gsVisitorNitsche< T > Class Template Reference

Detailed Description

template<class T>
class gismo::gsVisitorNitsche< T >

Visitor for adding the terms associated to weak (Nitsche-type) imposition of the Dirichlet boundary conditions.

This visitor adds the following term to the left-hand side (bilinear form):

\[ \alpha \int_{\Gamma_D} \nabla u \cdot \mathbf{n} v + \beta \int_{\Gamma_D} \nabla v \cdot \mathbf{n} u + \delta h^{-1} \int_{\Gamma_D} u v \]

and the following terms to the right-hand side (linear form):

\[ \beta \int_{\Gamma_D} g_D \nabla v \cdot \mathbf{n} u + \delta h^{-1} \int_{\Gamma_D} g_D v \cdot \mathbf{n} u, \]

where \(g_D\) is the Dirichlet value.

The default values for Nitsche.Alpha and Nitsche.Beta are \(\alpha=\beta=1\), which corresponds to the standard Nitsche method. The default value for Nitsche.Penalty is -1, which yields \(\delta=2.5(p+d)(p+1)\). If a positive value for Nitsche.Penalty is chosen, that value is taken for \(\delta\).

The (normal) grid sizes are estimated based on the geometry function. Use the option Nitsche.ParameterGridSize to just use the grid size on the parameter domain.

An analogous visitor for handling the internal smoothness weakly, is the gsVisitorDg.

Collaboration diagram for gsVisitorNitsche< T >:

Public Member Functions
void	assemble (gsDomainIterator< T > &element, const gsVector< T > &quWeights)
	Assemble on element.
void	evaluate (const gsBasis< T > &basis, const gsGeometry< T > &geo, const gsMatrix< T > &quNodes)
	Evaluate on element.
	gsVisitorNitsche (const gsPde< T > &pde, const boundary_condition< T > &bc)
	Constructor. More...
void	initialize (const gsBasis< T > &basis, const index_t, const gsOptionList &options, gsQuadRule< T > &rule)
	Initialize.
void	localToGlobal (const index_t patchIndex, const std::vector< gsMatrix< T > > &, gsSparseSystem< T > &system)
	Adds the contributions to the sparse system.
void	localToGlobal (const gsDofMapper &mapper, const gsMatrix< T > &eliminatedDofs, const index_t patchIndex, gsSparseMatrix< T > &sysMatrix, gsMatrix< T > &rhsMatrix)
	Adds the contributions to the sparse system.

Static Public Member Functions
static gsOptionList	defaultOptions ()
	Default options.

Private Attributes
T	m_alpha
	Parameter \(\alpha\) for the linear form.
T	m_beta
	Parameter \(\beta\) for the linear form.
const gsFunctionSet< T > *	m_dirdata_ptr
	Dirichlet function.
const gsPde< T > *	m_pde
	The underlying PDE.
T	m_penalty
	Parameter \(\delta\) for the linear form.
patchSide	m_side
	Patch side.

Constructor & Destructor Documentation

gsVisitorNitsche ( const gsPde< T > &  pde, const boundary_condition< T > &  bc  )

inline

Constructor.

Parameters

pde	Reference to gsPde object
bc	The boundary condition to be realized