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.

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.

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.

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.

	gsDofMapper ()
	Default empty constructor.

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

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

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

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

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

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.

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

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

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

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.

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.

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]].

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() [1/5]

template<class T >

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() [2/5]

template<class T >

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() [3/5]

template<class T >

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() [4/5]

template<class T >

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() [5/5]

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

◆ bindex()

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.

◆ freeIndex()

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.

◆ global_to_bindex()

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()

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.

◆ init()

template<class T >

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

◆ inverseAsVector()

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

◆ localToGlobal()

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

◆ localToGlobal2()

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

◆ permuteFreeDofs()

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.

◆ setMatchingInterfaces()

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

◆ gsDofMapper() [1/5]

◆ gsDofMapper() [2/5]

◆ gsDofMapper() [3/5]

◆ gsDofMapper() [4/5]

◆ gsDofMapper() [5/5]

Member Function Documentation

◆ bindex()

◆ freeIndex()

◆ global_to_bindex()

◆ index()

◆ init()

◆ inverseAsVector()

◆ localToGlobal()

◆ localToGlobal2()

◆ permuteFreeDofs()

◆ setMatchingInterfaces()