analytical_poisson.cpp

For more information and detailed explain of this example see COR-2: Solving the Poisson equation

/**
 * \file analytical_poisson.cpp
 * \ingroup mofem_simple_interface
 * \example analytical_poisson.cpp
 *
 * For more information and detailed explain of this
 * example see \ref poisson_tut1
 *
 *
 */
 
 
 
#include <BasicFiniteElements.hpp>
#include <PoissonOperators.hpp>
#include <AuxPoissonFunctions.hpp>
 
static char help[] = "...\n\n";
 
/**
 * \brief Function
 *
 * This is prescribed exact function. If this function is given by polynomial
 * order of "p" and order of approximation is "p" or higher, solution of
 * finite element method is exact (with machine precision).
 *
 *  \f[
 *  u = 1+x^2+y^2+z^3
 *  \f]
 *
 */
struct ExactFunction {
  double operator()(const double x, const double y, const double z) const {
    return 1 + x * x + y * y + z * z * z;
  }
};
 
/**
 * \brief Exact gradient
 */
struct ExactFunctionGrad {
  FTensor::Tensor1<double, 3> operator()(const double x, const double y,
                                         const double z) const {
    FTensor::Tensor1<double, 3> grad;
    grad(0) = 2 * x;
    grad(1) = 2 * y;
    grad(2) = 3 * z * z;
    return grad;
  }
};
 
/**
 * \brief Laplacian of function.
 *
 * This is Laplacian of \f$u\f$, it is calculated using formula
 * \f[
 * \nabla^2 u(x,y,z) = \nabla \cdot \nabla u
 * \frac{\partial^2 u}{\partial x^2}+
 * \frac{\partial^2 u}{\partial y^2}+
 * \frac{\partial^2 u}{\partial z^2}
 * \f]
 *
 */
struct ExactLaplacianFunction {
  double operator()(const double x, const double y, const double z) const {
    return 4 + 6 * z;
  }
};
 
int main(int argc, char *argv[]) {
 
  // Initialize PETSc
  MoFEM::Core::Initialize(&argc,&argv,(char *)0,help);
 
  try {
 
    // Create MoAB database
    moab::Core moab_core;              // create database
    moab::Interface &moab = moab_core; // create interface to database
 
    // Get command line options
    int order          = 3;           // default approximation order
    PetscBool flg_test = PETSC_FALSE; // true check if error is numerical error
    CHKERR PetscOptionsBegin(PETSC_COMM_WORLD, "", "Poisson's problem options",
                             "none");
    // Set approximation order
    CHKERR PetscOptionsInt("-order", "approximation order", "", order, &order,
                           PETSC_NULL);
    // Set testing (used by CTest)
    CHKERR PetscOptionsBool("-test", "if true is ctest", "", flg_test,
                            &flg_test, PETSC_NULL);
    ierr = PetscOptionsEnd();
    CHKERRG(ierr);
 
    // Create MoFEM database and link it to MoAB
    MoFEM::Core mofem_core(moab);           // create database
    MoFEM::Interface &m_field = mofem_core; // create interface to database
    // Register DM Manager
    CHKERR DMRegister_MoFEM("DMMOFEM"); // register MoFEM DM in PETSc
 
    // Create vector to store approximation global error
    Vec global_error;
    CHKERR PoissonExample::AuxFunctions(m_field).createGhostVec(&global_error);
 
    // First we crate elements, implementation of elements is problem independent,
    // we do not know yet what fields are present in the problem, or
    // even we do not decided yet what approximation base or spaces we
    // are going to use. Implementation of element is free from
    // those constrains and can be used in different context.
 
    // Elements used by KSP & DM to assemble system of equations
    boost::shared_ptr<ForcesAndSourcesCore> domain_lhs_fe;     ///< Volume element for the matrix
    boost::shared_ptr<ForcesAndSourcesCore> boundary_lhs_fe;   ///< Boundary element for the matrix
    boost::shared_ptr<ForcesAndSourcesCore> domain_rhs_fe;     ///< Volume element to assemble vector
    boost::shared_ptr<ForcesAndSourcesCore> boundary_rhs_fe;   ///< Volume element to assemble vector
    boost::shared_ptr<ForcesAndSourcesCore> domain_error;      ///< Volume element evaluate error
    boost::shared_ptr<PoissonExample::PostProcFE>
        post_proc_volume; ///< Volume element to Post-process results
    boost::shared_ptr<ForcesAndSourcesCore> null;              ///< Null element do nothing
    {
      // Add problem specific operators the generic finite elements to calculate matrices and vectors.
      CHKERR PoissonExample::CreateFiniteElements(m_field)
          .createFEToAssembleMatrixAndVector(
              ExactFunction(), ExactLaplacianFunction(), domain_lhs_fe,
              boundary_lhs_fe, domain_rhs_fe, boundary_rhs_fe);
      // Add problem specific operators the generic finite elements to calculate error on elements and global error
      // in H1 norm
      CHKERR PoissonExample::CreateFiniteElements(m_field)
          .createFEToEvaluateError(ExactFunction(), ExactFunctionGrad(),
                                   global_error, domain_error);
      // Post-process results
      CHKERR PoissonExample::CreateFiniteElements(m_field)
          .creatFEToPostProcessResults(post_proc_volume);
    }
 
    // Get simple interface is simplified version enabling quick and
    // easy construction of problem.
    Simple *simple_interface;
    // Query interface and get pointer to Simple interface
    CHKERR m_field.getInterface(simple_interface);
 
    // Build problem with simple interface
    {
 
      // Get options for simple interface from command line
      CHKERR simple_interface->getOptions();
      // Load mesh file to database
      CHKERR simple_interface->loadFile(); 
 
      // Add field on domain and boundary. Field is declared by space and base and rank. space
      // can be H1. Hcurl, Hdiv and L2, base can be AINSWORTH_LEGENDRE_BASE, DEMKOWICZ_JACOBI_BASE and more,
      // where rank is number of coefficients for dof.
      //
      // Simple interface assumes that there are four types of field; 1) defined
      // on body domain, 2) fields defined on body boundary, 3) skeleton field defined
      // on finite element skeleton. Finally data field is defined on body domain. Data field
      // is not solved but used for post-process or to keep material parameters, etc. Here
      // we using it to calculate approximation error on elements.
 
      // Add domain filed "U" in space H1 and Legendre base, Ainsworth recipe is used
      // to construct base functions.
      CHKERR simple_interface->addDomainField("U",H1,AINSWORTH_LEGENDRE_BASE,1); 
      // Add Lagrange multiplier field on body boundary
      CHKERR simple_interface->addBoundaryField("L",H1,AINSWORTH_LEGENDRE_BASE,1); 
      // Add error (data) field, we need only L2 norm. Later order is set to 0, so this
      // is piecewise discontinuous constant approx., i.e. 1 DOF for element. You can use
      // more DOFs and collate moments of error to drive anisotropic h/p-adaptivity, however
      // this is beyond this example.
      CHKERR simple_interface->addDataField("ERROR",L2,AINSWORTH_LEGENDRE_BASE,1); 
 
      // Set fields order domain and boundary fields.
      CHKERR simple_interface->setFieldOrder("U",order);  // to approximate function
      CHKERR simple_interface->setFieldOrder("L",order);  // to Lagrange multipliers
      CHKERR simple_interface->setFieldOrder("ERROR",0);  // approximation order for error
 
      // Setup problem. At that point database is constructed, i.e. fields, finite elements and
      // problem data structures with local and global indexing.
      CHKERR simple_interface->setUp(); 
 
    }
 
    // Get access to PETSC-MoFEM DM manager.
    // or more derails see <http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/DM/index.html>
    // Form that point internal MoFEM data structures are linked with PETSc interface. If
    // DM functions contains string MoFEM is is MoFEM specific DM interface function,
    // otherwise DM function part of standard PETSc interface.
 
    DM dm;
    // Get dm
    CHKERR simple_interface->getDM(&dm); 
 
    // Set KSP context for DM. At that point only elements are added to DM operators.
    // Calculations of matrices and vectors is executed by KSP solver. This part
    // of the code makes connection between implementation of finite elements and
    // data operators with finite element declarations in DM manager. From that
    // point DM takes responsibility for executing elements, calculations of
    // matrices and vectors, and solution of the problem.
    {
      // Set operators for KSP solver
      CHKERR DMMoFEMKSPSetComputeOperators(
          dm, simple_interface->getDomainFEName(), domain_lhs_fe, null, null);
      CHKERR DMMoFEMKSPSetComputeOperators(
          dm, simple_interface->getBoundaryFEName(), boundary_lhs_fe, null,
          null);
      // Set calculation of the right hand side vector for KSP solver
      CHKERR DMMoFEMKSPSetComputeRHS(dm, simple_interface->getDomainFEName(),
                                     domain_rhs_fe, null, null);
      CHKERR DMMoFEMKSPSetComputeRHS(dm, simple_interface->getBoundaryFEName(),
                                     boundary_rhs_fe, null, null);
    }
 
    // Solve problem, only PETEc interface here.
    {
 
      // Create the right hand side vector and vector of unknowns
      Vec F,D;
      CHKERR DMCreateGlobalVector(dm,&F); 
      // Create unknown vector by creating duplicate copy of F vector. only
      // structure is duplicated no values.
      CHKERR VecDuplicate(F,&D); 
 
      // Create solver and link it to DM
      KSP solver;
      CHKERR KSPCreate(PETSC_COMM_WORLD,&solver); 
      CHKERR KSPSetFromOptions(solver); 
      CHKERR KSPSetDM(solver,dm); 
      // Set-up solver, is type of solver and pre-conditioners
      CHKERR KSPSetUp(solver); 
      // At solution process, KSP solver using DM creates matrices, Calculate
      // values of the left hand side and the right hand side vector. then
      // solves system of equations. Results are stored in vector D.
      CHKERR KSPSolve(solver,F,D); 
 
      // Scatter solution on the mesh. Stores unknown vector on field on the mesh.
      CHKERR DMoFEMMeshToGlobalVector(dm,D,INSERT_VALUES,SCATTER_REVERSE); 
 
      // Clean data. Solver and vector are not needed any more.
      CHKERR KSPDestroy(&solver); 
      CHKERR VecDestroy(&D); 
      CHKERR VecDestroy(&F); 
    }
 
    // Calculate error
    {
      // Loop over all elements in mesh, and run users operators on each element.
      CHKERR DMoFEMLoopFiniteElements(dm, simple_interface->getDomainFEName(),
                                      domain_error);
      CHKERR PoissonExample::AuxFunctions(m_field).assembleGhostVector(
          global_error);
      CHKERR PoissonExample::AuxFunctions(m_field).printError(global_error);
      if (flg_test == PETSC_TRUE) {
        CHKERR PoissonExample::AuxFunctions(m_field).testError(global_error); 
      }
    }
 
    {
      // Loop over all elements in the mesh and for each execute post_proc_volume
      // element and operators on it.
      CHKERR DMoFEMLoopFiniteElements(dm, simple_interface->getDomainFEName(),
                                      post_proc_volume);
      // Write results
      post_proc_volume->writeFile("out_vol.h5m");
    }
 
    // Destroy DM, no longer needed.
    CHKERR DMDestroy(&dm); 
 
    // Destroy ghost vector
    CHKERR VecDestroy(&global_error);
  }
  CATCH_ERRORS;
 
  // finish work cleaning memory, getting statistics, etc.
  MoFEM::Core::Finalize(); 
 
  return 0;
 
}