Detailed Description

This module is responsible for generating matrices that discretize a PDE.

Namespaces
	gismo::expr
	This namespace contains expressions used for FE computations.

Classes
class	gsAssembler< T >
	The assembler class provides generic routines for volume and boundary integrals that are used for for matrix and right-hand side generation. More...

class	gsCDRAssembler< T >
	Implementation of an (multiple righ-hand side) Poisson solver. More...

class	gsCPPInterface< T >
	Provides a mapping between the corresponding sides of two patches sharing an interface, by means of a closest point projection. More...

class	gsGaussRule< T >
	Class that represents the (tensor) Gauss-Legendre quadrature rule. More...

class	gsGenericAssembler< T >
	Assembles mass and stiffness matrices and right-hand sides on a given domain. More...

class	gsHeatEquation< T >
	Constructs the assembler for the discretized isogeometric heat equation. More...

class	gsLobattoRule< T >
	Class that represents the (tensor) Gauss-Lobatto quadrature rule. More...

class	gsNewtonCotesRule< T >
	Class that represents the (tensor) Newton-Cotes quadrature rule. More...

class	gsOverIntegrateRule< T >
	Class that defines a mixed quadrature rule with different rules for the interior and the boundaries. More...

class	gsPatchRule< T >
	Class that represents the (tensor) patch quadrature rule. More...

class	gsPoissonAssembler< T >
	Implementation of an (multiple right-hand side) Poisson assembler. More...

class	gsQuadRule< T >
	Class representing a reference quadrature rule. More...

class	gsRemapInterface< T >
	Provides a mapping between the corresponding sides of two patches sharing an interface. More...

class	gsSparseSystem< T, symm >
	A sparse linear system indexed by sets of degrees of freedom. More...

class	gsVisitorBiharmonic< T >
	Visitor for the biharmonic equation. More...

class	gsVisitorCDR< T >
	Visitor for the convection-diffusion-reaction equation. More...

class	gsVisitorDg< T >
	Visitor for adding the interface conditions for the interior penalty methods of the Poisson problem. More...

class	gsVisitorGradGrad< T >
	The visitor computes element grad-grad integrals. More...

class	gsVisitorMass< T >
	The visitor computes element mass integrals. More...

class	gsVisitorMoments< T, paramCoef >
	Visitor for the moment vector of a function. More...

class	gsVisitorNeumann< T >
	Implementation of a Neumann BC for elliptic assemblers. More...

class	gsVisitorNeumannBiharmonic< T >
	Visitor for Neumann boundary condition for the biharmonic equation. More...

class	gsVisitorNitsche< T >
	Visitor for adding the terms associated to weak (Nitsche-type) imposition of the Dirichlet boundary conditions. More...

class	gsVisitorNitscheBiharmonic< T >
	Visitor for the weak imposition of the first-type dirichlet boundary condition. More...

class	gsVisitorPoisson< T, paramCoef >
	Visitor for the Poisson equation. More...

Functions
template<bool _coarsen, bool _admissible>
void	_markElements (const std::vector< T > &elError, const index_t refCriterion, const std::vector< gsHBoxCheck< 2, T > * > &predicates, HBoxContainer &elMarked) const
	Marks elements/cells for refinement. More...

template<class T >
void	gsMarkElementsForRef (const std::vector< T > &elError, int refCriterion, T refParameter, std::vector< bool > &elMarked)
	Marks elements/cells for refinement. More...

	gsPoissonAssembler (gsMultiPatch< T > const &patches, gsMultiBasis< T > const &basis, gsBoundaryConditions< T > const &bconditions, const gsFunction< T > &rhs, dirichlet::strategy dirStrategy=dirichlet::elimination, iFace::strategy intStrategy=iFace::glue)
	Constructor of the assembler object. More...

template<class T >
void	gsRefineMarkedElements (gsMultiBasis< T > &basis, const std::vector< bool > &elMarked, index_t refExtension=0)
	Refine a gsMultiBasis, based on a vector of element-markings. More...

template<class T >
void	gsUnrefineMarkedElements (gsMultiBasis< T > &basis, const std::vector< bool > &elMarked, index_t refExtension=0)
	Unrefine a gsMultiBasis, based on a vector of element-markings. More...

Function Documentation

void _markElements	(	const std::vector< T > &	elError,
		const index_t	refCriterion,
		const std::vector< gsHBoxCheck< 2, T > * > &	predicates,
		HBoxContainer &	elMarked
	)		const

private

Marks elements/cells for refinement.

Let the global error/error estimate \(\eta\) be a sum of element/cell-wise local contributions:

\[ \eta = \sum_{K} \eta_k \quad \mathrm{or} \quad \eta^2 = \sum_K \eta_K^2 \]

Computes a threshold \(\Theta\) and marks all elements \(K\) for refinement, for which

\[ \eta_K \geq \Theta \]

holds. Three criteria for computing \(\Theta\) are currently (26.Nov.2014) implemented:

Let \(\rho\) denote the m_input parameter parameter.

refCriterion = 1 = treshold, GARU-criterion (greatest appearing eRror utilization):
Threshold computed based on the largest of all appearing local errors:

\[ \Theta = \rho \cdot \max_K \{ \eta_K \} \]

The actual number of marked elements can vary in each refinement step, depending on the distribution of the error.

refCriterion = 2 = cellPercentage, PUCA-criterion (percentile-utilizing cutoff ascertainment):
In each step, a certain percentage of all elements are marked.

\[ \Theta = (1-\rho)\cdot 100\ \textrm{-percentile of}\ \{ \eta_K \}_K \]

For example, if \(\rho = 0.8\), those 20% of all elements which have the largest local errors are marked for refinement.

refCriterion = 3 = errorFraction, BULK-criterion ("Doerfler-marking"):
The threshold is chosen in such a manner that the local errors on the marked cells sum up to a certain fraction of the global error:

\[ \sum_{ K:\ \eta_K \geq \Theta } \eta_K \geq (1-\rho) \cdot \eta \]

Parameters

	elError	std::vector of local errors on some elements.
	refCriterion	selects the criterion (see above) for marking elements.
	parameter	parameter \( \rho \) for refinement criterion (see above). \(\rho = 0\) corresponds to global refinement, \( \rho=1\) corresponds to (almost) no refinement.
[out]	elMarked	std::vector of Booleans indicating whether the corresponding element is marked or not.

void gismo::gsMarkElementsForRef	(	const std::vector< T > &	elError,
		int	refCriterion,
		T	refParameter,
		std::vector< bool > &	elMarked
	)

Marks elements/cells for refinement.

Let the global error/error estimate \(\eta\) be a sum of element/cell-wise local contributions:

\[ \eta = \sum_{K} \eta_k \quad \mathrm{or} \quad \eta^2 = \sum_K \eta_K^2 \]

Computes a threshold \(\Theta\) and marks all elements \(K\) for refinement, for which

\[ \eta_K \geq \Theta \]

holds. Three criteria for computing \(\Theta\) are currently (26.Nov.2014) implemented:

Let \(\rho\) denote the input parameter refParameter.

refCriterion = 1 = treshold, GARU-criterion (greatest appearing eRror utilization):
Threshold computed based on the largest of all appearing local errors:

\[ \Theta = \rho \cdot \max_K \{ \eta_K \} \]

The actual number of marked elements can vary in each refinement step, depending on the distribution of the error.

refCriterion = 2 = cellPercentage, PUCA-criterion (percentile-utilizing cutoff ascertainment):
In each step, a certain percentage of all elements are marked.

\[ \Theta = (1-\rho)\cdot 100\ \textrm{-percentile of}\ \{ \eta_K \}_K \]

For example, if \(\rho = 0.8\), those 20% of all elements which have the largest local errors are marked for refinement.

refCriterion = 3 = errorFraction, BULK-criterion ("Doerfler-marking"):
The threshold is chosen in such a manner that the local errors on the marked cells sum up to a certain fraction of the global error:

\[ \sum_{ K:\ \eta_K \geq \Theta } \eta_K \geq (1-\rho) \cdot \eta \]

Parameters

	elError	std::vector of local errors on some elements.
	refCriterion	selects the criterion (see above) for marking elements.
	refParameter	parameter \( \rho \) for refinement criterion (see above). \(\rho = 0\) corresponds to global refinement, \( \rho=1\) corresponds to (almost) no refinement.
[out]	elMarked	std::vector of Booleans indicating whether the corresponding element is marked or not.

gsPoissonAssembler	(	gsMultiPatch< T > const &	patches,
		gsMultiBasis< T > const &	basis,
		gsBoundaryConditions< T > const &	bconditions,
		const gsFunction< T > &	rhs,
		dirichlet::strategy	dirStrategy = `dirichlet::elimination`,
		iFace::strategy	intStrategy = `iFace::glue`
	)

inline

Constructor of the assembler object.

Parameters

[in]	patches	is a gsMultiPatch object describing the geometry.
[in]	basis	a multi-basis that contains patch-wise bases
[in]	bconditions	is a gsBoundaryConditions object that holds all boundary conditions.
[in]	rhs	is the right-hand side of the Poisson equation, \(\mathbf{f}\).
[in]	dirStrategy	option for the treatment of Dirichlet boundary
[in]	intStrategy	option for the treatment of patch interfaces

void gismo::gsRefineMarkedElements	(	gsMultiBasis< T > &	basis,
		const std::vector< bool > &	elMarked,
		index_t	refExtension = `0`
	)

Refine a gsMultiBasis, based on a vector of element-markings.

Given the vector of element-markings (see gsRefineMarkedElements()), the corresponding element in the mesh underlying basis is refined.

It is possible to extend the refinement to the neighbouring elements of the marked area by setting the parameter refExtension.
This parameter is given as number of cells at the level of the marked element before refinement.

Remarks: The ordering/numbering of the elements is implicitly defined by the numbering of the patches in gsMultiBasis, and by the gsDomainIterator of the respective patch-wise basis!

Parameters

basis	gsMultiBasis to be refined adaptively.
elMarked	std::vector of Booleans indicating for each element of the mesh underlying basis, whether it should be refined or not.
refExtension	Specifies how large the refinement extension should be. Given as number of cells at the level before refinement.

Todo:: Make gsRefineMarkedElements a member of gsMultiBasis and propagate to gsBasis

void gismo::gsUnrefineMarkedElements	(	gsMultiBasis< T > &	basis,
		const std::vector< bool > &	elMarked,
		index_t	refExtension = `0`
	)

Unrefine a gsMultiBasis, based on a vector of element-markings.

Given the vector of element-markings (see gsRefineMarkedElements()), the corresponding element in the mesh underlying basis is refined.

It is possible to extend the refinement to the neighbouring elements of the marked area by setting the parameter refExtension.
This parameter is given as number of cells at the level of the marked element before refinement.

Remarks: The ordering/numbering of the elements is implicitly defined by the numbering of the patches in gsMultiBasis, and by the gsDomainIterator of the respective patch-wise basis!

Parameters

basis	gsMultiBasis to be refined adaptively.
elMarked	std::vector of Booleans indicating for each element of the mesh underlying basis, whether it should be refined or not.
refExtension	Specifies how large the refinement extension should be. Given as number of cells at the level before refinement.

Todo:: Make gsRefineMarkedElements a member of gsMultiBasis and propagate to gsBasis

Detailed Description

Namespaces

Classes

Functions

Function Documentation