A class representing small KKT systems on a single subdomain. More...

#include <bddc.hh>

Detailed Description

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>
class Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >

A class representing small KKT systems on a single subdomain.

This is intended to work together with BDDCSolver and KKTSolver, and represents subdomains, providing subdomain-local storage and processing capabilities. This is the basis for distributed domain decomposition solvers.

A Subdomain object represents the system

$B = \begin{bmatrix} A & C^T \\ C \end{bmatrix},$

and provides in particular access to the "Schur complement"

$S = \begin{bmatrix} 0 & I \end{bmatrix} \begin{bmatrix} A & C^T \\ C \end{bmatrix}^{-1} \begin{bmatrix} 0 \\ I \end{bmatrix}.$

Since $A$ is only positive semidefinite in general, the true Schur complement $- C A^{-1} C^T$ cannot be formed, but is equal in case of invertible $A$ .

The subdomain holds $A_i$ , $f_i$ , and the constraints block $C$ . It also holds a local solution vector $u_i$ . For the overall picture, we refer to KKTSolver.

Template Parameters

m	the number of vectorial components in $x$ (usually 1 for scalar systems, and 2 or 3 for vectorial ones)
Scalar	the field type $K$ , usually `double`
CoarseScalar	the field type $K_c$ to be used for representing the coarse solver factorization, usually `double`, but could also be `float`
Transfer	a space transfer policy class

Todo:: UMFPACK does not provide float factorization. Extract L and U factors and convert to float?

This is a reference implementation.

Definition at line 179 of file bddc.hh.

Public Types
using	Scalar = Scalar_
	The scalar field type used in coefficients. More...

using	XEntry = Dune::FieldVector< Scalar, components >

using	XVector = Dune::BlockVector< XEntry >

using	Vector = Dune::BlockVector< Dune::FieldVector< Scalar, 1 > >

using	TransmissionType = typename Transfer::TransmissionType
	A container type used for exchanging coefficients between subdomains. More...

using	AMatrix = NumaBCRSMatrix< Dune::FieldMatrix< Scalar, components, components > >

using	SMatrix = DynamicMatrix< Dune::FieldMatrix< Scalar, 1, 1 > >
	A matrix type with scalar entries, used for the Schur complement matrix. More...

Public Member Functions
std::vector< int >	neighbors () const
	Reports a list of its neighbor subdomains. More...

void	updateSolution (Scalar alpha)
	Updates the solution approximation. More...

void	getSolution (XVector &x) const
	Provides the current solution vector $x$ . More...

XVector	getSolution () const
	Provides the current solution vector $x$ . More...

void	set_solver_type (bool cg_solver)
	Set solver type. More...

void	updateIteration (int cg_itr)

void	getCorrection (XVector &dx) const
	Provides the current correction vector $dx$ . More...

void	getRawCorrection (XVector &dx) const

void	getResidual (XVector &rr) const

Vector const &	getRestrictedResidual () const

std::vector< bool >	getActiveSubdomains ()

void	setActiveSubdomains_sub (std::vector< bool > &activeSubdomains_)

Construction.
template<int cComponents>
	Subdomain (int id, AMatrix const &A, Interfaces const &interfaces, NumaBCRSMatrix< Dune::FieldMatrix< Scalar, cComponents, components > > const &C)
	Constructor. More...

template<class Interface >
	Subdomain (int id, AMatrix const &A, Interface const &ifs)

void	imposeDC_inActiveInterface (Vector &Aq, Vector &q)

void	imposeDCq (Vector &q)

void	update_rhs (XVector const &f)
	update rhs for the current subdomain More...

void	getInterfaceAveragingWeights (int s, XVector &rho) const
	Reports own interface averaging weights. More...

void	setInterfaceAveragingWeights (int s, XVector const &rho)
	Accumulates interface weights of adjacent subdomains. More...

Restriction support.
These methods implement the "restriction" of the residual to the "coarse" space. The restriction is defined as the transpose of the prolongation, i.e. $\Pi^T = \pi^T E^T$ with averaging $\pi$ and extension $E$ . The extension operator $E^T$ acts locally, realizing the dual harmonic extension $\begin{bmatrix} r_i \\ r_D \\ \bar r_D \end{bmatrix}_{\rm new} = \begin{bmatrix} I & \\ H^T & \\ -H^T & I \end{bmatrix} \begin{bmatrix} r_i \\ r_D \end{bmatrix}$ working on interior residual $r_i$ , interface residual $r_D$ , and averaged interface residual $\bar r_D$ . Here, $H = A_{ii}^{-1} A_{iD}$ denotes the harmonic extension of interface values into the interior. This local operation is performed by the preRestrict() method. The averaging (for a single degree of freedom shared by $k$ subdomains) is $\pi^T = \frac{1}{k} \begin{bmatrix} 1 & \dots & 1 \\ \vdots & \ddots & \vdots \\ 1 & \dots & 1 \end{bmatrix},$ therefore symmetric, and acts on the interface residual values $r_D$ only. It involves communication between subdomains, exchanging their interface residual $r_D$ , which is realized by the getInterfaceResidual() and setInterfaceResidual() methods. Finally, restrict() must be called as a sentinel to denote the end of communication, and to perform the actual averaging.
void	preRestrict ()
	First step of the restriction: Dirichlet solve. More...

void	getInterfaceResidualUpdate (int s, TransmissionType &dres) const
	Gets interface residual that shall be shared with neighboring subdomain. More...

void	setInterfaceResidualUpdate (int s, TransmissionType const &dres)
	Sets interface residual of the correction from neighboring subdomains. More...

void	restrict ()
	Performs the restriction of the residual vector. More...

Coarse solve support.
These methods implement the subdomain-local parts of the coarse space solver.
void	getS (SMatrix &S) const
	Compute $S$ . More...

void	getSchurResidual (Vector &lambda) const
	Provides the Schur residual. More...

void	setCorrection (Vector const &c)
	Computes the correction vector $[\delta x, \delta\lambda]$ . More...

Prolongation support.
These methods implement the "prolongation" of "coarse" space corrections to the "fine" space. The prolongation is defined as $\Pi = E\pi$ with averaging $\pi$ and extension $E$ . The averaging (for a single degree of freedom shared by $k$ subdomains) is $\pi = \frac{1}{k} \begin{bmatrix} 1 & \dots & 1 \\ \vdots & \ddots & \vdots \\ 1 & \dots & 1 \end{bmatrix}$ and acts on the interface degrees of freedom $x_D$ only. It involves communication between subdomains, exchanging their interface values $x_D$ , which is realized by the getInterfaceValues() and setInterfaceValues() methods. The extension operator $E$ acts locally, realizing the harmonic extension $\begin{bmatrix} x_i \\ x_D \end{bmatrix}_{\rm new} = \begin{bmatrix} I & H & - H \\ & & I \end{bmatrix} \begin{bmatrix} x_i \\ x_D \\ \bar x_D \end{bmatrix}$ working on interior dofs $x_i$ , interface dofs $x_D$ , and averaged interface values $\bar x_D$ . Here, $H = A_{ii}^{-1} A_{iD}$ denotes the harmonic extension of interface values into the interior. This local operation is performed by the prolongate() method.
void	preProlongate ()
	Prepares the exchange of interface values. More...

void	getInterfaceValues (int s, TransmissionType &values) const
	Gets boundary values that shall be shared with neighboring subdomain. More...

void	setInterfaceValues (int s, TransmissionType const &values)
	Sets boundary values of the correction from neighboring subdomains. More...

void	setActiveId (bool active)

Dune::FieldVector< double, 2 >	prolongate ()
	Perform averaging on the shared interfaces, projecting the solution to the subspace of functions continuous across the interfaces. More...

Dune::FieldVector< double, 1 >	updateSearchDirectionNorm ()

void	updateSearchDirection (double beta)
	Update search direction q for cg solver. More...

Static Public Attributes
static const int	components = m
	Number of (vectorial) components of $u$ . More...

Member Typedef Documentation

◆ AMatrix

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

using Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::AMatrix = NumaBCRSMatrix<Dune::FieldMatrix<Scalar,components,components> >

Definition at line 202 of file bddc.hh.

◆ Scalar

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

using Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::Scalar = Scalar_

The scalar field type used in coefficients.

Definition at line 190 of file bddc.hh.

◆ SMatrix

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

using Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::SMatrix = DynamicMatrix<Dune::FieldMatrix<Scalar,1,1> >

A matrix type with scalar entries, used for the Schur complement matrix.

Definition at line 205 of file bddc.hh.

◆ TransmissionType

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

using Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::TransmissionType = typename Transfer::TransmissionType

A container type used for exchanging coefficients between subdomains.

Definition at line 199 of file bddc.hh.

◆ Vector

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

using Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::Vector = Dune::BlockVector<Dune::FieldVector<Scalar,1> >

Definition at line 194 of file bddc.hh.

◆ XEntry

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

using Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::XEntry = Dune::FieldVector<Scalar,components>

Definition at line 192 of file bddc.hh.

◆ XVector

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

using Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::XVector = Dune::BlockVector<XEntry>

Definition at line 193 of file bddc.hh.

Constructor & Destructor Documentation

◆ Subdomain() [1/2]

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

template<int cComponents>

Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::Subdomain	(	int	id,
		AMatrix const &	A,
		Interfaces const &	interfaces,
		NumaBCRSMatrix< Dune::FieldMatrix< Scalar, cComponents, components > > const &	C
	)

Constructor.

This initializes the solution approximation to zero, which implies an admissible state over all subdomains.

Parameters

id	the subdomain number
A	the subdomain-local stiffness matrix
f	the subdomain-local right hand side
interfaces	a list of pairs (s,ids) of neighboring subdomain number and the degrees of freedom shared with this subdomain (in the given order)
C	the constraint matrix

◆ Subdomain() [2/2]

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

template<class Interface >

Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::Subdomain	(	int	id,
		AMatrix const &	A,
		Interface const &	ifs
	)

Member Function Documentation

◆ getActiveSubdomains()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

std::vector< bool > Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::getActiveSubdomains ( )

inline

Definition at line 499 of file bddc.hh.

◆ getCorrection()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::getCorrection ( XVector & dx ) const

Provides the current correction vector $dx$ .

Parameters

[out] dx on exit, contains the current correction

◆ getInterfaceAveragingWeights()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::getInterfaceAveragingWeights	(	int	s,
		XVector &	rho
	)		const

inline

Reports own interface averaging weights.

Parameters

s	number of adjacent subdomain
rho	weights on interface nodes (resized if needed)

Definition at line 248 of file bddc.hh.

◆ getInterfaceResidualUpdate()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::getInterfaceResidualUpdate	(	int	s,
		TransmissionType &	dres
	)		const

inline

Gets interface residual that shall be shared with neighboring subdomain.

Parameters

	s	the number of the neighboring subdomain
[out]	res	the residual vector

Definition at line 321 of file bddc.hh.

◆ getInterfaceValues()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::getInterfaceValues	(	int	s,
		TransmissionType &	values
	)		const

inline

Gets boundary values that shall be shared with neighboring subdomain.

Parameters

s	the number of the neighboring subdomain

Definition at line 425 of file bddc.hh.

◆ getRawCorrection()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::getRawCorrection ( XVector & dx ) const

◆ getResidual()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::getResidual ( XVector & rr ) const

◆ getRestrictedResidual()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

Vector const & Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::getRestrictedResidual ( ) const

inline

Definition at line 496 of file bddc.hh.

◆ getS()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::getS ( SMatrix & S ) const

Compute $S$ .

This computes

$S = \begin{bmatrix} 0 & I \end{bmatrix} \begin{bmatrix} A & C^T \\ C \end{bmatrix}^{-1} \begin{bmatrix} 0 \\ I \end{bmatrix}$

◆ getSchurResidual()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::getSchurResidual ( Vector & lambda ) const

Provides the Schur residual.

This solves the system

$\begin{bmatrix} A & C^T \\ C \end{bmatrix} \begin{bmatrix} x+\delta x \\ \lambda +\delta\lambda \end{bmatrix} = \begin{bmatrix} f\\ 0 \end{bmatrix}$

and returns the solution component $\delta\lambda$ in the provided vector lambda. The vectors $x$ and $\lambda$ are maintained internally as solution approximation.

Parameters

[out] lambda

◆ getSolution() [1/2]

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

XVector Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::getSolution ( ) const

Provides the current solution vector $x$ .

Returns: the current solution approximation

Note that the result is returned by value, which may be less efficient than providing a result vector to be filled.

◆ getSolution() [2/2]

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::getSolution ( XVector & x ) const

Provides the current solution vector $x$ .

Parameters

[out] x on exit, contains the current solution approximation

◆ imposeDC_inActiveInterface()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::imposeDC_inActiveInterface	(	Vector &	Aq,
		Vector &	q
	)

◆ imposeDCq()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::imposeDCq ( Vector & q )

◆ neighbors()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

std::vector< int > Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::neighbors ( ) const

Reports a list of its neighbor subdomains.

◆ preProlongate()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::preProlongate ( )

inline

Prepares the exchange of interface values.

Has to be called before getInterfaceValues() or setInterfaceValues().

Definition at line 416 of file bddc.hh.

◆ preRestrict()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::preRestrict ( )

First step of the restriction: Dirichlet solve.

This computes the transpose of the prolongation, i.e., with a suitable sorting of interior and bounday degrees of freedom, the

◆ prolongate()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

Dune::FieldVector< double, 2 > Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::prolongate ( )

Perform averaging on the shared interfaces, projecting the solution to the subspace of functions continuous across the interfaces.

Returns: a pair $(\delta x ^T r, \delta x^T A \delta x)$ for the correction $\delta x$ and the residual $r$ .

◆ restrict()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::restrict ( )

Performs the restriction of the residual vector.

◆ set_solver_type()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::set_solver_type ( bool cg_solver )

Set solver type.

◆ setActiveId()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::setActiveId ( bool active )

inline

Definition at line 440 of file bddc.hh.

◆ setActiveSubdomains_sub()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::setActiveSubdomains_sub ( std::vector< bool > & activeSubdomains_ )

inline

Definition at line 504 of file bddc.hh.

◆ setCorrection()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::setCorrection ( Vector const & c )

Computes the correction vector $[\delta x, \delta\lambda]$ .

◆ setInterfaceAveragingWeights()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::setInterfaceAveragingWeights	(	int	s,
		XVector const &	rho
	)

inline

Accumulates interface weights of adjacent subdomains.

Parameters

s	number of adjacent subdomain
rho	interface node weights of neighboring subdomain

Definition at line 258 of file bddc.hh.

◆ setInterfaceResidualUpdate()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::setInterfaceResidualUpdate	(	int	s,
		TransmissionType const &	dres
	)

inline

Sets interface residual of the correction from neighboring subdomains.

Parameters

s	the number of the neighboring subdomain

Definition at line 331 of file bddc.hh.

◆ setInterfaceValues()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::setInterfaceValues	(	int	s,
		TransmissionType const &	values
	)

inline

Sets boundary values of the correction from neighboring subdomains.

Parameters

s	the number of the neighboring subdomain

Definition at line 435 of file bddc.hh.

◆ update_rhs()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::update_rhs ( XVector const & f )

update rhs for the current subdomain

Parameters

f rhs

◆ updateIteration()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::updateIteration ( int cg_itr )

◆ updateSearchDirection()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::updateSearchDirection ( double beta )

Update search direction q for cg solver.

◆ updateSearchDirectionNorm()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

Dune::FieldVector< double, 1 > Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::updateSearchDirectionNorm ( )

◆ updateSolution()

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

void Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::updateSolution ( Scalar alpha )

Updates the solution approximation.

Member Data Documentation

◆ components

template<int m, class Scalar_ = double, class CoarseScalar = Scalar_, class Transfer = SpaceTransfer<m,Scalar_>>

const int Kaskade::BDDC::Subdomain< m, Scalar_, CoarseScalar, Transfer >::components = m

static

Number of (vectorial) components of $u$ .

Definition at line 185 of file bddc.hh.

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

bddc.hh

Detailed Description

Public Types

Public Member Functions

Static Public Attributes

Member Typedef Documentation

◆ AMatrix

◆ Scalar

◆ SMatrix

◆ TransmissionType

◆ Vector

◆ XEntry

◆ XVector

Constructor & Destructor Documentation

◆ Subdomain() [1/2]

◆ Subdomain() [2/2]

Member Function Documentation

◆ getActiveSubdomains()

◆ getCorrection()

◆ getInterfaceAveragingWeights()

◆ getInterfaceResidualUpdate()

◆ getInterfaceValues()

◆ getRawCorrection()

◆ getResidual()

◆ getRestrictedResidual()

◆ getS()

◆ getSchurResidual()

◆ getSolution() [1/2]

◆ getSolution() [2/2]

◆ imposeDC_inActiveInterface()

◆ imposeDCq()

◆ neighbors()

◆ preProlongate()

◆ preRestrict()

◆ prolongate()

◆ restrict()

◆ set_solver_type()

◆ setActiveId()

◆ setActiveSubdomains_sub()

◆ setCorrection()

◆ setInterfaceAveragingWeights()

◆ setInterfaceResidualUpdate()

◆ setInterfaceValues()

◆ update_rhs()

◆ updateIteration()

◆ updateSearchDirection()

◆ updateSearchDirectionNorm()

◆ updateSolution()

Member Data Documentation

◆ components