MFEM  v4.3.0 Finite element discretization library
mfem::L2ProjectionGridTransfer Class Reference

Transfer data in L2 and H1 finite element spaces between a coarse mesh and an embedded refined mesh using L2 projection. More...

#include <transfer.hpp>

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## Classes

class  L2Projection

class  L2ProjectionH1Space

class  L2ProjectionL2Space

class  L2Prolongation

## Public Member Functions

L2ProjectionGridTransfer (FiniteElementSpace &coarse_fes_, FiniteElementSpace &fine_fes_, bool force_l2_space_=false)

virtual ~L2ProjectionGridTransfer ()

virtual const OperatorForwardOperator ()
Return an Operator that transfers GridFunctions from the domain FE space to GridFunctions in the range FE space. More...

virtual const OperatorBackwardOperator ()
Return an Operator that transfers GridFunctions from the range FE space back to GridFunctions in the domain FE space. More...

Public Member Functions inherited from mfem::GridTransfer
GridTransfer (FiniteElementSpace &dom_fes_, FiniteElementSpace &ran_fes_)

virtual ~GridTransfer ()
Virtual destructor. More...

void SetOperatorType (Operator::Type type)
Set the desired Operator::Type for the construction of all operators defined by the underlying transfer algorithm. More...

virtual const OperatorTrueForwardOperator ()
Return an Operator that transfers true-dof Vectors from the domain FE space to true-dof Vectors in the range FE space. More...

virtual const OperatorTrueBackwardOperator ()
Return an Operator that transfers true-dof Vectors from the range FE space back to true-dof Vectors in the domain FE space. More...

## Protected Attributes

L2ProjectionF
Forward, coarse-to-fine, operator. More...

L2ProlongationB
Backward, fine-to-coarse, operator. More...

bool force_l2_space

Protected Attributes inherited from mfem::GridTransfer
FiniteElementSpacedom_fes
Domain FE space. More...

FiniteElementSpaceran_fes
Range FE space. More...

Operator::Type oper_type
Desired Operator::Type for the construction of all operators defined by the underlying transfer algorithm. It can be ignored by derived classes. More...

OperatorHandle fw_t_oper
Forward true-dof operator. More...

OperatorHandle bw_t_oper
Backward true-dof operator. More...

bool parallel

Protected Member Functions inherited from mfem::GridTransfer
bool Parallel () const

const OperatorMakeTrueOperator (FiniteElementSpace &fes_in, FiniteElementSpace &fes_out, const Operator &oper, OperatorHandle &t_oper)

## Detailed Description

Transfer data in L2 and H1 finite element spaces between a coarse mesh and an embedded refined mesh using L2 projection.

The forward, coarse-to-fine, transfer uses L2 projection. The backward, fine-to-coarse, transfer is defined as B = (F^t M_f F)^{-1} F^t M_f, where F is the forward transfer matrix, and M_f is the mass matrix on the coarse element. For L2 spaces, M_f is the mass matrix on the union of all fine elements comprising the coarse element. For H1 spaces, M_f is a diagonal (lumped) mass matrix computed through row-summation. Note that the backward transfer operator, B, is a left inverse of the forward transfer operator, F, i.e. B F = I. Both F and B are defined in physical space and, generally for L2 spaces, vary between different mesh elements.

This class supports H1 and L2 finite element spaces. Fine meshes are a uniform refinement of the coarse mesh, usually created through Mesh::MakeRefined. Generally, the coarse and fine FE spaces can have different orders, however, in order for the backward operator to be well-defined, the number of fine dofs (in a coarse element) should not be smaller than the number of coarse dofs.

Definition at line 168 of file transfer.hpp.

## Constructor & Destructor Documentation

 mfem::L2ProjectionGridTransfer::L2ProjectionGridTransfer ( FiniteElementSpace & coarse_fes_, FiniteElementSpace & fine_fes_, bool force_l2_space_ = false )
inline

Definition at line 338 of file transfer.hpp.

 mfem::L2ProjectionGridTransfer::~L2ProjectionGridTransfer ( )
virtual

Definition at line 865 of file transfer.cpp.

## Member Function Documentation

 const Operator & mfem::L2ProjectionGridTransfer::BackwardOperator ( )
virtual

Return an Operator that transfers GridFunctions from the range FE space back to GridFunctions in the domain FE space.

Implements mfem::GridTransfer.

Definition at line 877 of file transfer.cpp.

 const Operator & mfem::L2ProjectionGridTransfer::ForwardOperator ( )
virtual

Return an Operator that transfers GridFunctions from the domain FE space to GridFunctions in the range FE space.

Implements mfem::GridTransfer.

Definition at line 871 of file transfer.cpp.

## Member Data Documentation

 L2Prolongation* mfem::L2ProjectionGridTransfer::B
protected

Backward, fine-to-coarse, operator.

Definition at line 334 of file transfer.hpp.

 L2Projection* mfem::L2ProjectionGridTransfer::F
protected

Forward, coarse-to-fine, operator.

Definition at line 333 of file transfer.hpp.

 bool mfem::L2ProjectionGridTransfer::force_l2_space
protected

Definition at line 335 of file transfer.hpp.

The documentation for this class was generated from the following files: