gsVisitorCDR< T > Class Template Reference

Detailed Description

template<class T>
class gismo::gsVisitorCDR< T >

Visitor for the convection-diffusion-reaction equation.

Visitor for PDEs of the form
Find \( u: \mathbb R^d \rightarrow \mathbb R^d\)

\[ -\mathrm{div}( A \nabla u ) + b\cdot \nabla u + c u = f \]

(+ boundary conditions), where
\( A \) (diffusion coefficient) is a \(d\times d\)-matrix,
\( b \) (convection velocity) is a \(d\times 1\)-vector,
\( c \) (reaction coefficient) is a scalar

The coefficients are given as gsFunction with vector-valued return.
See the constructor gsVisitorCDR() for details on their format!

Obviously, setting \( A = I\), \( b = 0\), and \(c = 0\) results in the special case of the Poisson equation.

Collaboration diagram for gsVisitorCDR< T >:

Public Member Functions
void	assemble (gsDomainIterator< T > &element, const gsVector< T > &quWeights)
	Assemble.
void	evaluate (const gsBasis< T > &basis, const gsGeometry< T > &geo, const gsMatrix< T > &quNodes)
	Evaluate on element.
T	getSUPGParameter (const gsVector< T > &lo, const gsVector< T > &up)
	Returns the parameter required for SUPG.
	gsVisitorCDR (const gsPde< T > &pde)
	Constructor. More...
	gsVisitorCDR (const gsFunction< T > &rhs, const gsFunction< T > &coeff_A, const gsFunction< T > &coeff_b, const gsFunction< T > &coeff_c, stabilizerCDR::method flagStabilization=stabilizerCDR::SUPG)
	Constructor for gsVisitorCDR, convection-diffusion-reaction. More...
void	initialize (const gsBasis< T > &basis, const index_t, const gsOptionList &options, gsQuadRule< T > &rule)
	Initialize.

Constructor & Destructor Documentation

gsVisitorCDR ( const gsPde< T > &  pde )

inline

Constructor.

Parameters

pde	Reference to gsConvDiffRePde object

gsVisitorCDR ( const gsFunction< T > &  rhs, const gsFunction< T > &  coeff_A, const gsFunction< T > &  coeff_b, const gsFunction< T > &  coeff_c, stabilizerCDR::method  flagStabilization = stabilizerCDR::SUPG  )

inline

Constructor for gsVisitorCDR, convection-diffusion-reaction.

Parameters

[in]	rhs	Given right-hand-side function/source term that, for each evaluation point, returns a scalar.
[in]	coeff_A	gsFunction that, for each evaluation point, returns a vector of size \(d^2\). The entries of \(A\) should appear in the order (for \(d=3\)) \( (A_{11},A_{21},A_{31},A_{12},A_{22},A_{32},A_{13},A_{23},A_{33})^T\), such that A.resize(d,d) returns the correct matrix.
[in]	coeff_b	gsFunction that, for each evaluation point, returns a vector of size \(d\).
[in]	coeff_c	gsFunction that, for each evaluation point, returns a scalar.
[in]	flagStabilization	Specifies stabilization for the convection term. 0: no stabilization 1: SUPG-stabilization