An abstract class for an S matrix. More...

#include <smatrix.hh>

Inheritance diagram for concepts::SMatrixBase< F >:

Collaboration diagram for concepts::SMatrixBase< F >:

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.