gsBiharmonicPde< T > Class Template Reference

Detailed Description

template<class T>
class gismo::gsBiharmonicPde< T >

A Biharmonic PDE.

This class describes a Biharmonic PDE, with an arbitrary right-hand side function.

It has an extra gsBoundaryConditions object since the biharmonic has two essential (Dirichlet) and two natural (Neumann). The second gsBoundaryConditions contains the second kind of BC.

The first kind of BCs Dirichlet: Enforce \(v = 0 \) on the boundary Neumann: Add \( (g,v)_\Gamma \) on the right-hand side, where \(g = -\nabla \Delta u \cdot \mathbf{n}\)

The second kind of BCs Dirichlet: Enforce \( \nabla v \cdot \mathbf{n} = 0 \) on the boundary Neumann: Add \( (g,\nabla v \cdot \mathbf{n})_\Gamma \) on the right-hand side, where \(g = \Delta u \)

Inheritance diagram for gsBiharmonicPde< T >:

Collaboration diagram for gsBiharmonicPde< T >:

Public Member Functions
gsBoundaryConditions< T > &	boundaryConditions ()
	Returns a reference to the Pde boundary conditions. More...
GISMO_DEPRECATED short_t	dim () const
	returns the dimension of the domain
gsMultiPatch< T > &	domain ()
	Returns a reference to the Pde domain. More...
GISMO_DEPRECATED int	fieldDim (index_t field_id=0)
	gives the dimension of the i-th field it returns 1 for scalar fields, 2 for 2d vectors field etc. More...
	gsBiharmonicPde (const gsMultiPatch< T > &domain, const gsBoundaryConditions< T > &bc1, const gsBoundaryConditions< T > &bc2, const gsPiecewiseFunction< T > &rhs)
	Constructor.
virtual int	numRhs () const
	gives the number of rhs functions of the PDEs
int	numUnknowns () const
	Gives the number of unknown fields of the PDEs.
std::ostream &	print (std::ostream &os) const
	Prints the object as a string.
virtual gsPde< T > *	restrictToPatch (unsigned) const
	restrictToPatch creats a new PDE object for a single patch np. More...
const gsVector< unsigned > &	unknownDim () const
	Gives the vector of dimensions of the unknowns.

Protected Attributes
gsBoundaryConditions< T >	m_boundary_conditions
	Boundary conditions.
gsBoundaryConditions< T >	m_boundary_conditions_second
	Boundary conditions of the second kind.
gsMultiPatch< T >	m_domain
	Computational domain.
gsVector< unsigned >	m_unknownDim
	Description of the unknown fields: for each one the target dimension.

Member Function Documentation

gsBoundaryConditions<T>& boundaryConditions ( )

inlineinherited

Returns a reference to the Pde boundary conditions.

There is also a const version returning a const reference.

gsMultiPatch<T>& domain ( )

inlineinherited

Returns a reference to the Pde domain.

There is also a const version returning a const reference.

GISMO_DEPRECATED int fieldDim ( index_t  field_id = 0 )

inlineinherited

gives the dimension of the i-th field it returns 1 for scalar fields, 2 for 2d vectors field etc.

Parameters

field_id

the field index

virtual gsPde<T>* restrictToPatch ( unsigned  ) const

inlinevirtualinherited

restrictToPatch creats a new PDE object for a single patch np.

Parameters

np	the patch index

Returns

a pointer to an allocated gsPDE<T> object.

Reimplemented in gsPoissonPde< T >.