MFEM  v4.1.0 Finite element discretization library
mfem::L2ProjectionGridTransfer Class Reference

Transfer data between a coarse mesh and an embedded refined mesh using L2 projection. More...

#include <fespace.hpp>

Inheritance diagram for mfem::L2ProjectionGridTransfer:
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Collaboration diagram for mfem::L2ProjectionGridTransfer:
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## Classes

class  L2Projection

class  L2Prolongation

## Public Member Functions

L2ProjectionGridTransfer (FiniteElementSpace &coarse_fes, FiniteElementSpace &fine_fes)

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...

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 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 locally (on a coarse element) 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 union of all fine elements comprising the coarse element. 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, vary between different mesh elements.

This class currently only fully supports L2 finite element spaces and fine meshes that are a uniform refinement of the coarse mesh. 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 the fine dofs (in a coarse element) should not be smaller than the number of coarse dofs.

If used on H1 finite element spaces, the transfer will be performed locally, and the value of shared (interface) degrees of freedom will be determined by the value of the last transfer to be performed (according to the element numbering in the finite element space). As a consequence, the mass conservation properties for this operator from the L2 case do not carry over to H1 spaces.

Definition at line 859 of file fespace.hpp.

## Constructor & Destructor Documentation

 mfem::L2ProjectionGridTransfer::L2ProjectionGridTransfer ( FiniteElementSpace & coarse_fes, FiniteElementSpace & fine_fes )
inline

Definition at line 908 of file fespace.hpp.

## 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 2745 of file fespace.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 2739 of file fespace.cpp.

## Member Data Documentation

 L2Prolongation* mfem::L2ProjectionGridTransfer::B
protected

Backward, fine-to-coarse, operator.

Definition at line 905 of file fespace.hpp.

 L2Projection* mfem::L2ProjectionGridTransfer::F
protected

Forward, coarse-to-fine, operator.

Definition at line 904 of file fespace.hpp.

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