#include <deal.II/non_matching/quadrature_generator.h>

Detailed Description

template<int dim>
class NonMatching::internal::QuadratureGeneratorImplementation::QPartitioning< dim >

Class that stores quadrature rules to integrate over 4 different regions of a single BoundingBox, $B$ . Given multiple level set functions,

$\psi_i : \mathbb{R}^{dim} \rightarrow \mathbb{R}$ , $i = 0, 1, ...$ ,

the box, $B \subset \mathbb{R}^{dim}$ , is partitioned into a "negative", "positive", and "indefinite" region, $B = N \cup P \cup I$ , according to the signs of $\psi_i$ over each region:

$\‍[N = \{x \in B : \psi_i(x) < 0, \forall i \}, \\ P = \{x \in B : \psi_i(x) > 0, \forall i \}, \\ I = B \setminus (\overline{N} \cup \overline{P}). \‍]$

Thus, all $\psi_i$ are positive over $P$ and negative over $N$ . Over $I$ the level set functions differ in sign. This class holds quadrature rules for each of these regions. In addition, when there is a single level set function, $\psi$ , it holds a surface quadrature for the zero contour of $\psi$ :

$S = \{x \in B : \psi(x) = 0 \}$ .

Note that when there is a single level set function, $I$ is empty and $N$ and $P$ are the regions that one typically integrates over in an immersed finite element method.

Definition at line 812 of file quadrature_generator.h.

Public Member Functions
ExtendableQuadrature< dim > &	quadrature_by_definiteness (const Definiteness definiteness)
void	clear ()

Public Attributes
ExtendableQuadrature< dim >	negative
ExtendableQuadrature< dim >	positive
ExtendableQuadrature< dim >	indefinite
ImmersedSurfaceQuadrature< dim >	surface

Member Function Documentation

◆ quadrature_by_definiteness()

template<int dim>

ExtendableQuadrature< dim > & NonMatching::internal::QuadratureGeneratorImplementation::QPartitioning< dim >::quadrature_by_definiteness ( const Definiteness definiteness )

Return a reference to the "bulk" quadrature with the same name as the member in Definiteness.

Definition at line 670 of file quadrature_generator.cc.