(i) += t_base(0) * (t_dof(i) / t_coords(0));
          }
        }
        ++t_data;
        ++t_coords;
      }
    }
 
    if (dataVec.use_count()) {
      data.getFieldData().swap(dotVector);
    }
 
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<MatrixDouble> dataPtr;
  SmartPetscObj<Vec> dataVec;
  EntityType brokenType;
  boost::shared_ptr<Range> brokenRangePtr;
  boost::shared_ptr<double> scalePtr;
  const EntityHandle zeroType;
  VectorDouble dotVector;
};
 
/**
 * @brief Calculate trace of vector (Hdiv/Hcurl) space
 *
 * @tparam Tensor_Dim
 * @tparam OpBase
 */
template <int Tensor_Dim, typename OpBase>
struct OpCalculateHVecTensorTrace : public OpBase {
 
  OpCalculateHVecTensorTrace(const std::string field_name,
                             boost::shared_ptr<MatrixDouble> data_ptr,
                             boost::shared_ptr<double> scale_ptr,
                             const EntityType zero_type = MBEDGE,
                             const int zero_side = 0)
      : OpBase(field_name, OpBase::OPROW), dataPtr(data_ptr),
        scalePtr(scale_ptr), zeroType(zero_type), zeroSide(zero_side) {
    if (!dataPtr)
      THROW_MESSAGE("Pointer is not set");
  }
 
  OpCalculateHVecTensorTrace(const std::string field_name,
                             boost::shared_ptr<MatrixDouble> data_ptr,
                             const EntityType zero_type = MBEDGE,
                             const int zero_side = 0)
      : OpCalculateHVecTensorTrace(field_name, data_ptr, nullptr, zero_type,
                                   zero_side) {}
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
    const size_t nb_integration_points = OpBase::getGaussPts().size2();
    if (type == zeroType && side == 0) {
      dataPtr->resize(Tensor_Dim, nb_integration_points, false);
      dataPtr->clear();
    }
    const size_t nb_dofs = data.getFieldData().size();
    if (nb_dofs) {
      double scale_val = (scalePtr) ? *scalePtr : 1.0;
      auto t_normal = OpBase::getFTensor1NormalsAtGaussPts();
      const size_t nb_base_functions = data.getN().size2() / 3;
      auto t_base = data.getFTensor1N<3>();
      auto t_data = getFTensor1FromMat<Tensor_Dim>(*dataPtr);
      for (size_t gg = 0; gg != nb_integration_points; ++gg) {
        FTensor::Tensor1<double, Tensor_Dim> t_normalized_normal;
        t_normalized_normal(j) = t_normal(j);
        t_normalized_normal.normalize();
        auto t_dof = data.getFTensor1FieldData<Tensor_Dim>();
        size_t bb = 0;
        for (; bb != nb_dofs / Tensor_Dim; ++bb) {
          t_data(i) +=
              (scale_val * t_dof(i)) * (t_base(j) * t_normalized_normal(j));
          ++t_base;
          ++t_dof;
        }
        for (; bb < nb_base_functions; ++bb) {
          ++t_base;
        }
        ++t_data;
        ++t_normal;
      }
    }
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<MatrixDouble> dataPtr;
  boost::shared_ptr<double> scalePtr;
  const EntityHandle zeroType;
  const int zeroSide;
  FTensor::Index<'i', Tensor_Dim> i;
  FTensor::Index<'j', Tensor_Dim> j;
};
 
/**@}*/
 
/** \name Other operators */
 
/**@{*/
 
/**@}*/
 
/** \name Operators for faces */
 
/**@{*/
 
/** \brief Transform local reference derivatives of shape functions to global
derivatives
 
\ingroup mofem_forces_and_sources_tri_element
 
*/
template <int DIM, int DERIVATIVE = 1> struct OpSetInvJacSpaceForFaceImpl;
 
struct OpSetInvJacToScalarBasesBasic
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpSetInvJacToScalarBasesBasic(FieldSpace space,
                                boost::shared_ptr<MatrixDouble> inv_jac_ptr);
 
protected:
 
  /**
   * @brief Apply transformation to the input matrix
   *
   * @tparam D1 dimension of the derivative of base functions in input
   * @tparam D2 dimension of the derivative of base functions in output
   * @tparam J1 nb of rows in jacobian (= dimension of space)
   * @tparam J2 nb of columns in jacobian (= dimension of reference element)
   * @param diff_n
   * @return MoFEMErrorCode
   */
  template <int D1, int D2, int J1, int J2>
  inline MoFEMErrorCode applyTransform(MatrixDouble &diff_n) {
    MoFEMFunctionBegin;
 
    static_assert(D2 == J2, "Dimension of jacobian and dimension of <out> "
                            "directive does not match");
 
    size_t nb_functions = diff_n.size2() / D1;
    if (nb_functions) {
      size_t nb_gauss_pts = diff_n.size1();
 
  #ifndef NDEBUG
      if (nb_gauss_pts != getGaussPts().size2())
        SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                "Wrong number of Gauss Pts");
      if (diff_n.size2() % D1)
        SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                "Number of directives of base functions and D1 dimension does "
                "not match");
  #endif
 
      diffNinvJac.resize(diff_n.size1(), D2 * nb_functions, false);
 
      FTensor::Index<'i', D2> i;
      FTensor::Index<'k', D1> k;
      auto t_diff_n = getFTensor1FromPtr<D2>(&*diffNinvJac.data().begin());
      auto t_diff_n_ref = getFTensor1FromPtr<D1>(&*diff_n.data().begin());
      auto t_inv_jac = getFTensor2FromMat<J1, J2>(*invJacPtr);
      for (size_t gg = 0; gg != nb_gauss_pts; ++gg, ++t_inv_jac) {
        for (size_t dd = 0; dd != nb_functions; ++dd) {
          t_diff_n(i) = t_inv_jac(k, i) * t_diff_n_ref(k);
          ++t_diff_n;
          ++t_diff_n_ref;
        }
      }
 
      diff_n.swap(diffNinvJac);
    }
    MoFEMFunctionReturn(0);
  }
 
  boost::shared_ptr<MatrixDouble> invJacPtr;
  MatrixDouble diffNinvJac;
};
 
template <>
struct OpSetInvJacSpaceForFaceImpl<2, 1>
    : public OpSetInvJacToScalarBasesBasic {
 
  using OpSetInvJacToScalarBasesBasic::OpSetInvJacToScalarBasesBasic;
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
};
 
template <>
struct OpSetInvJacSpaceForFaceImpl<3, 1>
    : public OpSetInvJacSpaceForFaceImpl<2, 1> {
 
  using OpSetInvJacSpaceForFaceImpl<2, 1>::OpSetInvJacSpaceForFaceImpl;
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
};
 
template <>
struct OpSetInvJacSpaceForFaceImpl<2, 2>
    : public OpSetInvJacSpaceForFaceImpl<2, 1> {
 
  using OpSetInvJacSpaceForFaceImpl<2, 1>::OpSetInvJacSpaceForFaceImpl;
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
};
 
template <int DERIVARIVE = 1>
struct OpSetInvJacH1ForFace
    : public OpSetInvJacSpaceForFaceImpl<2, DERIVARIVE> {
  OpSetInvJacH1ForFace(boost::shared_ptr<MatrixDouble> inv_jac_ptr)
      : OpSetInvJacSpaceForFaceImpl<2, DERIVARIVE>(H1, inv_jac_ptr) {}
};
 
template <int DERIVARIVE = 1>
struct OpSetInvJacL2ForFace
    : public OpSetInvJacSpaceForFaceImpl<2, DERIVARIVE> {
  OpSetInvJacL2ForFace(boost::shared_ptr<MatrixDouble> inv_jac_ptr)
      : OpSetInvJacSpaceForFaceImpl<2, DERIVARIVE>(L2, inv_jac_ptr) {}
};
 
template <int DERIVARIVE = 1>
struct OpSetInvJacH1ForFaceEmbeddedIn3DSpace
    : public OpSetInvJacSpaceForFaceImpl<3, DERIVARIVE> {
  OpSetInvJacH1ForFaceEmbeddedIn3DSpace(
      boost::shared_ptr<MatrixDouble> inv_jac_ptr)
      : OpSetInvJacSpaceForFaceImpl<3, DERIVARIVE>(H1, inv_jac_ptr) {}
};
 
template <int DERIVARIVE = 1>
struct OpSetInvJacL2ForFaceEmbeddedIn3DSpace
    : public OpSetInvJacSpaceForFaceImpl<3, DERIVARIVE> {
  OpSetInvJacL2ForFaceEmbeddedIn3DSpace(
      boost::shared_ptr<MatrixDouble> inv_jac_ptr)
      : OpSetInvJacSpaceForFaceImpl<3, DERIVARIVE>(L2, inv_jac_ptr) {}
};
 
/**
 * \brief Transform local reference derivatives of shape function to
 global derivatives for face
 
 * \ingroup mofem_forces_and_sources_tri_element
 */
template <int DIM> struct OpSetInvJacHcurlFaceImpl;
 
template <>
struct OpSetInvJacHcurlFaceImpl<2>
    : public FaceElementForcesAndSourcesCore::UserDataOperator {
 
  OpSetInvJacHcurlFaceImpl(boost::shared_ptr<MatrixDouble> inv_jac_ptr)
      : FaceElementForcesAndSourcesCore::UserDataOperator(HCURL),
        invJacPtr(inv_jac_ptr) {}
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
protected:
  boost::shared_ptr<MatrixDouble> invJacPtr;
  MatrixDouble diffHcurlInvJac;
};
 
template <>
struct OpSetInvJacHcurlFaceImpl<3> : public OpSetInvJacHcurlFaceImpl<2> {
  using OpSetInvJacHcurlFaceImpl<2>::OpSetInvJacHcurlFaceImpl;
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
};
 
using OpSetInvJacHcurlFace = OpSetInvJacHcurlFaceImpl<2>;
using OpSetInvJacHcurlFaceEmbeddedIn3DSpace = OpSetInvJacHcurlFaceImpl<3>;
 
/**
 * @brief Make Hdiv space from Hcurl space in 2d
 * @ingroup mofem_forces_and_sources_tri_element
 */
struct OpMakeHdivFromHcurl
    : public FaceElementForcesAndSourcesCore::UserDataOperator {
 
  OpMakeHdivFromHcurl()
      : FaceElementForcesAndSourcesCore::UserDataOperator(HCURL) {}
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
};
 
/** \brief Transform Hcurl base fluxes from reference element to physical
 * triangle
 */
template <int DIM> struct OpSetCovariantPiolaTransformOnFace2DImpl;
 
/** \brief Apply contravariant (Piola) transfer to Hdiv space on face
 *
 * Covariant Piola transformation
 \f[
 \psi_i|_t = J^{-1}_{ij}\hat{\psi}_j\\
 \left.\frac{\partial \psi_i}{\partial \xi_j}\right|_t
 = J^{-1}_{ik}\frac{\partial \hat{\psi}_k}{\partial \xi_j}
 \f]
 
 */
template <>
struct OpSetCovariantPiolaTransformOnFace2DImpl<2>
    : public FaceElementForcesAndSourcesCore::UserDataOperator {
 
  OpSetCovariantPiolaTransformOnFace2DImpl(
      boost::shared_ptr<MatrixDouble> inv_jac_ptr);
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
private:
  boost::shared_ptr<MatrixDouble> invJacPtr;
 
  MatrixDouble piolaN;
  MatrixDouble diffPiolaN;
};
 
using OpSetCovariantPiolaTransformOnFace2D =
    OpSetCovariantPiolaTransformOnFace2DImpl<2>;
 
/** \brief Apply contravariant (Piola) transfer to Hdiv space on face
 *
 * \note Hdiv space is generated by Hcurl space in 2d.
 *
 * Contravariant Piola transformation
 * \f[
 * \psi_i|_t = \frac{1}{\textrm{det}(J)}J_{ij}\hat{\psi}_j\\
 * \left.\frac{\partial \psi_i}{\partial \xi_j}\right|_t
 * =
 * \frac{1}{\textrm{det}(J)}J_{ik}\frac{\partial \hat{\psi}_k}{\partial \xi_j}
 * \f]
 *
 * \ingroup mofem_forces_and_sources
 *
 */
template <int DIM> struct OpSetContravariantPiolaTransformOnFace2DImpl;
 
template <>
struct OpSetContravariantPiolaTransformOnFace2DImpl<2>
    : public FaceElementForcesAndSourcesCore::UserDataOperator {
 
  OpSetContravariantPiolaTransformOnFace2DImpl(
      boost::shared_ptr<MatrixDouble> jac_ptr)
      : FaceElementForcesAndSourcesCore::UserDataOperator(HCURL),
        jacPtr(jac_ptr) {}
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
protected:
  boost::shared_ptr<MatrixDouble> jacPtr;
  MatrixDouble piolaN;
  MatrixDouble piolaDiffN;
};
 
template <>
struct OpSetContravariantPiolaTransformOnFace2DImpl<3>
    : public OpSetContravariantPiolaTransformOnFace2DImpl<2> {
  using OpSetContravariantPiolaTransformOnFace2DImpl<
      2>::OpSetContravariantPiolaTransformOnFace2DImpl;
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
};
 
using OpSetContravariantPiolaTransformOnFace2D =
    OpSetContravariantPiolaTransformOnFace2DImpl<2>;
using OpSetContravariantPiolaTransformOnFace2DEmbeddedIn3DSpace =
    OpSetContravariantPiolaTransformOnFace2DImpl<3>;
 
/**@}*/
 
/** \name Operators for edges */
 
/**@{*/
 
struct OpSetContravariantPiolaTransformOnEdge2D
    : public EdgeElementForcesAndSourcesCore::UserDataOperator {
 
  OpSetContravariantPiolaTransformOnEdge2D(const FieldSpace space = HCURL)
      : EdgeElementForcesAndSourcesCore::UserDataOperator(space) {}
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
};
 
/**
 * @deprecated Name is deprecated and this is added for backward compatibility
 */
using OpSetContrariantPiolaTransformOnEdge =
    OpSetContravariantPiolaTransformOnEdge2D;
 
/**@}*/
 
/** \name Operator for fat prisms */
 
/**@{*/
 
/**
 * @brief Operator for fat prism element updating integration weights in the
 * volume.
 *
 * Jacobian on the distorted element is nonconstant. This operator updates
 * integration weight on prism to take into account nonconstat jacobian.
 *
 * \f[
 * W_i = w_i \left( \frac{1}{2V} \left\| \frac{\partial \mathbf{x}}{\partial
 * \pmb\xi} \right\| \right)
 * \f]
 * where \f$w_i\f$ is integration weight at integration point \f$i\f$,
 * \f$\mathbf{x}\f$ is physical coordinate, and \f$\pmb\xi\f$ is reference
 * element coordinate.
 *
 */
struct OpMultiplyDeterminantOfJacobianAndWeightsForFatPrisms
    : public FatPrismElementForcesAndSourcesCore::UserDataOperator {
 
  OpMultiplyDeterminantOfJacobianAndWeightsForFatPrisms()
      : FatPrismElementForcesAndSourcesCore::UserDataOperator(H1) {}
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
};
 
/** \brief Calculate inverse of jacobian for face element
 
  It is assumed that face element is XY plane. Applied
  only for 2d problems.
 
  FIXME Generalize function for arbitrary face orientation in 3d space
  FIXME Calculate to Jacobins for two faces
 
  \ingroup mofem_forces_and_sources_prism_element
 
*/
struct OpCalculateInvJacForFatPrism
    : public FatPrismElementForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateInvJacForFatPrism(boost::shared_ptr<MatrixDouble> inv_jac_ptr)
      : FatPrismElementForcesAndSourcesCore::UserDataOperator(H1),
        invJacPtr(inv_jac_ptr), invJac(*invJacPtr) {}
 
  OpCalculateInvJacForFatPrism(MatrixDouble &inv_jac)
      : FatPrismElementForcesAndSourcesCore::UserDataOperator(H1),
        invJac(inv_jac) {}
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
private:
  const boost::shared_ptr<MatrixDouble> invJacPtr;
  MatrixDouble &invJac;
};
 
/** \brief Transform local reference derivatives of shape functions to global
derivatives
 
FIXME Generalize to curved shapes
FIXME Generalize to case that top and bottom face has different shape
 
\ingroup mofem_forces_and_sources_prism_element
 
*/
struct OpSetInvJacH1ForFatPrism
    : public FatPrismElementForcesAndSourcesCore::UserDataOperator {
 
  OpSetInvJacH1ForFatPrism(boost::shared_ptr<MatrixDouble> inv_jac_ptr)
      : FatPrismElementForcesAndSourcesCore::UserDataOperator(H1),
        invJacPtr(inv_jac_ptr), invJac(*invJacPtr) {}
 
  OpSetInvJacH1ForFatPrism(MatrixDouble &inv_jac)
      : FatPrismElementForcesAndSourcesCore::UserDataOperator(H1),
        invJac(inv_jac) {}
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
private:
  const boost::shared_ptr<MatrixDouble> invJacPtr;
  MatrixDouble &invJac;
  MatrixDouble diffNinvJac;
};
 
// Flat prism
 
/** \brief Calculate inverse of jacobian for face element
 
  It is assumed that face element is XY plane. Applied
  only for 2d problems.
 
  FIXME Generalize function for arbitrary face orientation in 3d space
  FIXME Calculate to Jacobins for two faces
 
  \ingroup mofem_forces_and_sources_prism_element
 
*/
struct OpCalculateInvJacForFlatPrism
    : public FlatPrismElementForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateInvJacForFlatPrism(MatrixDouble &inv_jac_f3)
      : FlatPrismElementForcesAndSourcesCore::UserDataOperator(H1),
        invJacF3(inv_jac_f3) {}
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
private:
  MatrixDouble &invJacF3;
};
 
/** \brief Transform local reference derivatives of shape functions to global
derivatives
 
FIXME Generalize to curved shapes
FIXME Generalize to case that top and bottom face has different shape
 
\ingroup mofem_forces_and_sources_prism_element
 
*/
struct OpSetInvJacH1ForFlatPrism
    : public FlatPrismElementForcesAndSourcesCore::UserDataOperator {
 
  OpSetInvJacH1ForFlatPrism(MatrixDouble &inv_jac_f3)
      : FlatPrismElementForcesAndSourcesCore::UserDataOperator(H1),
        invJacF3(inv_jac_f3) {}
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
private:
  MatrixDouble &invJacF3;
  MatrixDouble diffNinvJac;
};
 
/**@}*/
 
/** \name Operation on matrices at integration points */
 
/**@{*/
 
/**
 * @brief Operator for inverting matrices at integration points
 *
 * This template structure computes the inverse of square matrices and their
 * determinants at integration points. It's commonly used in finite element
 * methods for coordinate transformations, constitutive relations, and other
 * matrix operations requiring matrix inversion.
 *
 * @tparam DIM Dimension of the square matrix to be inverted
 */
template <int DIM>
struct OpInvertMatrix : public ForcesAndSourcesCore::UserDataOperator {
 
  /**
   * @brief Constructor for matrix inversion operator
   *
   * @param in_ptr Shared pointer to input matrix to be inverted
   * @param det_ptr Shared pointer to vector for storing matrix determinants
   * @param out_ptr Shared pointer to output matrix for storing inverted matrices
   */
  OpInvertMatrix(boost::shared_ptr<MatrixDouble> in_ptr,
                 boost::shared_ptr<VectorDouble> det_ptr,
                 boost::shared_ptr<MatrixDouble> out_ptr)
      : ForcesAndSourcesCore::UserDataOperator(NOSPACE), inPtr(in_ptr),
        outPtr(out_ptr), detPtr(det_ptr) {}
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
private:
  boost::shared_ptr<MatrixDouble> inPtr;
  boost::shared_ptr<MatrixDouble> outPtr;
  boost::shared_ptr<VectorDouble> detPtr;
};
 
template <int DIM>
MoFEMErrorCode OpInvertMatrix<DIM>::doWork(int side, EntityType type,
                                           EntitiesFieldData::EntData &data) {
  MoFEMFunctionBegin;
 
  if (!inPtr)
    SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
            "Pointer for inPtr matrix not allocated");
  if (!detPtr)
    SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
            "Pointer for detPtr matrix not allocated");
 
  const auto nb_rows = inPtr->size1();
  const auto nb_integration_pts = inPtr->size2();
 
  // Calculate determinant
  {
    detPtr->resize(nb_integration_pts, false);
    auto t_in = getFTensor2FromMat<DIM, DIM>(*inPtr);
    auto t_det = getFTensor0FromVec(*detPtr);
    for (size_t gg = 0; gg != nb_integration_pts; ++gg) {
      t_det = determinantTensor(t_in);
      ++t_in;
      ++t_det;
    }
  }
 
  // Invert jacobian
  if (outPtr) {
    outPtr->resize(nb_rows, nb_integration_pts, false);
    auto t_in = getFTensor2FromMat<DIM, DIM>(*inPtr);
    auto t_out = getFTensor2FromMat<DIM, DIM>(*outPtr);
    auto t_det = getFTensor0FromVec(*detPtr);
    for (size_t gg = 0; gg != nb_integration_pts; ++gg) {
      CHKERR invertTensor(t_in, t_det, t_out);
      ++t_in;
      ++t_out;
      ++t_det;
    }
  }
 
  MoFEMFunctionReturn(0);
}
 
/**@}*/
 
/**
 * @brief Operator for calculating the trace of matrices at integration points
 *
 * This template structure computes the trace (sum of diagonal elements) of
 * square matrices at integration points. The trace is commonly used in
 * mechanics for calculating volumetric strain, pressure, and other scalar
 * quantities derived from tensors.
 *
 * @tparam DIM Dimension of the square matrix
 *
 * @ingroup mofem_forces_and_sources
 */
template <int DIM>
struct OpCalculateTraceFromMat : public ForcesAndSourcesCore::UserDataOperator {
 
  /**
   * @brief Constructor for matrix trace calculation operator
   *
   * @param in_ptr Shared pointer to input matrix for trace calculation
   * @param out_ptr Shared pointer to output vector for storing calculated traces
   */
  OpCalculateTraceFromMat(boost::shared_ptr<MatrixDouble> in_ptr,
                          boost::shared_ptr<VectorDouble> out_ptr)
      : ForcesAndSourcesCore::UserDataOperator(NOSPACE), inPtr(in_ptr),
        outPtr(out_ptr) {}
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
private:
  FTensor::Index<'i', DIM> i;
  boost::shared_ptr<MatrixDouble> inPtr;
  boost::shared_ptr<VectorDouble> outPtr;
};
 
template <int DIM>
MoFEMErrorCode
OpCalculateTraceFromMat<DIM>::doWork(int side, EntityType type,
                                     EntitiesFieldData::EntData &data) {
  MoFEMFunctionBegin;
 
  if (!inPtr)
    SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
            "Pointer for inPtr matrix not allocated");
 
  const auto nb_integration_pts = inPtr->size2();
  // Invert jacobian
  if (outPtr) {
    outPtr->resize(nb_integration_pts, false);
    auto t_in = getFTensor2FromMat<DIM, DIM>(*inPtr);
    auto t_out = getFTensor0FromVec(*outPtr);
 
    for (size_t gg = 0; gg != nb_integration_pts; ++gg) {
      t_out = t_in(i, i);
      ++t_in;
      ++t_out;
    }
  }
 
  MoFEMFunctionReturn(0);
}
 
/**@}*/
 
/** \brief Calculates the trace of an input matrix
 
\ingroup mofem_forces_and_sources
 
*/
 
template <int DIM>
struct OpCalculateTraceFromSymmMat
    : public ForcesAndSourcesCore::UserDataOperator {
 
  OpCalculateTraceFromSymmMat(boost::shared_ptr<MatrixDouble> in_ptr,
                              boost::shared_ptr<VectorDouble> out_ptr)
      : ForcesAndSourcesCore::UserDataOperator(NOSPACE), inPtr(in_ptr),
        outPtr(out_ptr) {}
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
private:
  FTensor::Index<'i', DIM> i;
  boost::shared_ptr<MatrixDouble> inPtr;
  boost::shared_ptr<VectorDouble> outPtr;
};
 
template <int DIM>
MoFEMErrorCode
OpCalculateTraceFromSymmMat<DIM>::doWork(int side, EntityType type,
                                         EntitiesFieldData::EntData &data) {
  MoFEMFunctionBegin;
 
  if (!inPtr)
    SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
            "Pointer for inPtr matrix not allocated");
 
  const auto nb_integration_pts = inPtr->size2();
  // Invert jacobian
  if (outPtr) {
    outPtr->resize(nb_integration_pts, false);
    auto t_in = getFTensor2SymmetricFromMat<DIM>(*inPtr);
    auto t_out = getFTensor0FromVec(*outPtr);
 
    for (size_t gg = 0; gg != nb_integration_pts; ++gg) {
      t_out = t_in(i, i);
      ++t_in;
      ++t_out;
    }
  }
 
  MoFEMFunctionReturn(0);
}
 
} // namespace MoFEM
 
#endif // __USER_DATA_OPERATORS_HPP__
 
/**
 * \defgroup mofem_forces_and_sources_user_data_operators Users Operators
 *
 * \brief Classes and functions used to evaluate fields at integration pts,
 *jacobians, etc..
 *
 * \ingroup mofem_forces_and_sources
 **/