gsIetiMapper< T > Class Template Reference

Detailed Description

template<typename T>
class gismo::gsIetiMapper< T >

Ieti Mapper.

Algorithms that help with assembling the matrices required for IETI-Solvers

This class is written to work with the expression assembler and with assemblers derived from gsAssembler. If applied to a system, it is expected that individual instances of this class are used for each of the variables.

The objects of this class are initialized using a global dof mapper and a vector that contains function values for the eliminated variables (usually for the Dirichlet boundary).

This class then allows to obtain the jump matrices (jumpMatrix), the patch-local dof mappers (dofMapperLocal) and the patch-local function values for the eliminated dofs (fixedPart). The member function initFeSpace allows to pass dof mapper and the function values for the eliminated dofs to a variable object of the gsExprAssembler.

Moreover, this class allows to construct the primal degrees of freedom, which are then handled by the class gsPrimalSystem.

Finally, the member constructGlobalSolutionFromLocalSolutions allows the combination of the patch-local solutions to a global one.

Collaboration diagram for gsIetiMapper< T >:

Public Member Functions
void	computeJumpMatrices (bool fullyRedundant, bool excludeCorners)
	This function computes the jump matrices.
Matrix	constructGlobalSolutionFromLocalSolutions (const std::vector< Matrix > &localContribs)
	Construct the global solution from a vector of patch-local ones.
void	cornersAsPrimals ()
	Set up the corners as primal dofs.
void	customPrimalConstraints (std::vector< std::pair< index_t, SparseVector > > data)
	With this function, the caller can register more primal constraints.
const gsDofMapper &	dofMapperGlobal () const
	The global dof mapper.
const gsDofMapper &	dofMapperLocal (index_t k) const
	The dof mapper for the given patch Only available after computeJumpMatrices has been called.
const Matrix &	fixedPart (index_t k) const
	The function values for the eliminated dofs on the given patch Only available after computeJumpMatrices has been called.
	gsIetiMapper ()
	Default constructor.
	gsIetiMapper (const gsMultiBasis< T > &multiBasis, gsDofMapper dofMapperGlobal, const Matrix &fixedPart)
	Create the ieti mapper.
Matrix	incorporateFixedPart (index_t k, const gsMatrix< T > &localSolution) const
	Incorporates fixedPart (eg. from eliminated Dirichlet dofs) to given patch-local solution.
void	init (const gsMultiBasis< T > &multiBasis, gsDofMapper dofMapperGlobal, const Matrix &fixedPart)
	Init the ieti mapper after default construction.
void	initFeSpace (typename gsExprAssembler< T >::space u, index_t k)
	Apply the required changes to a space object of the expression assembler.
void	interfaceAveragesAsPrimals (const gsMultiPatch< T > &geo, short_t d)
	Set up interface averages as primal dofs.
const JumpMatrix &	jumpMatrix (index_t k) const
	Returns the jump matrix \( B_k \) for the given patch Only available after computeJumpMatrices has been called.
const gsMultiBasis< T > &	multiBasis () const
	Reference to the multi basis object being passed to constructur or init.
index_t	nLagrangeMultipliers ()
	Returns the number of Lagrange multipliers.
index_t	nPrimalDofs () const
	Returns the size of the primal problem (number of primal dofs)
const std::vector< SparseVector > &	primalConstraints (index_t k) const
	Returns the primalConstraints (as vectors) for the given patch.
const std::vector< index_t > &	primalDofIndices (index_t k) const
	Returns the indices of the primal dofs that are associated to the primal constraints for the given patch.
std::vector< index_t >	skeletonDofs (index_t patch) const
	Returns a list of dofs that are (on the coarse level) coupled.

Private Types
typedef gsSparseMatrix< T, RowMajor >	JumpMatrix
	Sparse matrix type for jumps.
typedef gsMatrix< T >	Matrix
	Matrix type.
typedef gsSparseVector< T >	SparseVector
	Sparse matrix type.

Static Private Member Functions
static gsSparseVector< T >	assembleAverage (const gsGeometry< T > &geo, const gsBasis< T > &basis, const gsDofMapper &dm, boxComponent bc)
	Assembles for interfaceAveragesAsPrimals.

Private Attributes
gsDofMapper	m_dofMapperGlobal
	The global dof mapper.
std::vector< gsDofMapper >	m_dofMapperLocal
	A vector of the patch-local dof mappers.
std::vector< Matrix >	m_fixedPart
	The values for the elminated (Dirichlet) dofs.
std::vector< JumpMatrix >	m_jumpMatrices
	The jump matrices.
const gsMultiBasis< T > *	m_multiBasis
	Pointer to the respective multibasis.
index_t	m_nPrimalDofs
	The number of primal dofs already created.
std::vector< std::vector< SparseVector > >	m_primalConstraints
	The primal constraints.
std::vector< std::vector< index_t > >	m_primalDofIndices
	The primal dof indices for each of the primal constraints.
unsigned	m_status
	A status flag that is checked by assertions.

Constructor & Destructor Documentation

gsIetiMapper()

template<typename T >

gsIetiMapper ( const gsMultiBasis< T > &  multiBasis, gsDofMapper  dofMapperGlobal, const Matrix &  fixedPart  )

inline

Create the ieti mapper.

Parameters

multiBasis	The corresponding gsMultiBasis
dofMapperGlobal	The dof mapper for the global problem
fixedPart	The function values for the eliminated dofs

The multibasis object has to outlive the ieti mapper.

Member Function Documentation

computeJumpMatrices()

template<class T >

void computeJumpMatrices	(	bool	fullyRedundant,
		bool	excludeCorners
	)

This function computes the jump matrices.

Parameters

fullyRedundant	Compute the jump matrices in a fullyRedundant way; if false, then no redundancy
excludeCorners	Ignore corners for jump matrices. This makes sense if the corners are chosen as primal dofs

customPrimalConstraints()

template<class T >

void customPrimalConstraints

(

std::vector< std::pair< index_t, SparseVector > >

data

)

With this function, the caller can register more primal constraints.

All primal constraints in the vector are considered to be one single primal dof. Each component of the vector contains a pair consisting of the patch index and the vector representing the primal constraint.

init()

template<class T >

void init	(	const gsMultiBasis< T > &	multiBasis,
		gsDofMapper	dofMapperGlobal,
		const Matrix &	fixedPart
	)

Init the ieti mapper after default construction.

Parameters

multiBasis	The corresponding gsMultiBasis
dofMapperGlobal	The dof mapper for the global problem
fixedPart	The function values for the eliminated dofs

Instances of the class can be reused using this member function.

initFeSpace()

template<typename T >

void initFeSpace ( typename gsExprAssembler< T >::space  u, index_t  k  )

inline

Apply the required changes to a space object of the expression assembler.

It is assumed that the space object is fully functioning, i.e., the setup member has been called.

This function exposes the dofMapperLocal and the fixedPart to the space.

interfaceAveragesAsPrimals()

template<class T >

void interfaceAveragesAsPrimals	(	const gsMultiPatch< T > &	geo,
		short_t	d
	)

Set up interface averages as primal dofs.

Parameters

geo	gsMultiPatch object describing the geometry
d	The dimension of the interfaces to be considered: d=1 yields edge averages, d=2 yields face averages

Adds contributions only iff the interface (edge, face,...) belongs to at least two patches. This function also works if d=geo.dim(), i.e., for the patch averages. In this case, the requirement that it contributes to at least two patches does not apply. For corners, use cornersAsPrimals instead.

primalConstraints()

template<typename T >

const std::vector< SparseVector > & primalConstraints ( index_t  k ) const

inline

Returns the primalConstraints (as vectors) for the given patch.

These vectors form the matrix \( C_k \) in the local saddle point system, see gsPrimalSystem

skeletonDofs()

template<class T >

std::vector< index_t > skeletonDofs

(

index_t

patch

)

const

Returns a list of dofs that are (on the coarse level) coupled.

Parameters

patch

Number of the patch