Reference documentation for deal.II version GIT 1e9e64a91d 2022-09-28 19:20:02+00:00
NonMatching::FaceQuadratureGenerator< dim > Class Template Reference

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

Inheritance diagram for NonMatching::FaceQuadratureGenerator< dim >:
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## Public Member Functions

void generate (const Function< dim > &level_set, const BoundingBox< dim > &box, const unsigned int face_index)

void set_1D_quadrature (const unsigned int q_index)

## Detailed Description

### template<int dim> class NonMatching::FaceQuadratureGenerator< dim >

This class creates immersed quadrature rules over a face, $$F$$, of a BoundingBox, when the domain is described by a level set function, $$\psi$$.

In the same way as in the QuadratureGenerator class, this class generates quadrature rules to integrate over 3 different regions of the face, $$F \subset \mathbb{R}^{dim}$$:

$N = \{x \in F : \psi(x) < 0 \}, \\ P = \{x \in F : \psi(x) > 0 \}, \\ S = \{x \in F : \psi(x) = 0 \},$

which are again referred to as the "inside", $$N$$, "outside", $$P$$, and "surface" region, $$S$$. These type of quadrature rules are in general needed in immersed discontinuous Galerkin methods.

Under the hood, this class uses the QuadratureGenerator class to build these rules. This is done by restricting the dim-dimensional level set function to the face, thus creating a (dim-1)-dimensional level set function, $$\phi$$. It then creates the (dim-1)-dimensional quadratures by calling QuadratureGenerator with $$\phi$$. This means that what holds for the QuadratureGenerator class in general also holds for this class. In particular, if the 1D-quadrature that is used as base contains $$n$$ points, the number of points will be proportional to $$n^{dim-1}$$ in the in the inside/outside quadratures and to $$n^{dim-2}$$ in the surface quadrature.

Definition at line 292 of file quadrature_generator.h.

## Member Typedef Documentation

template<int dim>

Definition at line 295 of file quadrature_generator.h.

## Constructor & Destructor Documentation

template<int dim>
 NonMatching::FaceQuadratureGenerator< dim >::FaceQuadratureGenerator ( const hp::QCollection< 1 > & quadratures1D, const AdditionalData & additional_data = AdditionalData() )

Constructor. Each Quadrature<1> in quadratures1D can be chosen as base for generating the immersed quadrature rules.

Note
It is important that each 1D-quadrature rule in the hp::QCollection does not contain the points 0 and 1.

Definition at line 1703 of file quadrature_generator.cc.

## ◆ generate()

template<int dim>
 void NonMatching::FaceQuadratureGenerator< dim >::generate ( const Function< dim > & level_set, const BoundingBox< dim > & box, const unsigned int face_index )

Construct immersed quadratures rules for the incoming level set function on a given face of the BoundingBox.

Note
Both value, gradient and hessian need to be implemented on the incoming function.

Definition at line 1713 of file quadrature_generator.cc.

template<int dim>

Return the quadrature rule for the region $$\{x \in F : \psi(x) < 0 \}$$ created in the previous call to generate(). Here, $$F$$ is the face of the BoundingBox passed to generate().

Definition at line 1775 of file quadrature_generator.cc.

template<int dim>

Return the quadrature rule for the region $$\{x \in F : \psi(x) > 0 \}$$ created in the previous call to generate(). Here, $$F$$ is the face of the BoundingBox passed to generate().

Definition at line 1783 of file quadrature_generator.cc.

template<int dim>

Return the quadrature rule for the region $$\{x \in F : \psi(x) = 0 \}$$ created in the previous call to generate(). Here, $$F$$ is the face of the BoundingBox passed to generate().

Note
The normal at the quadrature points will be parallel to $$\nabla \psi$$.

Definition at line 1792 of file quadrature_generator.cc.

template<int dim>

Set which 1D-quadrature in the collection passed to the constructor should be used to create the immersed quadratures.

Definition at line 1766 of file quadrature_generator.cc.

## Member Data Documentation

template<int dim>
private

Definition at line 366 of file quadrature_generator.h.