Reference documentation for deal.II version GIT relicensing-687-gbf51c6da8c 2024-05-21 02:00:02+00:00
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Public Member Functions | Public Attributes | List of all members
NonMatching::internal::QuadratureGeneratorImplementation::QPartitioning< dim > Class Template Reference

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: