NonMatching::internal::QuadratureGeneratorImplementation::QPartitioning< dim > Class Template Reference

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 810 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 669 of file quadrature_generator.cc.

clear()

template<int dim>

void NonMatching::internal::QuadratureGeneratorImplementation::QPartitioning< dim >::clear

(

)

Clears all quadratures.

Definition at line 687 of file quadrature_generator.cc.

Member Data Documentation

negative

template<int dim>

ExtendableQuadrature<dim> NonMatching::internal::QuadratureGeneratorImplementation::QPartitioning< dim >::negative

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

Definition at line 830 of file quadrature_generator.h.

positive

template<int dim>

ExtendableQuadrature<dim> NonMatching::internal::QuadratureGeneratorImplementation::QPartitioning< dim >::positive

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

Definition at line 836 of file quadrature_generator.h.

indefinite

template<int dim>

ExtendableQuadrature<dim> NonMatching::internal::QuadratureGeneratorImplementation::QPartitioning< dim >::indefinite

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

Definition at line 842 of file quadrature_generator.h.

surface

template<int dim>

ImmersedSurfaceQuadrature<dim> NonMatching::internal::QuadratureGeneratorImplementation::QPartitioning< dim >::surface

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

Definition at line 848 of file quadrature_generator.h.

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

• include/deal.II/non_matching/quadrature_generator.h
• source/non_matching/quadrature_generator.cc