FormsIntegrators.hpp File Reference

Forms integrators. More...

Go to the source code of this file.

Classes
struct	MoFEM::EssentialBcStorage
	[Storage and set boundary conditions] More...
struct	MoFEM::OpSetBc
	Set indices on entities on finite element. More...
struct	MoFEM::OpUnSetBc
	Unset indices on entities on finite element. More...
struct	MoFEM::AssemblyTypeSelector< A >
	Template selector for assembly type. More...
struct	MoFEM::OpBaseImpl< A, EleOp >
struct	MoFEM::FormsIntegrators< EleOp >
	Integrator forms. More...
struct	MoFEM::FormsIntegrators< EleOp >::Assembly< A >
	Assembly methods. More...

Namespaces
namespace	MoFEM
	implementation of Data Operators for Forces and Sources

Typedefs
using	MoFEM::ScalarFun = boost::function< double(const double, const double, const double)>
	Scalar function type.
using	MoFEM::TimeFun = boost::function< double(double)>
	Lambda function used to scale with time.
using	MoFEM::FEFun = boost::function< double(const FEMethod *fe_ptr)>
	Lambda function used to scale with time.
using	MoFEM::ConstantFun = boost::function< double()>
	Constant function type.
template<int DIM>
using	MoFEM::VectorFun = boost::function< FTensor::Tensor1< double, DIM >(const double, const double, const double)>
	Vector function type.

Enumerations
enum	MoFEM::AssemblyType {   MoFEM::PETSC , MoFEM::SCHUR , MoFEM::BLOCK_MAT , MoFEM::BLOCK_SCHUR ,   MoFEM::BLOCK_PRECONDITIONER_SCHUR , MoFEM::USER_ASSEMBLE , MoFEM::LAST_ASSEMBLE }
	[Storage and set boundary conditions] More...
enum	MoFEM::IntegrationType { MoFEM::GAUSS , MoFEM::USER_INTEGRATION , MoFEM::LAST_INTEGRATION }
	Form integrator integration types. More...

Functions
template<>
MoFEMErrorCode	MoFEM::VecSetValues< EssentialBcStorage > (Vec V, const EntitiesFieldData::EntData &data, const double *ptr, InsertMode iora)
	Set values to vector in operator.
template<>
MoFEMErrorCode	MoFEM::MatSetValues< EssentialBcStorage > (Mat M, const EntitiesFieldData::EntData &row_data, const EntitiesFieldData::EntData &col_data, const double *ptr, InsertMode iora)
	Set values to matrix in operator.
template<>
MoFEMErrorCode	MoFEM::MatSetValues< AssemblyTypeSelector< PETSC > > (Mat M, const EntitiesFieldData::EntData &row_data, const EntitiesFieldData::EntData &col_data, const double *ptr, InsertMode iora)
template<>
MoFEMErrorCode	MoFEM::VecSetValues< AssemblyTypeSelector< PETSC > > (Vec V, const EntitiesFieldData::EntData &data, const double *ptr, InsertMode iora)
double	MoFEM::scalar_fun_one (const double, const double, const double)
	Default scalar function returning 1.

Detailed Description

Forms integrators.

This file provides a higher-level abstraction layer over MoFEM's generic UserDataOperator system for finite element computations. It implements structured approaches to linear and bilinear form integration within finite element operator pipelines.

Forms as Operator Abstractions

Forms integrators represent one level of abstraction above generic user data operators, providing structured interfaces for common finite element operations:

• LinearForm: Operators that integrate over single fields to produce vectors (load vectors, source terms, boundary conditions)
• BiLinearForm: Operators that integrate over field pairs to produce matrices
  (stiffness matrices, mass matrices, coupling terms)
• TriLinearForm: Operators for nonlinear terms involving multiple fields

These forms encapsulate the integration logic while maintaining compatibility with MoFEM's finite element pipeline architecture.

Integration with Finite Element Pipelines

Forms integrators work within MoFEM's operator pipeline system:

1. Finite Element Context: Forms operate within specific finite elements that define geometry, connectivity, and field definitions
2. Operator Sequencing: Forms are added to finite element operator pipelines alongside preprocessing, integration, and postprocessing operators
3. Data Flow: Forms access field data, geometry, and integration points through the standard ForcesAndSourcesCore infrastructure
4. Assembly: Computed local contributions are assembled into global algebraic structures (vectors, matrices)

Assembly Type Abstraction

Assembly types control how local finite element contributions are assembled into global algebraic structures:

• PETSC: Standard assembly into PETSc Vec/Mat objects
• SCHUR: Assembly for Schur complement methods
  
• BLOCK_MAT: Assembly into block-structured matrices
• BLOCK_SCHUR: Block-based Schur complement assembly
• BLOCK_PRECONDITIONER_SCHUR: Specialized preconditioner assembly
• USER_ASSEMBLE: Custom assembly controlled by user functions

Assembly types are compile-time template parameters, enabling optimized code generation for different algebraic backends and solution strategies.

Integration Method Selection

Integration methods determine how numerical integration is performed:

• GAUSS: Gaussian quadrature integration using standard rules
• USER_INTEGRATION: Custom integration schemes defined by user functions

Integration methods are template parameters that work with assembly types to provide flexible, efficient integration strategies for different physics and discretization requirements.

Note: Specialized methods can be introduced for specific cases, such as fast integration exploiting Bernstein–Bézier basis with Duffy transforms on simplex elements, or dedicated GPU backends for element-wise integration and assembly. These can be expressed as additional integration tags and paired with corresponding assembly strategies.

Typical Workflow

1. Select assembly type based on algebraic solution strategy
2. Choose integration method appropriate for physics and accuracy requirements
   
3. Instantiate specific form type (Linear/BiLinear/TriLinear)
4. Configure field operations and boundary conditions
5. Add form operators to finite element pipeline
6. Execute pipeline to assemble global algebraic system

This abstraction enables systematic construction of finite element methods while maintaining performance and flexibility for advanced solution techniques.

Definition in file FormsIntegrators.hpp.