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

#include <element.hh>

Inheritance 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`. More...

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. More...

uint	m () const
	Returns the number of rows. More...

uint	n () const
	Returns the number of columns. More...

virtual void	operator() (const ElementMatrix< F > &A, ElementMatrix< F > &B) const =0
	Application operator. More...

virtual void	operator() (const ElementMatrix<::std::complex< F > > &A, ElementMatrix<::std::complex< F > > &B) const =0

void	setM (uint m)

	TMatrixBase (const uint m, const uint n)
	Constructor. More...

	TMatrixBase (const uint n)
	Constructor. More...

virtual void	usedIdx (TColumn< bool > &c) const =0
	Marks the used local indices in `c` with `true`, the local indices which are not set to `false`. More...

virtual	~TMatrixBase ()

Protected Member Functions
virtual ::std::ostream &	info (::std::ostream &os) const

Protected Attributes
uint	m_
	Number of rows. More...

uint	n_
	Number of columns. More...

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 be the number of local shape functions $\{\phi_j^K\}_{j=1}^{m_K}$ in the element and 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 describes how the restriction of the global basis functions $\{\Phi_i\}_{i=1}^N$ onto the element 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 37 of file element.hh.

Constructor & Destructor Documentation

◆ TMatrixBase() [1/2]

template<class F >

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

Constructor.

Sets the number of rows to zero.

Parameters

n	Number of columns

◆ TMatrixBase() [2/2]

template<class F >

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

Constructor.

Parameters

m	Number of rows
n	Number of columns

◆ ~TMatrixBase()

template<class F >

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

virtual

Member Function Documentation

◆ extract() [1/2]

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

◆ extract() [2/2]

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 >, and concepts::TIndex< concepts::Real >.

◆ index()

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 >, and concepts::TIndex< concepts::Real >.

◆ info()

template<class F >

virtual ::std::ostream& concepts::TMatrixBase< F >::info ( ::std::ostream & os ) const

protected

◆ m()

template<class F >

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

inline

Returns the number of rows.

Definition at line 388 of file tmatrix.hh.

◆ n()

template<class F >

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

inline

Returns the number of columns.

Definition at line 393 of file tmatrix.hh.

◆ operator()() [1/2]

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

◆ operator()() [2/2]

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 >, and concepts::TIndex< concepts::Real >.

◆ setM()

template<class F >

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

inline

Definition at line 390 of file tmatrix.hh.

◆ usedIdx()

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 local indices which are not set to false.

Precondition: c has the correct size

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

Member Data Documentation

◆ m_

template<class F >

uint concepts::TMatrixBase< F >::m_

protected

Number of rows.

Definition at line 420 of file tmatrix.hh.

◆ n_

template<class F >

uint concepts::TMatrixBase< F >::n_

protected

Number of columns.

Definition at line 418 of file tmatrix.hh.

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

space/element.hh
space/tmatrix.hh

concepts::TMatrixBase< F > Class Template ReferenceabstractElements and Space | Bilinear and Linear Forms &ndash; Matrices and Vectors

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

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

Constructor & Destructor Documentation

◆ TMatrixBase() [1/2]

◆ TMatrixBase() [2/2]

◆ ~TMatrixBase()

Member Function Documentation

◆ extract() [1/2]

◆ extract() [2/2]

◆ index()

◆ info()

◆ m()

◆ n()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ setM()

◆ usedIdx()

Member Data Documentation

◆ m_

◆ n_

concepts::TMatrixBase< F > Class Template Referenceabstract
Elements and Space | Bilinear and Linear Forms – Matrices and Vectors

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