An abstract class for a T matrix. More...

#include <tmatrix.hh>

Inheritance diagram for concepts::TMatrixBase< F >:

Collaboration diagram for concepts::TMatrixBase< F >:

Public Member Functions
virtual void	extract (const concepts::Vector< F > &solution, concepts::Array< F > &coeff) const =0
	Extracts the part of `solution` belonging to this T matrix into `coeff`.
virtual void	extract (const concepts::Vector< std::complex< F > > &solution, concepts::Array< std::complex< F > > &coeff) const =0
virtual uint	index (const uint i) const =0
	Maps the local index i to the global index.
uint	m () const
	Returns the number of rows.
uint	n () const
	Returns the number of columns.
virtual void	operator() (const ElementMatrix< F > &A, ElementMatrix< F > &B) const =0
	Application operator.
virtual void	operator() (const ElementMatrix< std::complex< F > > &A, ElementMatrix< std::complex< F > > &B) const =0
void	setM (uint m)
	TMatrixBase (const uint n)
	Constructor.
virtual void	usedIdx (TColumn< bool > &c) const =0
	Marks the used local indices in `c` with `true`, the indices which are set to `false`.
virtual	~TMatrixBase ()
Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Protected Attributes
uint	m_
	Number of rows.
uint	n_
	Number of columns.

Detailed Description

template<class F>
class concepts::TMatrixBase< F >

An abstract class for a T matrix.

A T matrix describes the mapping of local degrees of freedom to global degrees of freedom.

A T matrix describes how the local shape functions are glued together to form to global (continuous) shape functions. It contains the informatin how an element matrix is assembled into the global matrix. It is defined as follows:
Let $m_K$ be the number of local shape functions $\{\phi_j^K\}_{j=1}^{m_K}$ in the element $K$ and $N$ the number of global basis functions $\{\Phi_i\}_{i=1}^N$ . The T matrix $T_K \in R^{m_K \times N}$ of the element $K$ describes how the restriction of the global basis functions $\{\Phi_i\}_{i=1}^N$ onto the element $K$ are constructed from the local shape functions:

$\Phi_i|_{K} = \sum_{j=1}^{m_K} [T_K]_{ji} \phi_j^K$

and in vector notation: $\vec \Phi|_{K} = T_K^\top \vec \phi^K$ .

Definition at line 340 of file tmatrix.hh.

Constructor & Destructor Documentation

template<class F>

concepts::TMatrixBase< F >::TMatrixBase ( const uint n )

Constructor.

Sets the number of rows to zero.

Parameters:

n	Number of columns

template<class F>

virtual concepts::TMatrixBase< F >::~TMatrixBase ( ) [virtual]

Member Function Documentation

template<class F>

virtual void concepts::TMatrixBase< F >::extract	(	const concepts::Vector< F > &	solution,
		concepts::Array< F > &	coeff
	)		const `[pure virtual]`

Extracts the part of solution belonging to this T matrix into coeff.

coeff is resized and zeroed before filling it with the coefficients.

Parameters:

solution	Vector in the global space (input)
coeff	Local coefficients of this T matrix (output)

Implemented in concepts::TIndex< F >, concepts::TMatrix< F >, vectorial::TMatrixOffset< F >, vectorial::TMatrix< F >, concepts::TMatrix< Real >, and vectorial::TMatrix< Real >.

template<class F>

virtual void concepts::TMatrixBase< F >::extract	(	const concepts::Vector< std::complex< F > > &	solution,
		concepts::Array< std::complex< F > > &	coeff
	)		const `[pure virtual]`

Implemented in concepts::TIndex< F >, concepts::TMatrix< F >, vectorial::TMatrixOffset< F >, vectorial::TMatrix< F >, concepts::TMatrix< Real >, and vectorial::TMatrix< Real >.

template<class F>

virtual uint concepts::TMatrixBase< F >::index ( const uint i ) const [pure virtual]

Maps the local index i to the global index.

Implemented in concepts::TIndex< F >, concepts::TMatrix< F >, and concepts::TMatrix< Real >.

template<class F>

virtual std::ostream& concepts::TMatrixBase< F >::info ( std::ostream & os ) const [protected, virtual]

Returns information in an output stream.

Reimplemented from concepts::OutputOperator.

Reimplemented in concepts::TIndex< F >, concepts::TMatrix< F >, vectorial::TMatrixOffset< F >, vectorial::TMatrix< F >, concepts::TMatrix< Real >, vectorial::TMatrixOffset< Real >, and vectorial::TMatrix< Real >.

template<class F>

uint concepts::TMatrixBase< F >::m ( ) const [inline]

Returns the number of rows.

Reimplemented in vectorial::TMatrixOffset< F >, and vectorial::TMatrixOffset< Real >.

Definition at line 374 of file tmatrix.hh.

template<class F>

uint concepts::TMatrixBase< F >::n ( ) const [inline]

Returns the number of columns.

Reimplemented in vectorial::TMatrixOffset< F >, and vectorial::TMatrixOffset< Real >.

Definition at line 379 of file tmatrix.hh.

template<class F>

virtual void concepts::TMatrixBase< F >::operator()	(	const ElementMatrix< std::complex< F > > &	A,
		ElementMatrix< std::complex< F > > &	B
	)		const `[pure virtual]`

Implemented in concepts::TIndex< F >, concepts::TMatrix< F >, vectorial::TMatrixOffset< F >, vectorial::TMatrix< F >, concepts::TMatrix< Real >, and vectorial::TMatrix< Real >.

template<class F>

virtual void concepts::TMatrixBase< F >::operator()	(	const ElementMatrix< F > &	A,
		ElementMatrix< F > &	B
	)		const `[pure virtual]`

Application operator.

Computes the application of the T matrix on A and returns B: $B = A \cdot T$ . Typical usage: assembling the element matrices. The element matrix A is transformed using

$((AT)^\top \cdot T)^\top = T^\top A T$

and then simply added entry by entry into the global matrix. This is the case for element matrices which have the same "left" and "right" T matrix. Otherwise, this looks like

$((A T_y)^\top \cdot T_x)^\top = T_x^\top A T_y.$

Parameters:

A	Element matrix
B	Result

Implemented in concepts::TIndex< F >, concepts::TMatrix< F >, vectorial::TMatrixOffset< F >, vectorial::TMatrix< F >, concepts::TMatrix< Real >, and vectorial::TMatrix< Real >.

template<class F>

void concepts::TMatrixBase< F >::setM ( uint m ) [inline]

Definition at line 376 of file tmatrix.hh.

template<class F>

virtual void concepts::TMatrixBase< F >::usedIdx ( TColumn< bool > & c ) const [pure virtual]

Marks the used local indices in c with true, the indices which are set to false.

Precondition:: c has the correct size

Implemented in concepts::TIndex< F >, concepts::TMatrix< F >, vectorial::TMatrixOffset< F >, vectorial::TMatrix< F >, concepts::TMatrix< Real >, vectorial::TMatrixOffset< Real >, and vectorial::TMatrix< Real >.

Member Data Documentation

template<class F>

uint concepts::TMatrixBase< F >::m_ [protected]

Number of rows.

Definition at line 405 of file tmatrix.hh.

template<class F>

uint concepts::TMatrixBase< F >::n_ [protected]

Number of columns.

Definition at line 403 of file tmatrix.hh.

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

space/tmatrix.hh

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

template<class F> class concepts::TMatrixBase< F >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class F>
class concepts::TMatrixBase< F >