Reference documentation for deal.II version 9.4.1
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NonMatching::internal::QuadratureGeneratorImplementation::QPartitioning< dim > Class Template Reference

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

## Detailed Description

template<int 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 753 of file quadrature_generator.h.

## Member Function Documentation

template<int dim>

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

Definition at line 658 of file quadrature_generator.cc.

## ◆ negative

template<int dim>

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

Definition at line 767 of file quadrature_generator.h.

## ◆ positive

template<int dim>

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

Definition at line 773 of file quadrature_generator.h.

## ◆ indefinite

template<int dim>

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

Definition at line 779 of file quadrature_generator.h.

## ◆ surface

template<int dim>

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

Definition at line 785 of file quadrature_generator.h.

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