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Reference documentation for deal.II version 9.4.1
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#include <deal.II/non_matching/quadrature_generator.h>
Public Member Functions | |
ExtendableQuadrature< dim > & | quadrature_by_definiteness (const Definiteness definiteness) |
Public Attributes | |
ExtendableQuadrature< dim > | negative |
ExtendableQuadrature< dim > | positive |
ExtendableQuadrature< dim > | indefinite |
ImmersedSurfaceQuadrature< dim > | surface |
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.
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 658 of file quadrature_generator.cc.
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 767 of file quadrature_generator.h.
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 773 of file quadrature_generator.h.
ExtendableQuadrature<dim> NonMatching::internal::QuadratureGeneratorImplementation::QPartitioning< dim >::indefinite |
Quadrature for a region where the level set functions have different sign.
Definition at line 779 of file quadrature_generator.h.
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 785 of file quadrature_generator.h.