Class documentation of Concepts

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concepts::SMatrixBase< F > Class Template Referenceabstract

#include <smatrix.hh>

Inheritance diagram for concepts::SMatrixBase< F >:
concepts::OutputOperator concepts::SMatrixBlock< F, dim > concepts::SMatrixCompose< F > concepts::SMatrixGeneralTensor< F, dim > concepts::SMatrixTensor< F, dim >

Public Member Functions

virtual void operator() (const TColumn< F > &src, TColumn< F > &dest) const =0
 Application operator.
 
virtual uint size () const =0
 Returns the size of the S matrix.
 

Protected Member Functions

virtual std::ostream & info (std::ostream &os) const
 Returns information in an output stream.
 

Detailed Description

template<class F>
class concepts::SMatrixBase< F >

An abstract class for an S matrix.

An S matrix describes how a T matrix has to be changed to reflect a refinement of an element.

The definition of an S matrix is as follows:
Let $K' \subset K$ be the result of a refinement of element $K$. The S matrix $S_{K'K} \in R^{m_{K'} \times m_K}$ describes how the restriction of the shape functions $\{\phi_j^K\}_{j=1}^{m_K}$ onto $K'$ are constructed from the shape functions $\{\phi_l^{K'}\}_{l=1}^{m_{K'}}$ of $K'$:

\[
  \phi_j^K|_{K'} = \sum_{l=1}^{m_{K'}} [S_{K'K}]_{lj} \phi_l^{K'}
\]

and in vector notation: $\vec \phi^K|_{K'} = S_{K'K}^\top \vec \phi^{K'}.$ In the trivial case $K = K'$ (i. e. no refinement), the S matrix $S_{KK}$ is defined as the identity matrix.

See also
TMatrixBase
TColumn
Author
Philipp Frauenfelder, 2001.

Definition at line 55 of file smatrix.hh.

Member Function Documentation

◆ info()

template<class F >
virtual std::ostream & concepts::SMatrixBase< F >::info ( std::ostream &  os) const
protectedvirtual

◆ operator()()

◆ size()


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