Detailed Description

Maintains a mapping from patch-local dofs to global dof indices and allows the elimination of individual dofs.

A dof (degree of freedom) is, roughly speaking, an unknown in a discretization of a PDE. However, some dofs may be eliminated before solving the system and won't actually translate into unknowns. An example are dofs on Dirichlet boundaries.

This class creates a mapping between an arbitrary number of per-patch local dofs to an enumeration of global dofs. Furthermore, dofs can also be marked as eliminated.

This is a a many-to-one mapping: many patch-local dofs are mapped to a single global dfo (index). Every global dof gets a unique number, forming a continuous range starting from 0. This range has length gsDofMapper::size(). The dofs are numbered in the following order:

first the standard free (non-eliminated) dofs, ie. dofs that are not coupled on the boundary. For the standard dofs there is unique pre-image pair (patch,localdof).
then the free dofs which are coupled with other dofs For the coupled dofs there is a list of pre-image pairs of the form (patch,localdof).

Upto here we get all the dofs which are free (number: gsDofMapper::freeSize() ). Then a final group follows:
then the dofs that are on Dirichlet boundaries (number: gsDofMapper::boundarySize()). These dofs might have a unique pre-image or not.

The boundary (eg. eliminated) dofs have their own 0-based numbering. The index of an boundary global dof in this numbering can be queried with gsDofMapper::bindex().

The object must be finalized before it is used, i.e. gsDofMapper::finalize() has to be called once before use.

Public Member Functions
void	addShift (index_t shift)
	Add a shift amount to the global numbering.

bool	allFree () const
	Returns true iff all DoFs are considered as free.

std::pair< index_t, index_t >	anyPreImage (index_t gl) const
	For gl being a global index, this function returns a pair (patch,dof) that maps to gl.

std::vector< std::pair < index_t, index_t > >	anyPreImages (index_t comp=0) const
	For all global index, this function assigns a pair (patch,dof) that maps to that global index.

gsVector< index_t >	asVector (index_t comp=0) const
	Returns a vector taking flat local indices to global.

index_t	bindex (index_t i, index_t k=0, index_t c=0) const
	Returns the boundary index of local dof i of patch k. More...

index_t	boundarySize () const
	Returns the number of eliminated dofs.

index_t	cindex (index_t i, index_t k=0, index_t c=0) const
	Returns the coupled dof index.

void	colapseDofs (index_t k, const gsMatrix< unsigned > &b, index_t comp=0)
	Calls matchDof() for all dofs on the given patch side i ps. Thus, the whole set of dofs collapses to a single global dof. More...

index_t	coupledSize () const
	Returns the number of coupled (not eliminated) dofs.

void	eliminateDof (index_t i, index_t k, index_t comp=0)
	Mark the local dof i of patch k as eliminated.

void	finalize ()
	Must be called after all boundaries and interfaces have been marked to set up the dof numbering.

gsVector< index_t >	findBoundary (const index_t k) const
	Returns all boundary dofs on patch k (local dof indices)

gsVector< index_t >	findCoupled (const index_t k, const index_t j=-1) const
	Returns all coupled dofs on patch k (local dof indices)

gsVector< index_t >	findFree (const index_t k) const
	Returns all free dofs on patch k (local dof indices)

gsVector< index_t >	findFreeUncoupled (const index_t k) const
	Returns all free, not coupled dofs on patch k (local dof indices)

gsVector< index_t >	findTagged (const index_t k) const
	Returns all tagged dofs on patch k (local dof indices)

index_t	firstIndex (index_t comp=0) const
	Returns the smallest value of the indices for comp.

index_t	freeIndex (index_t i, index_t k=0, index_t c=0) const
	Returns the index associated to local dof i of patch k without shifts. More...

index_t	freeSize () const
	Returns the number of free (not eliminated) dofs.

const std::vector< index_t > &	getTagged () const
	Returns the vector of tagged (not eliminated) dofs.

index_t	global_to_bindex (index_t gl) const
	Returns the boundary index of global dof gl. More...

	gsDofMapper ()
	Default empty constructor.

template<class T >
	gsDofMapper (const gsMultiBasis< T > &bases, const gsBoundaryConditions< T > &dirichlet, int unk=0)
	construct a dof mapper that identifies the degrees of freedom in the multibasis and eliminates the degrees of freedom on the Dirichlet boundary More...

template<class T >
	gsDofMapper (const gsMultiBasis< T > &bases, index_t nComp=1)
	construct a dof mapper that identifies the degrees of freedom in the multibasis More...

template<class T >
	gsDofMapper (std::vector< const gsMultiBasis< T > * > const &bases)
	construct a dof mapper that identifies the degrees of freedom for a vector of multibasis More...

template<class T >
	gsDofMapper (const gsBasis< T > &basis, index_t nComp=1)
	construct a dof mapper that manages the degrees of freedom in a gsBasis More...

	gsDofMapper (const gsVector< index_t > &patchDofSizes, index_t nComp=1)
	construct a dof mapper with a given number of dofs per patch More...

index_t	index (index_t i, index_t k=0, index_t c=0) const
	Returns the global dof index associated to local dof i of patch k. More...

bool	indexOnPatch (const index_t gl, const index_t k) const
	For gl being a global index, this function returns true whenever gl corresponds to patch k.

template<typename T >
void	init (const gsMultiBasis< T > &bases, index_t nComp=1)
	Initialize by a gsMultiBasis.

template<typename T >
void	init (std::vector< const gsMultiBasis< T > * > const &bases)
	Initialize by a vector of gsMultiBasis.

template<class T >
void	init (const gsMultiBasis< T > &basis, const gsBoundaryConditions< T > &dirichlet, int unk=0)

gsVector< index_t >	inverseAsVector (index_t comp=0) const
	Returns a vector taking global indices to flat local. More...

std::map< index_t, index_t >	inverseOnPatch (const index_t k) const
	Produces the inverse of the mapping on patch k assuming that the map is invertible on that patch.

bool	is_boundary (index_t i, index_t k=0, index_t c=0) const
	Returns true if local dof i of patch k is eliminated.

bool	is_boundary_index (index_t gl) const
	Returns true if global dof gl is eliminated.

bool	is_coupled (index_t i, index_t k=0, index_t c=0) const
	Returns true if local dof i of patch k is coupled.

bool	is_coupled_index (index_t gl) const
	Returns true if gl is a coupled dof.

bool	is_free (index_t i, index_t k=0, index_t c=0) const
	Returns true if local dof i of patch k is not eliminated.

bool	is_free_index (index_t gl) const
	Returns true if global dof gl is not eliminated.

bool	is_tagged (index_t i, index_t k=0, index_t c=0) const
	Returns true if local dof i of patch k is tagged.

bool	is_tagged_index (index_t gl) const
	Returns true if gl is a tagged dof.

bool	isFinalized () const
	Checks whether finalize() has been called.

bool	isPermutation () const
	Returns true iff the mapper is a permuatation.

index_t	lastIndex () const
	Returns one past the biggest value of the free indices.

void	localToGlobal (const gsMatrix< index_t > &locals, index_t patchIndex, gsMatrix< index_t > &globals, index_t comp=0) const
	Computes the global indices of the input local indices. More...

void	localToGlobal2 (const gsMatrix< index_t > &locals, index_t patchIndex, gsMatrix< index_t > &globals, index_t &numFree, index_t comp=0) const
	Computes the global indices of the input local indices. More...

index_t	mapIndex (index_t n) const
	For n being an index which is already offsetted, it returns the global index where it is mapped to by the dof mapper.

size_t	mapSize () const
	Returns the total number of patch-local degrees of freedom that are being mapped.

void	markBoundary (index_t k, const gsMatrix< index_t > &boundaryDofs, index_t comp=0)
	Mark the local dofs boundaryDofs of patch k as eliminated.

void	markCoupled (index_t i, index_t k, index_t comp=0)
	Mark the local dof i of patch k as coupled.

void	markCoupledAsTagged ()
	Mark all coupled dofs as tagged.

void	markTagged (index_t i, index_t k, index_t comp=0)
	Mark a local dof i of patch k as tagged.

void	matchDof (index_t u, index_t i, index_t v, index_t j, index_t comp=0)
	Couples dof i of patch u with dof j of patch v such that they refer to the same global dof at component comp.

void	matchDofs (index_t u, const gsMatrix< index_t > &b1, index_t v, const gsMatrix< index_t > &b2, index_t comp=0)
	Couples dofs b1 of patch u with dofs b2 of patch v one by one such that they refer to the same global dof.

index_t	numComponents () const
	Returns the number of components present in the mapper.

size_t	numPatches () const
	Returns the number of patches present underneath the mapper.

size_t	offset (int k) const
	Returns the offset corresponding to patch k.

size_t	patchSize (const index_t k, const index_t c=0) const
	Returns the total number of patch-local DoFs that live on patch k for component c.

void	permuteFreeDofs (const gsVector< index_t > &permutation, index_t comp=0)
	Permutes the mapped free indices according to permutation, i.e., dofs_perm[idx] = dofs_old[permutation[idx]]. More...

void	preImage (index_t gl, std::vector< std::pair< index_t, index_t > > &result) const
	For gl being a global index, this function returns a vector of pairs (patch,dof) that contains all the pairs which map to gl.

std::ostream &	print (std::ostream &os=gsInfo) const
	Print summary.

void	setBoundaryShift (index_t shift)
	Set the shift amount for the boundary numbering.

void	setIdentity (index_t nPatches, size_t nDofs, size_t nComp=1)
	Set this mapping to be the identity.

void	setMatchingInterfaces (const gsBoxTopology &mp)

void	setShift (index_t shift)
	Set the shift amount for the global numbering.

index_t	size () const
	Returns the total number of dofs (free and eliminated).

index_t	size (index_t comp) const
	Returns the total number of dofs (free and eliminated).

index_t	taggedSize () const
	Returns the number of tagged dofs.

index_t	tindex (index_t i, index_t k=0, index_t c=0) const
	Returns the tagged dof index.

Private Member Functions
void	initPatchDofs (const gsVector< index_t > &patchDofSizes, index_t nComp=1)
	Initialize by vector of DoF indices and dimension.

template<typename T >
void	initSingle (const gsBasis< T > &basis, index_t nComp=1)
	Initialize by a single basis patch.

Private Attributes
index_t	m_bshift
	Shifting of the boundary index (zero by default)

std::vector< index_t >	m_numCpldDofs
	Offsets of coupled dofs, nComp+1.

std::vector< index_t >	m_numElimDofs
	Offsets of eliminated dofs, nComp+1.

std::vector< index_t >	m_numFreeDofs
	Offsets of free dofs, nComp+1.

std::vector< size_t >	m_offset
	Offsets.

index_t	m_shift
	Shifting of the global index (zero by default)

std::vector< index_t >	m_tagged
	Stores the tagged indices.

Constructor & Destructor Documentation

gsDofMapper	(	const gsMultiBasis< T > &	bases,
		const gsBoundaryConditions< T > &	dirichlet,
		int	unk = `0`
	)

inline

construct a dof mapper that identifies the degrees of freedom in the multibasis and eliminates the degrees of freedom on the Dirichlet boundary

Parameters

bases
dirichlet
unk

gsDofMapper	(	const gsMultiBasis< T > &	bases,
		index_t	nComp = `1`
	)

inline

construct a dof mapper that identifies the degrees of freedom in the multibasis

Parameters

bases

gsDofMapper ( std::vector< const gsMultiBasis< T > * > const & bases )

inline

construct a dof mapper that identifies the degrees of freedom for a vector of multibasis

Parameters

bases

gsDofMapper	(	const gsBasis< T > &	basis,
		index_t	nComp = `1`
	)

inline

construct a dof mapper that manages the degrees of freedom in a gsBasis

Parameters

basis

gsDofMapper	(	const gsVector< index_t > &	patchDofSizes,
		index_t	nComp = `1`
	)

inline

construct a dof mapper with a given number of dofs per patch

Parameters

patchDofSizes

Member Function Documentation

index_t bindex	(	index_t	i,
		index_t	k = `0`,
		index_t	c = `0`
	)		const

inline

Returns the boundary index of local dof i of patch k.

Produces undefined results if local dof (i,k) does not lie on the boundary.

void colapseDofs	(	index_t	k,
		const gsMatrix< unsigned > &	b,
		index_t	comp = `0`
	)

Calls matchDof() for all dofs on the given patch side i ps. Thus, the whole set of dofs collapses to a single global dof.

index_t freeIndex	(	index_t	i,
		index_t	k = `0`,
		index_t	c = `0`
	)		const

inline

Returns the index associated to local dof i of patch k without shifts.

Note: This method only works after all interfaces and boundaries have been marked and finalize() has been called.

index_t global_to_bindex ( index_t gl ) const

inline

Returns the boundary index of global dof gl.

Produces undefined results if dof gl does not lie on the boundary.

index_t index	(	index_t	i,
		index_t	k = `0`,
		index_t	c = `0`
	)		const

inline

Returns the global dof index associated to local dof i of patch k.

Note: This method only works after all interfaces and boundaries have been marked and finalize() has been called.

void init	(	const gsMultiBasis< T > &	basis,
		const gsBoundaryConditions< T > &	dirichlet,
		int	unk = `0`
	)

Initialize by gsMultiBasis, boundary conditions and the index of the unknown to be eliminated

Todo:: move this code to gsMultiBasis::getMapper

gsVector< index_t > inverseAsVector ( index_t comp = 0 ) const

Returns a vector taking global indices to flat local.

Assumes that the mapper is a permutation

void localToGlobal	(	const gsMatrix< index_t > &	locals,
		index_t	patchIndex,
		gsMatrix< index_t > &	globals,
		index_t	comp = `0`
	)		const

Computes the global indices of the input local indices.

Parameters

[in]	locals	a column matrix with the local indices
[in]	patchIndex	the index of the patch where the local indices belong to
[out]	globals	the global indices of the patch

void localToGlobal2	(	const gsMatrix< index_t > &	locals,
		index_t	patchIndex,
		gsMatrix< index_t > &	globals,
		index_t &	numFree,
		index_t	comp = `0`
	)		const

Computes the global indices of the input local indices.

Parameters

[in]	locals	a column matrix with the local indices
[in]	patchIndex	the index of the patch where the local indices belong to
[out]	globals	the local-global correspondance
[out]	numFree	the number of free indices in local

void permuteFreeDofs	(	const gsVector< index_t > &	permutation,
		index_t	comp = `0`
	)

Permutes the mapped free indices according to permutation, i.e., dofs_perm[idx] = dofs_old[permutation[idx]].

Warning: Applying a permutation makes the functions regarding coupled dofs (cindex, is_coupled_index,.. ) invalid. The dofs are still coupled, but you have no way of extracting them. If you need this functions, first call markCoupledAsTagged() and then use the corresponding functions for tagged dofs.

void setMatchingInterfaces ( const gsBoxTopology & mp )

Called to initialize the gsDofMapper with matching interfaces after m_bases have already been set

Detailed Description

Public Member Functions

Private Member Functions

Private Attributes

Constructor & Destructor Documentation

Member Function Documentation