MFEM
v4.5.2
Finite element discretization library

#include <doftrans.hpp>
Public Member Functions  
int  Size () const 
int  Height () const 
int  NumRows () const 
int  Width () const 
int  NumCols () const 
void  SetFaceOrientations (const Array< int > &face_orientation) 
Configure the transformation using face orientations for the current element. More...  
const Array< int > &  GetFaceOrientations () const 
virtual void  TransformPrimal (double *v) const =0 
virtual void  TransformPrimal (Vector &v) const 
virtual void  TransformPrimalCols (DenseMatrix &V) const 
Transform groups of DoFs stored as dense matrices. More...  
virtual void  InvTransformPrimal (double *v) const =0 
virtual void  InvTransformPrimal (Vector &v) const 
virtual void  TransformDual (double *v) const =0 
virtual void  TransformDual (Vector &v) const 
virtual void  InvTransformDual (double *v) const =0 
virtual void  InvTransformDual (Vector &v) const 
virtual void  TransformDual (DenseMatrix &V) const 
virtual void  TransformDualRows (DenseMatrix &V) const 
Transform groups of dual DoFs stored as dense matrices. More...  
virtual void  TransformDualCols (DenseMatrix &V) const 
virtual  ~DofTransformation () 
Protected Member Functions  
DofTransformation (int size)  
Protected Attributes  
int  size_ 
Array< int >  Fo 
The DofTransformation class is an abstract base class for a family of transformations that map local degrees of freedom (DoFs), contained within individual elements, to global degrees of freedom, stored within GridFunction objects. These transformations are necessary to ensure that basis functions in neighboring elements align correctly. Closely related but complementary transformations are required for the entries stored in LinearForm and BilinearForm objects. The DofTransformation class is designed to apply the action of both of these types of DoF transformations.
Let the "primal transformation" be given by the operator T. This means that given a local element vector v the data that must be placed into a GridFunction object is v_t = T * v.
We also need the inverse of the primal transformation T^{1} so that we can recover the local element vector from data read out of a GridFunction e.g. v = T^{1} * v_t.
We need to preserve the action of our linear forms applied to primal vectors. In other words, if f is the local vector computed by a linear form then f * v = f_t * v_t (where "*" represents an inner product of vectors). This requires that f_t = T^{T} * f i.e. the "dual transform" is given by the transpose of the inverse of the primal transformation.
For bilinear forms we require that v^T * A * v = v_t^T * A_t * v_t. This implies that A_t = T^{T} * A * T^{1}. This can be accomplished by performing dual transformations of the rows and columns of the matrix A.
For discrete linear operators the range must be modified with the primal transformation rather than the dual transformation because the result is a primal vector rather than a dual vector. This leads to the transformation D_t = T * D * T^{1}. This can be accomplished by using a primal transformation on the columns of D and a dual transformation on its rows.
Definition at line 56 of file doftrans.hpp.

inlineprotected 
Definition at line 63 of file doftrans.hpp.

inlinevirtual 
Definition at line 117 of file doftrans.hpp.

inline 
Definition at line 80 of file doftrans.hpp.

inline 
Definition at line 69 of file doftrans.hpp.

pure virtual 
Inverse Transform dual DoFs
Implemented in mfem::ND_WedgeDofTransformation, mfem::ND_TetDofTransformation, mfem::ND_TriDofTransformation, and mfem::VDofTransformation.

virtual 
Definition at line 88 of file doftrans.cpp.

pure virtual 
Inverse transform local DoFs. Used to transform DoFs from a global vector back to their elementlocal form. For example, this must be used to transform the vector obtained using GridFunction::GetSubVector before it can be used to compute a local interpolation.
Implemented in mfem::ND_WedgeDofTransformation, mfem::ND_TetDofTransformation, mfem::ND_TriDofTransformation, and mfem::VDofTransformation.

virtual 
Definition at line 60 of file doftrans.cpp.

inline 
Definition at line 72 of file doftrans.hpp.

inline 
Definition at line 70 of file doftrans.hpp.

inline 
Configure the transformation using face orientations for the current element.
The face_orientation array can be obtained from Mesh::GetElementFaces.
Definition at line 77 of file doftrans.hpp.

inline 
Definition at line 68 of file doftrans.hpp.

pure virtual 
Transform dual DoFs as computed by a LinearFormIntegrator before summing into a LinearForm object.
Implemented in mfem::ND_WedgeDofTransformation, mfem::ND_TetDofTransformation, mfem::ND_TriDofTransformation, and mfem::VDofTransformation.

virtual 
Definition at line 30 of file doftrans.cpp.

virtual 
Transform a matrix of dual DoFs entries as computed by a BilinearFormIntegrator before summing into a BilinearForm object.
Definition at line 35 of file doftrans.cpp.

virtual 
Definition at line 52 of file doftrans.cpp.

virtual 
Transform groups of dual DoFs stored as dense matrices.
Definition at line 41 of file doftrans.cpp.

pure virtual 
Transform local DoFs to align with the global DoFs. For example, this transformation can be used to map the local vector computed by FiniteElement::Project() to the transformed vector stored within a GridFunction object.
Implemented in mfem::ND_WedgeDofTransformation, mfem::ND_TetDofTransformation, mfem::ND_TriDofTransformation, and mfem::VDofTransformation.

virtual 
Definition at line 17 of file doftrans.cpp.

virtual 
Transform groups of DoFs stored as dense matrices.
Definition at line 22 of file doftrans.cpp.

inline 
Definition at line 71 of file doftrans.hpp.

protected 
Definition at line 61 of file doftrans.hpp.

protected 
Definition at line 59 of file doftrans.hpp.