gsMultiBasis< T > Class Template Reference

Detailed Description

template<class T>
class gismo::gsMultiBasis< T >

Holds a set of patch-wise bases and their topology information.

Template Parameters

T	coefficient type

Inheritance diagram for gsMultiBasis< T >:

Collaboration diagram for gsMultiBasis< T >:

Public Types
typedef BasisContainer::iterator	iterator
	Type definitions.

Public Member Functions
gsMatrix< index_t >	active (const gsMatrix< T > &u) const
	Returns the indices of active (nonzero) functions at points u, as a list of indices. More...
virtual void	active_into (const gsMatrix< T > &u, gsMatrix< index_t > &result) const
	Indices of active (non-zero) function(s) for each point. More...
void	addBasis (gsBasis< T > *g)
	Add a basis (ownership of the pointer is also acquired)
void	addBasis (typename gsBasis< T >::uPtr g)
	Add a basis.
void	addInterface (gsBasis< T > *g1, boxSide s1, gsBasis< T > *g2, boxSide s2)
	Add an interface joint between side s1 of geometry g1 side s2 of geometry g2. More...
void	addPatchBoundary (gsBasis< T > *g, boxSide s)
	Add side s of patch g to the outer boundary of the domain.
const_reference	at (size_t i) const
	Assess i-th parametric basis.
const gsBasis< T > &	basis (const index_t k) const
	Helper which casts and returns the k-th piece of this function set as a gsBasis.
const gsBasis< T > &	basis (const size_t i) const
	Return the i-th basis block.
gsBasis< T > &	basis (const size_t i)
	Return the i-th basis block.
const_iterator	begin () const
iterator	begin ()
void	clear ()
	Clear (delete) all patches.
uPtr	clone ()
	Clone methode. Produceds a deep copy inside a uPtr.
gsBasis< T >::uPtr	componentBasis (patchComponent p) const
	Returns the basis that corresponds to the component.
gsBasis< T >::uPtr	componentBasis_withIndices (patchComponent pc, const gsDofMapper &dm, gsMatrix< index_t > &indices, bool no_lower=true) const
	Returns the basis that corresponds to the component. More...
std::vector< typename gsBasis < T >::uPtr >	componentBasis_withIndices (const std::vector< patchComponent > &pc, const gsDofMapper &dm, gsMatrix< index_t > &indices, bool no_lower=true) const
	Returns the bases that correspond to the components. More...
virtual void	compute (const gsMatrix< T > &in, gsFuncData< T > &out) const
	Computes function data. More...
short_t	degree (size_t i=0, short_t comp=0) const
	Returns the polynomial degree of basis i in component j, if the basis is of polynomial or piecewise polynomial type.
void	degreeDecrease (short_t const i=1, short_t const dir=-1)
	Increase the degree of every basis by the given amount. (keeping the multiplicity)
void	degreeElevate (short_t const i=1, short_t const dir=-1)
	Elevate the degree of every basis by the given amount. (keeping the smoothness)
void	degreeIncrease (short_t const i=1, short_t const dir=-1)
	Increase the degree of every basis by the given amount. (keeping the multiplicity)
void	degreeReduce (short_t const i=1)
	Reduce the degree of the basis by the given amount.
gsMatrix< T >	deriv (const gsMatrix< T > &u) const
	Evaluate the derivatives,. More...
gsMatrix< T >	deriv2 (const gsMatrix< T > &u) const
	Evaluates the second derivatives of active (i.e., non-zero) functions at points u. More...
virtual void	deriv2_into (const gsMatrix< T > &u, gsMatrix< T > &result) const
	Second derivatives. More...
virtual void	deriv_into (const gsMatrix< T > &u, gsMatrix< T > &result) const
	First derivatives. More...
short_t	dim () const
	Dimension of the parameter domain (must match for all bases).
short_t	domainDim () const
	Dimension of the (source) domain. More...
const_iterator	end () const
iterator	end ()
gsMatrix< T >	eval (const gsMatrix< T > &u) const
	Evaluate the function,. More...
virtual void	eval_into (const gsMatrix< T > &u, gsMatrix< T > &result) const
	Evaluates the function(s). More...
std::vector< gsMatrix< T > >	evalAllDers (const gsMatrix< T > &u, int n, bool sameElement=false) const
	Evaluate all derivatives upto order n,. More...
virtual void	evalAllDers_into (const gsMatrix< T > &u, int n, std::vector< gsMatrix< T > > &result, bool sameElement=false) const
	Evaluate the nonzero functions and their derivatives up to order n at points u into result. More...
int	findBasisIndex (gsBasis< T > *g) const
	Search for the given basis and return its index.
const gsFunction< T > &	function (const index_t k) const
	Helper which casts and returns the k-th piece of this function set as a gsFunction.
	gsMultiBasis ()
	Default empty constructor.
	gsMultiBasis (const gsMultiPatch< T > &mpatch, bool numeratorOnly=false)
	Create a multi-basis instance from a gsMultiPatch. More...
	gsMultiBasis (BasisContainer &bases, const gsBoxTopology &topology)
	Create from a vector of bases and topology.
	gsMultiBasis (const gsBasis< T > &geo, bool numeratorOnly=false)
	Create a single-basis instance.
	gsMultiBasis (BasisContainer &bases, const std::vector< patchSide > &boundary, const std::vector< boundaryInterface > &interfaces)
	Create from bases and boundary/interface information.
	gsMultiBasis (const gsMultiBasis &other)
	Copy constructor (makes deep copy)
void	matchInterface (const boundaryInterface &bi, gsDofMapper &mapper) const
	Matches the degrees of freedom along an interface. More...
short_t	maxCwiseDegree () const
	Maximum degree with respect to all variables.
short_t	maxDegree (short_t k) const
	Maximum degree with respect to variable k.
short_t	minCwiseDegree () const
	Minimum degree with respect to all variables.
short_t	minDegree (short_t k) const
	Minimum degree with respect to variable k.
size_t	nBases () const
	Number of patch-wise bases.
index_t	nPieces () const
	Number of patch-wise bases.
gsMultiBasis &	operator= (gsMultiBasis other)
	Assignment operator (uses copy-and-swap idiom)
const gsBasis< T > &	piece (const index_t i) const
	Returns the piece(s) of the function(s) at subdomain k.
std::ostream &	print (std::ostream &os) const
	Prints the object as a string.
void	reduceContinuity (int const i=1)
	Reduce the continuity by i.
void	refine (size_t k, gsMatrix< T > const &boxes, int refExt)
	Refine the are defined by boxes on patch k with extension refExt. More...
void	refineElements (int k, std::vector< index_t > const &boxes)
	Refine the are defined by boxes on patch k. More...
bool	repairInterface (const boundaryInterface &bi)
	Checks if the interface is fully matching, and if not, repairs it. More...
bool	repairInterface2d (const boundaryInterface &bi)
	Checks if the 2D-interface is fully matching, and if not, repairs it. More...
template<short_t d>
bool	repairInterfaceFindElements (const boundaryInterface &bi, std::vector< index_t > &refEltsFirst, std::vector< index_t > &refEltsSecond)
	Finds the elements that need to be refined in order to repair an interface. More...
void	repairInterfaces (const std::vector< boundaryInterface > &bivec)
	Checks if the interfaces bivec are fully matching, and if not, repairs them, i.e., makes them fully matching. More...
void	setDegree (short_t const &i)
	Set the degree of the basis.
int	size (size_t i) const
	The number of basis functions in basis i.
index_t	size () const
	size More...
void	swap (gsMultiBasis &other)
	Swap with another gsMultiBasis.
short_t	targetDim () const
	Dimension of the target space. More...
void	tileParameters ()
size_t	totalElements () const
	The total number of elements in all patches.
size_t	totalSize () const
	The total number of basis functions in all bases.
void	uniformCoarsen (int numKnots=1)
	Coarsen every basis uniformly. More...
void	uniformCoarsen_withTransfer (gsSparseMatrix< T, RowMajor > &transfer, const gsBoundaryConditions< T > &boundaryConditions, const gsOptionList &assemblerOptions, int numKnots=1, index_t unk=0)
	Coarsen every basis uniformly. More...
void	uniformRefine (int numKnots=1, int mul=1, int dir=-1)
	Refine every basis uniformly. More...
void	uniformRefine_withTransfer (gsSparseMatrix< T, RowMajor > &transfer, const gsBoundaryConditions< T > &boundaryConditions, const gsOptionList &assemblerOptions, int numKnots=1, int mul=1, index_t unk=0)
	Refine every basis uniformly. More...
void	uniformRefineComponent (int comp, int numKnots=1, int mul=1)
	Refine the component comp of every basis uniformly by inserting numKnots new knots on each knot span.
	~gsMultiBasis ()
	Destructor.

Static Public Member Functions
static void	combineTransferMatrices (const std::vector< gsSparseMatrix< T, RowMajor > > &localTransferMatrices, const gsDofMapper &coarseMapper, const gsDofMapper &fineMapper, gsSparseMatrix< T, RowMajor > &transferMatrix)
	This function takes local transfer matrices (per patch) and combines them using given DofMappers to a global transfer matrix. Simultanously, this function restricts the matrices to the free dofs, e.g., Dirichlet dofs might be eliminated. More...

Constructor & Destructor Documentation

gsMultiBasis ( const gsMultiPatch< T > &  mpatch, bool  numeratorOnly = false  )

explicit

Create a multi-basis instance from a gsMultiPatch.

Parameters

mpatch	used gsMultiPatch
numeratorOnly	If true, and the bases are derived from gsRationalBasis, then only the source bases (numerators) are returned

Note

In the case of NURBS, the numerator possess the same approximation power, while the evaluation of values and partial derivatives are much less expensive

Member Function Documentation

gsMatrix<index_t> active ( const gsMatrix< T > &  u ) const

inlineinherited

Returns the indices of active (nonzero) functions at points u, as a list of indices.

See Also

active_into()

void active_into ( const gsMatrix< T > &  u, gsMatrix< index_t > &  result  ) const

virtualinherited

Indices of active (non-zero) function(s) for each point.

The columns are sorted in increasing order, if on a point there are less active then the number of rows in the result matrix (some other point has more actives) then the rest of the column is filled with 0s.

Parameters

u
result

Reimplemented in gsHTensorBasis< d, T >, gsBasis< T >, gsBasis< Scalar >, gsBasis< real_t >, gsTensorBSplineBasis< 1, T >, gsTensorBSplineBasis< d, T >, gsTensorBSplineBasis< domainDim+1, T >, gsTensorBasis< d, T >, gsTensorBasis< 1, T >, gsTHBSplineBasis< d, T >, gsLagrangeBasis< T >, gsMappedSingleBasis< d, T >, gsFunction< T >, gsConstantBasis< T >, gsLegendreBasis< T >, gsMonomialBasis< T >, and gsMvLegendreBasis< T >.

void addInterface	(	gsBasis< T > *	g1,
		boxSide	s1,
		gsBasis< T > *	g2,
		boxSide	s2
	)

Add an interface joint between side s1 of geometry g1 side s2 of geometry g2.

Todo:

add orientation information

const_iterator begin ( ) const

inline

Get a const-iterator to the patches

Returns

an iterator to the beginning of the patches

iterator begin ( )

inline

Get an iterator to the beginning of the patches

Returns

an iterator to the beginning of the patches

void combineTransferMatrices ( const std::vector< gsSparseMatrix< T, RowMajor > > &  localTransferMatrices, const gsDofMapper &  coarseMapper, const gsDofMapper &  fineMapper, gsSparseMatrix< T, RowMajor > &  transferMatrix  )

static

This function takes local transfer matrices (per patch) and combines them using given DofMappers to a global transfer matrix. Simultanously, this function restricts the matrices to the free dofs, e.g., Dirichlet dofs might be eliminated.

Parameters

[in]	localTransferMatrices	The local and full (also non-free dofs) transfer matrices per patch
[in]	coarseMapper	The DofMapper on the coarse grid
[in]	fineMapper	The DofMapper on the fine grid
[out]	transferMatrix	The combined transfer matrix restricted to the free dofs

gsBasis< T >::uPtr componentBasis_withIndices	(	patchComponent	pc,
		const gsDofMapper &	dm,
		gsMatrix< index_t > &	indices,
		bool	no_lower = true
	)		const

Returns the basis that corresponds to the component.

Parameters

pc	The component
dm	The dof mapper to be used
indices	The row vector where the indices are stored to
no_lower	If true, the transfer matrix does not include parts belonging to lower-order components (i.e., edges without corners or faces without corners and edges)

std::vector< typename gsBasis< T >::uPtr > componentBasis_withIndices	(	const std::vector< patchComponent > &	pc,
		const gsDofMapper &	dm,
		gsMatrix< index_t > &	indices,
		bool	no_lower = true
	)		const

Returns the bases that correspond to the components.

Parameters

pc	The components
dm	The dof mapper to be used
indices	The row vector where the indices are stored to
no_lower	If true, the transfer matrix does not include parts belonging to lower-order components (i.e., edges without corners or faces without corners and edges)

void compute ( const gsMatrix< T > &  in, gsFuncData< T > &  out  ) const

virtualinherited

Computes function data.

This function evaluates the functions and their derivatives at the points in and writes them in the corresponding fields of out. Which field to write (and what to compute) is controlled by the out.flags (see also gsFuncData).

The input points in are expected to be compatible with the implementation/representation of the function, i.e. they should be points inside the domain of definitition of the function

Parameters

[in]	in
[out]	out

Reimplemented in gsGeometry< T >, and gsConstantFunction< T >.

gsMatrix< T > deriv ( const gsMatrix< T > &  u ) const

inherited

Evaluate the derivatives,.

See Also

deriv_into()

gsMatrix< T > deriv2 ( const gsMatrix< T > &  u ) const

inherited

Evaluates the second derivatives of active (i.e., non-zero) functions at points u.

See documentation for deriv2_into() (the one without input parameter coefs) for details.

See Also

deriv2_into()

Parameters

[in]

u

Evaluation points in columns.

Returns

For every column of u, a column containing the second derivatives. See documentation for deriv2_into() (the one without input parameter coefs) for details.

void deriv2_into ( const gsMatrix< T > &  u, gsMatrix< T > &  result  ) const

virtualinherited

Second derivatives.

For scalar valued functions \(f_1, \ldots, f_S\) from \(\mathbb{R}^n\rightarrow\mathbb{R}\) format is:

\[ \left[ \begin{array}{ccccc} \partial_{1}\partial_{1}f_1(p_1) & \partial_{1}\partial_{1}f_1(p_2) & \ldots & \partial_{1}\partial_{1}f_1(p_N)\\ \partial_{2}\partial_{2}f_1(p_1) & \partial_{2}\partial_{2}f_1(p_2) & \ldots & \partial_{2}\partial_{2}f_1(p_N)\\ \vdots & \vdots & & \vdots\\ \partial_{k}\partial_{k}f_1(p_1) & \partial_{k}\partial_{k}f_1(p_2) & \ldots & \partial_{k}\partial_{k}f_1(p_N)\\ \partial_{1}\partial_{2}f_1(p_1) & \partial_{1}\partial_{2}f_1(p_2) & \ldots & \partial_{1}\partial_{2}f_1(p_N)\\ \partial_{1}\partial_{3}f_1(p_1) & \partial_{1}\partial_{3}f_1(p_2) & \ldots & \partial_{1}\partial_{3}f_1(p_N)\\ \vdots & \vdots & & \vdots\\ \partial_{1}\partial_{k}f_1(p_1) & \partial_{1}\partial_{k}f_1(p_2) & \ldots & \partial_{1}\partial_{k}f_1(p_N)\\ \partial_{2}\partial_{3}f_1(p_1) & \partial_{2}\partial_{3}f_1(p_2) & \ldots & \partial_{2}\partial_{3}f_1(p_N)\\ \vdots & \vdots & & \vdots\\ \partial_{2}\partial_{k}f_1(p_1) & \partial_{2}\partial_{k}f_1(p_2) & \ldots & \partial_{2}\partial_{k}f_1(p_N)\\ \partial_{3}\partial_{4}f_1(p_1) & \partial_{3}\partial_{4}f_1(p_2) & \ldots & \partial_{3}\partial_{4}f_1(p_N)\\ \vdots & \vdots & & \vdots\\ \partial_{k-1}\partial_{k}f_1(p_1) & \partial_{k-1}\partial_{k}f_1(p_2) & \ldots & \partial_{k-1}\partial_{k}f_1(p_N)\\ \partial_{1}\partial_{1}f_2(p_1) & \partial_{1}\partial_{1}f_2(p_2) & \ldots & \partial_{1}\partial_{1}f_2(p_N)\\ \vdots & \vdots & & \vdots\\ \partial_{k-1}\partial_{k}f_S(p_1) & \partial_{k-1}\partial_{k}f_S(p_2) & \ldots & \partial_{k-1}\partial_{k}f_S(p_N)\\ \end{array} \right] \]

For vector valued functions function \(f_1, \ldots, f_S\) from \(\mathbb{R}^n\rightarrow\mathbb{R}^{m}\) the format is:

\[ \left[ \begin{array}{ccccc} \partial_{1}\partial_{1}f_1^{(1)}(p_1) & \partial_{1}\partial_{1}f_1^{(1)}(p_2) & \ldots & \partial_{1}\partial_{1}f_1^{(1)}(p_N)\\ \partial_{2}\partial_{2}f_1^{(1)}(p_1) & \partial_{2}\partial_{2}f_1^{(1)}(p_2) & \ldots & \partial_{2}\partial_{2}f_1^{(1)}(p_N)\\ \vdots & \vdots & & \vdots\\ \partial_{k}\partial_{k}f_1^{(1)}(p_1) & \partial_{k}\partial_{k}f_1^{(1)}(p_2) & \ldots & \partial_{k}\partial_{k}f_1^{(1)}(p_N)\\ \partial_{1}\partial_{2}f_1^{(1)}(p_1) & \partial_{1}\partial_{2}f_1^{(1)}(p_2) & \ldots & \partial_{1}\partial_{2}f_1^{(1)}(p_N)\\ \partial_{1}\partial_{3}f_1^{(1)}(p_1) & \partial_{1}\partial_{3}f_1^{(1)}(p_2) & \ldots & \partial_{1}\partial_{3}f_1^{(1)}(p_N)\\ \vdots & \vdots & & \vdots\\ \partial_{k-1}\partial_{k}f_1{(1)}(p_1) & \partial_{k-1}\partial_{k}f_1^{(1)}(p_2) & \ldots & \partial_{k-1}\partial_{k}f_1^{(1)}(p_N)\\ \partial_{1}\partial_{1}f_1^{(2)}(p_1) & \partial_{1}\partial_{1}f_1^{(2)}(p_2) & \ldots & \partial_{1}\partial_{1}f_1^{(2)}(p_N)\\ \vdots & \vdots & & \vdots\\ \partial_{k-1}\partial_{k}f_1^{(m)}(p_1) & \partial_{k-1}\partial_{k}f_1^{(m)}(p_2) & \ldots & \partial_{k-1}\partial_{k}f_1^{(m)}(p_N)\\ \vdots & \vdots & & \vdots\\ \partial_{k-1}\partial_{k}f_S^{(m)}(p_1) & \partial_{k-1}\partial_{k}f_S^{(m)}(p_2) & \ldots & \partial_{k-1}\partial_{k}f_S^{(m)}(p_N)\\ \end{array} \right] \]

where \( f^{(i)}_j\) is the \(i\)-th component of function \( f_j\) of the set.

Parameters

u
result

Reimplemented in gsBasis< T >, gsBasis< Scalar >, gsBasis< real_t >, gsTensorBSplineBasis< 1, T >, gsTensorBasis< d, T >, gsTensorBasis< 1, T >, gsGeometry< T >, gsFunctionExpr< T >, gsFunction< T >, gsLagrangeBasis< T >, gsMappedSingleBasis< d, T >, gsConstantFunction< T >, gsTHBSplineBasis< d, T >, gsPreCICEFunction< T >, gsLegendreBasis< T >, gsAffineFunction< T >, gsHBSplineBasis< d, T >, gsMappedSingleSpline< d, T >, gsMonomialBasis< T >, gsMvLegendreBasis< T >, gsGeometryTransform< T >, and gsFuncCoordinate< T >.

void deriv_into ( const gsMatrix< T > &  u, gsMatrix< T > &  result  ) const

virtualinherited

First derivatives.

For scalar valued functions \(f_1, \ldots, f_S\) from \(\mathbb{R}^n\rightarrow\mathbb{R}\) format is:

\[ \left[ \begin{array}{ccccc} \partial_{1}f_1(p_1) & \partial_{1}f_1(p_2) & \ldots & \partial_{1}f_1(p_N)\\ \partial_{2}f_1(p_1) & \partial_{2}f_1(p_2) & \ldots & \partial_{2}f_1(p_N)\\ \vdots & \vdots & & \vdots\\ \partial_{k}f_1(p_1) & \partial_{k}f_1(p_2) & \ldots & \partial_{k}f_1(p_N)\\ \partial_{1}f_2(p_1) & \partial_{1}f_2(p_2) & \ldots & \partial_{1}f_2(p_N)\\ \vdots & \vdots & & \vdots\\ \partial_{k}f_S(p_1) & \partial_{k}f_S(p_2) & \ldots & \partial_{k}f_S(p_N)\\ \end{array} \right] \]

For vector valued functions function \(f_1, \ldots, f_S\) from \(\mathbb{R}^n\rightarrow\mathbb{R}^{m}\) the format is:

\[ \left[ \begin{array}{ccccc} \partial_{1}f_1^1(p_1) & \partial_{1}f_1^1(p_2) & \ldots & \partial_{1}f_1^1(p_N)\\ \partial_{2}f_1^1(p_1) & \partial_{1}f_2^1(p_2) & \ldots & \partial_{1}f_2^1(p_N)\\ \vdots & \vdots & & \vdots\\ \partial_{k}f_1^1(p_1) & \partial_{k}f_1^1(p_2) & \ldots & \partial_{k}f_1^1(p_N)\\ \partial_{1}f_1^2(p_1) & \partial_{1}f_1^2(p_2) & \ldots & \partial_{1}f_1^2(p_N)\\ \vdots & \vdots & & \vdots\\ \partial_{k}f_1^2(p_1) & \partial_{k}f_1^2(p_2) & \ldots & \partial_{k}f_1^2(p_N)\\ \partial_{1}f_2^1(p_1) & \partial_{1}f_2^1(p_2) & \ldots & \partial_{1}f_2^1(p_N)\\ \vdots & \vdots & & \vdots\\ \partial_{k}f_S^{(m)}(p_1) & \partial_{k}f_S^{(m)}(p_2) & \ldots & \partial_{k}f_S^{(m)}(p_N) \end{array} \right] \]

where \(f^{(i)}_j\) is the \(i\)-th component of function \(f_j\) of the set.

Parameters

u
result

Reimplemented in gsBasis< T >, gsBasis< Scalar >, gsBasis< real_t >, gsTensorBasis< d, T >, gsTensorBasis< 1, T >, gsTensorBSplineBasis< 1, T >, gsGeometry< T >, gsFunctionExpr< T >, gsLagrangeBasis< T >, gsMappedSingleBasis< d, T >, gsFunction< T >, gsConstantFunction< T >, gsTHBSplineBasis< d, T >, gsPreCICEFunction< T >, gsAffineFunction< T >, gsHBSplineBasis< d, T >, gsLegendreBasis< T >, gsMappedSingleSpline< d, T >, gsMvLegendreBasis< T >, gsMonomialBasis< T >, gsConstantBasis< T >, gsGeometrySlice< T >, gsSquaredDistance< T >, gsBasisFun< T >, gsGeometryTransform< T >, and gsFuncCoordinate< T >.

short_t domainDim ( ) const

inlinevirtual

Dimension of the (source) domain.

Returns

For \(f:\mathbb{R}^n\rightarrow\mathbb{R}^m\), returns \(n\).

Implements gsFunctionSet< T >.

const_iterator end ( ) const

inline

Get a const iterator to the end of the patches

Returns

an iterator to the end of the patches

iterator end ( )

inline

Get an iterator to the end of the patches

Returns

an iterator to the end of the patches

gsMatrix< T > eval ( const gsMatrix< T > &  u ) const

inherited

Evaluate the function,.

See Also

eval_into()

void eval_into ( const gsMatrix< T > &  u, gsMatrix< T > &  result  ) const

virtualinherited

Evaluates the function(s).

For scalar valued functions \(f_1, \ldots, f_S\) from \(\mathbb{R}^n\rightarrow\mathbb{R}\) format is:

\[ \left[ \begin{array}{ccccc} f_1(p_1) & f_1(p_2) & \ldots & f_1(p_N)\\ f_2(p_1) & f_2(p_2) & \ldots & f_2(p_N)\\ \vdots & \vdots & & \vdots\\ f_S(p_1) & f_S(p_2) & \ldots & f_S(p_N) \end{array} \right] \]

For vector valued functions function \(f_1, \ldots, f_S\) from \(\mathbb{R}^n\rightarrow\mathbb{R}^m\) the format is:

\[ \left[ \begin{array}{ccccc} f_1^1(p_1) & f_1^{(1)}(p_2) & \ldots & f_1^{(1)}(p_N)\\ f_1^2(p_1) & f_1^{(2)}(p_2) & \ldots & f_1^{(2)}(p_N)\\ \vdots & \vdots & & \vdots\\ f_1^{(m)}(p_1) & f_1^{(m)}(p_2) & \ldots & f_1^{(m)}(p_N)\\ f_2^{(1)}(p_1) & f_2^{(1)}(p_2) & \ldots & f_2^{(1)}(p_N)\\ \vdots & \vdots & & \vdots\\ f_S^{(m)}(p_1) & f_S^{(m)}(p_2) & \ldots & f_S^{(m)}(p_N) \end{array} \right] \]

where \(f^{(i)}_j\) is the \(i\)-th component of function \(f_j\) of the set.

Parameters

u
result

Reimplemented in gsBasis< T >, gsBasis< Scalar >, gsBasis< real_t >, gsTHBSplineBasis< d, T >, gsPatchIdField< T >, gsMaterialMatrixEvalSingle< T, out >, gsParamField< T >, gsTensorBSplineBasis< 1, T >, gsTensorBasis< d, T >, gsTensorBasis< 1, T >, gsShellStressFunction< T >, gsMaterialMatrixIntegrateSingle< T, out >, gsNormalField< T >, gsFsiLoad< T >, gsFunctionExpr< T >, gsGeometry< T >, gsLagrangeBasis< T >, gsMappedSingleBasis< d, T >, gsPiecewiseFunction< T >, gsConstantFunction< T >, gsJacDetField< T >, gsDetFunction< T >, gsRemapInterface< T >, gsFunction< T >, gsGradientField< T >, gsCPPInterface< T >, gsHBSplineBasis< d, T >, gsAffineFunction< T >, gsPreCICEFunction< T >, gsLegendreBasis< T >, gsMvLegendreBasis< T >, gsMappedSingleSpline< d, T >, gsConstantBasis< T >, gsMonomialBasis< T >, gsCauchyStressFunction< T >, gsBasisFun< T >, gsGeometrySlice< T >, gsGeometryTransform< T >, gsFuncCoordinate< T >, gsAbsError< T >, gsElementErrorPlotter< T >, and gsSquaredDistance< T >.

std::vector< gsMatrix< T > > evalAllDers ( const gsMatrix< T > &  u, int  n, bool  sameElement = false  ) const

inherited

Evaluate all derivatives upto order n,.

See Also

evalAllDers_into

void evalAllDers_into ( const gsMatrix< T > &  u, int  n, std::vector< gsMatrix< T > > &  result, bool  sameElement = false  ) const

virtualinherited

Evaluate the nonzero functions and their derivatives up to order n at points u into result.

The derivatives (the 0-th derivative is the function value) are stored in a result. result is a std::vector, where result[i] is a gsMatrix which contains the i-th derivatives.

The entries in result[0], result[1], and result[2] are ordered as in eval_into(), deriv_into(), and deriv2_into(), respectively. For i > 2, the derivatives are stored in lexicographical order, e.g. for order i = 3 and dimension 2 the derivatives are stored as follows: \( \partial_{xxx}, \, \partial_{xxy}, \, \partial_{xyy}, \, \partial_{yyy}.\, \)

Parameters

[in]	u	Evaluation points, each column corresponds to one evaluation point.
[in]	n	All derivatives up to order n are computed and stored in result.
[in,out]	result	See above for format.

Reimplemented in gsTensorBSplineBasis< 1, T >, gsTensorBasis< d, T >, gsTensorBasis< 1, T >, gsGeometry< T >, gsMappedSingleBasis< d, T >, gsConstantFunction< T >, gsTHBSplineBasis< d, T >, gsMappedSingleSpline< d, T >, and gsSquaredDistance< T >.

void matchInterface	(	const boundaryInterface &	bi,
		gsDofMapper &	mapper
	)		const

Matches the degrees of freedom along an interface.

The boundaryInterface specifying the interface is passed as argument.
The degrees of freedom (DOFs) along the interface from both patches are matched in the sense that they are then treated as one global DOF by the mapper.

Todo:

Check if this description is accurate.

Remarks

This function assumes tensor-product-structure with matching mesh along the interface! If the gsMultiBasis contains bases of class gsHTensorBasis (or derived), it calls the function matchInterfaceHTensor().

Parameters

bi	specifies the interface to be matched
mapper	the gsDofMapper which should know that these interface-DOFs are matched.

void refine ( size_t  k, gsMatrix< T > const &  boxes, int  refExt  )

inline

Refine the are defined by boxes on patch k with extension refExt.

See gsHTensorBasis::refineWithExtension() for further documentation.

void refineElements ( int  k, std::vector< index_t > const &  boxes  )

inline

Refine the are defined by boxes on patch k.

See gsHTensorBasis::refineElements() for further documentation.

bool repairInterface

(

const boundaryInterface &

bi

)

Checks if the interface is fully matching, and if not, repairs it.

Remarks

Designed for gsHTensorBasis and derived bases. Assumes that the respective meshes on all levels of the gsHTensorBasis are fully matching.

Returns

true, if something was repaired, i.e., if the mesh on the interface was changed.

bool repairInterface2d

(

const boundaryInterface &

bi

)

Checks if the 2D-interface is fully matching, and if not, repairs it.

Same as repairInterface(), but only for 2D and a bit more efficient.

Returns

true, if something was repaired, i.e., if the mesh on the interface was changed.

bool repairInterfaceFindElements	(	const boundaryInterface &	bi,
		std::vector< index_t > &	refEltsFirst,
		std::vector< index_t > &	refEltsSecond
	)

Finds the elements that need to be refined in order to repair an interface.

This function compares the hierarchical meshes on both patches associated with the boundaryInterface bi. The elements that need to be refined on bi.first() and bi.second() are stored in refEltsFirst and refEltsSecond, respectively.

Subsequent calls of the functions
m_bases[ bi.first().patch ]->refineElements( refEltsFirst )
m_bases[ bi.second().patch ]->refineElements( refEltsSecond )
will repair the interface in the sense that the resulting meshes are fully matching (this is done in repairInterface()).

Parameters

[in]	bi	bondaryInterface to be checked.
[out]	refEltsFirst	Contains elements (and levels) specifying needed refinement on patch bi.first().
[out]	refEltsSecond	Contains elements (and levels) specifying needed refinement on patch bi.second().

Returns

True, if anything needs to be refined (i.e., if refEltsFirst.size() > 0 or refEltsSecond.size() > 0).
False if the patches are already fully matching at interface bi.

Is called by repairInterface(), templated over dimension.

void repairInterfaces ( const std::vector< boundaryInterface > &  bivec )

inline

Checks if the interfaces bivec are fully matching, and if not, repairs them, i.e., makes them fully matching.

Remarks

Designed for gsHTensorBasis and derived bases. Assumes that the meshes on all levels of the gsHTensorBasis are fully matching.

Calls repairInterface() for each boundaryInterface in bivec.

index_t size ( ) const

inlinevirtual

size

Warning

gsFunction and gsGeometry have size() == 1. This should not be confused with the size eg. of gsGeometry::basis(), which is the number of basis functions in the basis

Returns

the size of the function set: the total number of functions

Reimplemented from gsFunctionSet< T >.

short_t targetDim ( ) const

inlinevirtual

Dimension of the target space.

Returns

For \(f:\mathbb{R}^n\rightarrow\mathbb{R}^m\), returns \(m\).

Reimplemented from gsFunctionSet< T >.

void tileParameters

(

)

Tile the parameter domains of the pieces according to the topology

void uniformCoarsen ( int  numKnots = 1 )

inline

Coarsen every basis uniformly.

This calls gsBasis::uniformCoarsen(numKnots) for all patches

void uniformCoarsen_withTransfer	(	gsSparseMatrix< T, RowMajor > &	transfer,
		const gsBoundaryConditions< T > &	boundaryConditions,
		const gsOptionList &	assemblerOptions,
		int	numKnots = 1,
		index_t	unk = 0
	)

Coarsen every basis uniformly.

The function writes a sparse matrix into the variable transfer that indicates how the functions on the coarse grid are represented as linear combinations as fine grid functions.

For computing the transfer matrix (but not for refinement), the boundaryConditions and the assemblerOptions have to be provided. By deault, the boundary conditions for unknown 0 are chosen. Use the parameter unk to choose another one.

See Also

gsMultiBasis::uniformCoarsen

void uniformRefine ( int  numKnots = 1, int  mul = 1, int  dir = -1  )

inline

Refine every basis uniformly.

This calls gsBasis::uniformRefine(numKnots,mul) for all patches

void uniformRefine_withTransfer	(	gsSparseMatrix< T, RowMajor > &	transfer,
		const gsBoundaryConditions< T > &	boundaryConditions,
		const gsOptionList &	assemblerOptions,
		int	numKnots = 1,
		int	mul = 1,
		index_t	unk = 0
	)

Refine every basis uniformly.

The function writes a sparse matrix into the variable transfer that indicates how the functions on the coarse grid are represented as linear combinations as fine grid functions.

For computing the transfer matrix (but not for refinement), the boundaryConditions and the assemblerOptions have to be provided. By deault, the boundary conditions for unknown 0 are chosen. Use the parameter unk to choose another one.

See Also

gsMultiBasis::uniformRefine