MFEM
v4.6.0
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 
virtual void  TransformPrimal (const Array< int > &face_orientation, double *v) const =0 
void  TransformPrimal (const Array< int > &face_orientation, Vector &v) const 
virtual void  InvTransformPrimal (const Array< int > &face_orientation, double *v) const =0 
void  InvTransformPrimal (const Array< int > &face_orientation, Vector &v) const 
virtual void  TransformDual (const Array< int > &face_orientation, double *v) const =0 
void  TransformDual (const Array< int > &face_orientation, Vector &v) const 
virtual void  InvTransformDual (const Array< int > &face_orientation, double *v) const =0 
void  InvTransformDual (const Array< int > &face_orientation, Vector &v) const 
Protected Member Functions  
StatelessDofTransformation (int size)  
Protected Attributes  
int  size_ 
The StatelessDofTransformation 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.
In this context "stateless" means that the concrete classes derived from StatelessDofTransformation do not store information about the relative orientations of the faces with respect to their neighboring elements. In other words there is no information specific to a particular element (aside from the element type e.g. tetrahedron, wedge, or pyramid). The StatelessDofTransformation provides access to the transformation operators for specific relative face orientations. These are useful, for example, when relating DoFs associated with distinct overlapping meshes such as parent and submeshes.
These transformations are necessary to ensure that basis functions in neighboring (or overlapping) elements align correctly. Closely related but complementary transformations are required for the entries stored in LinearForm and BilinearForm objects. The StatelessDofTransformation 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 68 of file doftrans.hpp.

inlineprotected 
Definition at line 73 of file doftrans.hpp.

inline 
Definition at line 78 of file doftrans.hpp.

pure virtual 
Inverse Transform dual DoFs
Implemented in mfem::ND_StatelessDofTransformation, and mfem::StatelessVDofTransformation.

inline 
Definition at line 115 of file doftrans.hpp.

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_StatelessDofTransformation, and mfem::StatelessVDofTransformation.

inline 
Definition at line 100 of file doftrans.hpp.

inline 
Definition at line 81 of file doftrans.hpp.

inline 
Definition at line 79 of file doftrans.hpp.

inline 
Definition at line 77 of file doftrans.hpp.

pure virtual 
Transform dual DoFs as computed by a LinearFormIntegrator before summing into a LinearForm object.
Implemented in mfem::ND_StatelessDofTransformation, and mfem::StatelessVDofTransformation.

inline 
Definition at line 108 of file doftrans.hpp.

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_StatelessDofTransformation, and mfem::StatelessVDofTransformation.

inline 
Definition at line 89 of file doftrans.hpp.

inline 
Definition at line 80 of file doftrans.hpp.

protected 
Definition at line 71 of file doftrans.hpp.