gsHeatEquation< T > Class Template Reference

Detailed Description

template<class T>
class gismo::gsHeatEquation< T >

Constructs the assembler for the discretized isogeometric heat equation.

Spatial solution is discretized using Galerkin's approach. Time integration scheme (method of lines) is controlled by the theta parameter (to be set in options)t. In particular

• Explicit Euler scheme (theta=0)
• Crank-Nicolson semi-implicit scheme (theta=0.5)
• implicit Euler scheme (theta=1)

Inheritance diagram for gsHeatEquation< T >:

Collaboration diagram for gsHeatEquation< T >:

Public Member Functions
const std::vector< gsMatrix< T > > &	allFixedDofs () const
	Returns all the Dirichlet values (if applicable)
void	assemble ()
	Initial assembly routine.
virtual void	assemble (const gsMultiPatch< T > &curSolution)
	Main non-linear assemble routine with input from current solution.
void	assembleMass ()
	Mass assembly routine.
bool	check ()
	checks for consistency and legal values of the stored members.
virtual gsAssembler *	clone () const
	Clone this Assembler, making a deep copy.
void	computeDirichletDofs (short_t unk=0)
	Triggers computation of the Dirichlet dofs. More...
virtual void	constructSolution (const gsMatrix< T > &solVector, gsMultiPatch< T > &result, short_t unk=0) const
	Construct solution from computed solution vector for a single unknows. More...
virtual void	constructSolution (const gsMatrix< T > &solVector, gsMultiPatch< T > &result, const gsVector< index_t > &unknowns) const
	Construct solution from computed solution vector for a set of unknowns. The result is a vectorfield, where each component is given the corresponding entry of. More...
virtual gsAssembler *	create () const
	Create an empty Assembler of the derived type and return a pointer to it. Call the initialize functions to set the members.
void	finalize ()
	finishes the assembling of the system matrix, i.e. calls its .makeCompressed() method.
const gsMatrix< T > &	fixedDofs (short_t unk=0) const
	Returns the Dirichlet values for a unknown (if applicable) More...
	gsHeatEquation (gsAssembler< T > &stationary)
	Construction receiving all necessary data.
void	homogenizeFixedDofs (short_t unk=0)
	Sets any Dirichlet values to homogeneous (if applicable) More...
void	initialize (const gsPde< T > &pde, const gsStdVectorRef< gsMultiBasis< T > > &bases, const gsOptionList &opt=defaultOptions())
	Intitialize function for, sets data fields using the pde, a vector of multi-basis and assembler options.
void	initialize (typename gsPde< T >::Ptr pde, const gsStdVectorRef< gsMultiBasis< T > > &bases, const gsOptionList &opt=defaultOptions())
	Intitialize function for, sets data fields using the pde, a vector of multi-basis and assembler options.
void	initialize (const gsPde< T > &pde, const gsMultiBasis< T > &bases, const gsOptionList &opt=defaultOptions())
	Intitialize function for, sets data fields using the pde, a multi-basis and assembler options.
void	initialize (const gsPde< T > &pde, const gsBasisRefs< T > &basis, const gsOptionList &opt=defaultOptions())
	Intitialize function for, sets data fields using the pde, a vector of bases and assembler options.
const gsSparseMatrix< T > &	matrix () const
	Returns the left-hand global matrix.
const gsMultiBasis< T > &	multiBasis (index_t k=0) const
	Return the multi-basis.
gsMultiBasis< T > &	multiBasis (index_t k=0)
	Return the multi-basis. Note: if the basis is altered, then refresh() should be called.
void	nextTimeStep (const gsMatrix< T > &curSolution, const T Dt)
	Computes the matrix and right-hand side for the next timestep. More...
index_t	numColNz () const
	Provides an estimation of the number of non-zero matrix entries per column. This value can be used for sparse matrix memory allocation.
index_t	numDofs () const
	Returns the number of (free) degrees of freedom.
size_t	numMultiBasis () const
	Returns the number of multi-bases.
const gsMultiPatch< T > &	patches () const
	Return the multipatch.
const gsPde< T > &	pde () const
	Return the Pde.
void	penalizeDirichletDofs (short_t unk=0)
T	penalty (index_t k) const
	Penalty constant for patch k, used for Nitsche and / Discontinuous Galerkin methods.
template<class ElementVisitor >
void	push ()
	Iterates over all elements of the domain and applies the ElementVisitor.
template<class BElementVisitor >
void	push (const bcContainer &BCs)
	Iterates over all elements of the boundaries BCs and applies the BElementVisitor.
template<class ElementVisitor >
void	push (const ElementVisitor &visitor)
	Iterates over all elements of the domain and applies the ElementVisitor.
template<class BElementVisitor >
void	push (const BElementVisitor &visitor, const boundary_condition< T > &BC)
	Applies the BElementVisitor to the boundary condition BC.
template<class InterfaceVisitor >
void	pushInterface ()
	Iterates over all elements of interfaces and applies the InterfaceVisitor.
virtual void	refresh ()
	Creates the mappers and setups the sparse system. to be implemented in derived classes, see scalarProblemGalerkinRefresh() for a possible implementation.
const gsMatrix< T > &	rhs () const
	Returns the left-hand side vector(s) ( multiple right hand sides possible )
void	setFixedDofs (const gsMatrix< T > &coefMatrix, short_t unk=0, size_t patch=0)
	the user can manually set the dirichlet Dofs for a given patch and unknown, based on the Basis coefficients More...
void	setFixedDofVector (gsMatrix< T > vals, short_t unk=0)
	the user can manually set the dirichlet Dofs for a given patch and unknown. More...
void	setSparseSystem (gsSparseSystem< T > &sys)
	Swaps the actual sparse system with the given one.
const gsSparseSystem< T > &	system () const
	Returns the left-hand global matrix.
virtual void	updateSolution (const gsMatrix< T > &solVector, gsMultiPatch< T > &result, T theta=(T)(1)) const
	Update solution by adding the computed solution vector to the current solution specified by. More...

Static Public Member Functions
static gsOptionList	defaultOptions ()
	Returns the list of default options for assembly.

Protected Member Functions
template<class ElementVisitor >
void	apply (ElementVisitor &visitor, size_t patchIndex=0, boxSide side=boundary::none)
	Generic assembly routine for volume or boundary integrals. More...
template<class InterfaceVisitor >
void	apply (InterfaceVisitor &visitor, const boundaryInterface &bi)
	Generic assembly routine for patch-interface integrals.
void	computeDirichletDofsIntpl (const gsDofMapper &mapper, const gsMultiBasis< T > &mbasis, const short_t unk_=0)
	calculates the values of the eliminated dofs based on Interpolation. More...
void	computeDirichletDofsL2Proj (const gsDofMapper &mapper, const gsMultiBasis< T > &mbasis, const short_t unk_=0)
	calculates the values of the eliminated dofs based on L2 Projection. More...
void	scalarProblemGalerkinRefresh ()
	A prototype of the refresh function for a "standard" scalar problem. Creats one mapper based on the set options and initializes the sparse system (without allocating memory.

Protected Attributes
std::vector< gsMultiBasis< T > >	m_bases
std::vector< gsMatrix< T > >	m_ddof
gsSparseMatrix< T >	m_mass
	The mass matrix.
gsOptionList	m_options
	Options.
memory::shared_ptr< gsPde< T > >	m_pde_ptr
gsSparseSystem< T >	m_system
	Global sparse linear system.
T	m_theta
	Theta parameter determining the scheme.

Member Function Documentation

void apply ( ElementVisitor &  visitor, size_t  patchIndex = 0, boxSide  side = boundary::none  )

protectedinherited

Generic assembly routine for volume or boundary integrals.

Parameters

[in]	visitor	The visitor for the boundary or volume integral
[in]	patchIndex	The considered patch
[in]	side	The considered boundary side, only necessary for boundary integrals.

void computeDirichletDofs ( short_t  unk = 0 )

inherited

Triggers computation of the Dirichlet dofs.

Parameters

[in]

unk

the considered unknown

void computeDirichletDofsIntpl ( const gsDofMapper &  mapper, const gsMultiBasis< T > &  mbasis, const short_t  unk_ = 0  )

protectedinherited

calculates the values of the eliminated dofs based on Interpolation.

Parameters

[in]	mapper	the dofMapper for the considered unknown
[in]	mbasis	the multipabasis for the considered unknown
[in]	unk_	the considered unknown

void computeDirichletDofsL2Proj ( const gsDofMapper &  mapper, const gsMultiBasis< T > &  mbasis, const short_t  unk_ = 0  )

protectedinherited

calculates the values of the eliminated dofs based on L2 Projection.

Parameters

[in]	mapper	the dofMapper for the considered unknown
[in]	mbasis	the multipabasis for the considered unknown
[in]	unk_	the considered unknown

void constructSolution ( const gsMatrix< T > &  solVector, gsMultiPatch< T > &  result, short_t  unk = 0  ) const

virtualinherited

Construct solution from computed solution vector for a single unknows.

Parameters

[in]	solVector	the solution vector obtained from the linear system
[out]	result	the solution in form of a gsMultiBasis
[in]	unk	the considered unknown

void constructSolution ( const gsMatrix< T > &  solVector, gsMultiPatch< T > &  result, const gsVector< index_t > &  unknowns  ) const

virtualinherited

Construct solution from computed solution vector for a set of unknowns. The result is a vectorfield, where each component is given the corresponding entry of.

unknowns. This method assumes that the specified unknowns have the

same basis.

Parameters

[in]	solVector	the solution vector obtained from the linear system
[out]	result	the solution seen as vectorfield in form of a gsMultiBasis
[in]	unknowns	the considered vector of unknowns

const gsMatrix<T>& fixedDofs ( short_t  unk = 0 ) const

inlineinherited

Returns the Dirichlet values for a unknown (if applicable)

Parameters

[in]

unk

the considered unknown

void homogenizeFixedDofs ( short_t  unk = 0 )

inlineinherited

Sets any Dirichlet values to homogeneous (if applicable)

Parameters

[in]

unk

the considered unknown

void nextTimeStep	(	const gsMatrix< T > &	curSolution,
		const T	Dt
	)

Computes the matrix and right-hand side for the next timestep.

The right-hand side function is assumed constant with respect to time

Parameters

curSolution	The solution of the previous timestep
Dt	Length of time interval of the current time step

void penalizeDirichletDofs ( short_t  unk = 0 )

inherited

Enforce Dirichlet boundary conditions by diagonal penalization

Parameters

[in]

unk

the considered unknown

void setFixedDofs ( const gsMatrix< T > &  coefMatrix, short_t  unk = 0, size_t  patch = 0  )

inherited

the user can manually set the dirichlet Dofs for a given patch and unknown, based on the Basis coefficients

Parameters

[in]	coefMatrix	the coefficients of the function
[in]	unk	the consideren unknown
[in]	patch	the patch index

void setFixedDofVector ( gsMatrix< T >  vals, short_t  unk = 0  )

inherited

the user can manually set the dirichlet Dofs for a given patch and unknown.

Parameters

[in]	vals	the values of the eliminated dofs.
[in]	unk	the considered unknown

void updateSolution ( const gsMatrix< T > &  solVector, gsMultiPatch< T > &  result, T  theta = (T)(1)  ) const

virtualinherited

Update solution by adding the computed solution vector to the current solution specified by.

result. This method assumes that all

unknowns have the same basis.

Parameters

[in]	solVector	the solution vector obtained from the linear system
[out]	result	the solution in form of a gsMultiBasis,

solVector is added to the

coefficients of result.

Parameters

[in]

theta

damping factor for update, theta = 1 corresponds to a full step.

Member Data Documentation

std::vector< gsMultiBasis<T> > m_bases

protectedinherited

The discretization bases corresponding to the patches and to the number of solution fields that are to be computed. One entry of the vector corresponds to one or more unknown (in case of a system of PDEs)

std::vector<gsMatrix<T> > m_ddof

protectedinherited

Fixed DoF values (if applicable, for instance eliminated Dirichlet DoFs). One entry of the vector corresponds to exactly one unknown, i.e. the size of m_ddof must fit m_system.colBlocks().

memory::shared_ptr<gsPde<T> > m_pde_ptr

protectedinherited

The PDE: contains multi-patch domain, boundary conditions and coeffcient functions