Reference documentation for deal.II version 9.6.1
 
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NonMatching::internal::QuadratureGeneratorImplementation::QPartitioning< dim > Class Template Reference

#include <deal.II/non_matching/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
 

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 815 of file quadrature_generator.h.

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 669 of file quadrature_generator.cc.

◆ clear()

Clears all quadratures.

Definition at line 687 of file quadrature_generator.cc.

Member Data Documentation

◆ negative

Quadrature for the region $\{x \in B : \psi_i(x) < 0 \forall i \}$ of the box, $B$.

Definition at line 835 of file quadrature_generator.h.

◆ positive

Quadrature for the region $\{x \in B : \psi_i(x) > 0 \forall i \}$ of the box, $B$.

Definition at line 841 of file quadrature_generator.h.

◆ indefinite

Quadrature for a region where the level set functions have different sign.

Definition at line 847 of file quadrature_generator.h.

◆ surface

Quadrature for the region $\{x \in B : \psi(x) = 0 \}$ of the box, $B$.

Definition at line 853 of file quadrature_generator.h.


The documentation for this class was generated from the following files: