NonMatching::internal::QuadratureGeneratorImplementation::UpThroughDimensionCreator< dim, spacedim > Class Template Reference

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

Public Member Functions
	UpThroughDimensionCreator (const hp::QCollection< 1 > &q_collection1D, const AdditionalQGeneratorData &additional_data)
void	generate (const std::vector< std::reference_wrapper< const Function< dim > > > &level_sets, const BoundingBox< dim > &box, const Quadrature< dim - 1 > &low_dim_quadrature, const unsigned int height_function_direction, QPartitioning< dim > &q_partitioning)
void	set_1D_quadrature (const unsigned int q_index)

Private Member Functions
void	create_surface_point (const Point< dim - 1 > &point, const double weight, const std::vector< std::reference_wrapper< const Function< dim > > > &level_sets, const BoundingBox< dim > &box, const unsigned int height_function_direction, ImmersedSurfaceQuadrature< dim > &surface_quadrature)

Private Attributes
const SmartPointer< const hp::QCollection< 1 > >	q_collection1D
const AdditionalQGeneratorData	additional_data
unsigned int	q_index
std::vector< Functions::PointRestriction< dim - 1 > >	point_restrictions
RootFinder	root_finder
std::vector< double >	roots

Detailed Description

template<int dim, int spacedim>
class NonMatching::internal::QuadratureGeneratorImplementation::UpThroughDimensionCreator< dim, spacedim >

This class is responsible for creating quadrature points for the \(dim\)-dimensional quadrature partitioning from an \((dim - 1)\)-dimensional "indefinite" quadrature (see QPartitioning documentation).

To be precise, let \([L, R]\) be the extents of the box in the height function direction and let \(I \subset \mathbb{R}^{dim-1}\) be the lower dimensional indefinite region. This class will create quadrature points over \(I \times [L, R] \subset \mathbb{R}^{dim}\) and in the case \(dim=spacedim\), points for the surface quadrature.

For each lower dimensional quadrature point, \((x_I, w_I)\) in the indefinite quadrature, we create several 1D-level set functions by restricting \(\psi_j\) to \(x_I\). We then partition the interval \([L, R]\) into \([y_0, y_1, ..., y_n]\), where \(y_0 = L\), \(y_n = R\), and the remaining \(y_i\) are the roots of the 1D-level set functions in \([L, R]\). Since the level set functions change sign between the roots, each interval belong to different regions in the quadrature partitioning.

In each interval, \([y_i, y_{i+1}]\), we distribute points according to the 1D-base quadrature, \((x_q, w_q)\) and take the cartesian product with \((x_I, w_I)\) to create the \(dim\)-dimensional quadrature points, \((X_q, W_q)\): \(X_q = x_I \times (y_i + (y_{i+1} - y_i) x_q)\), \(W_q = w_I (y_{i+1} - y_i) w_q\).

When \(dim=spacedim\), we have a single level set function, \(\psi\). Since we have fulfilled the implicit function theorem, there is a single root \(y_1 \in [L, R]\). The point, \(x_s = x_I \times y_1\), will be added as a point in the surface quadrature. One can show that the correct weight of this point is

\(w_s = \frac{\|\nabla \psi(x_s)\|}{|\partial_i \psi(x_s)|} w_I\),

where \(i\) is the height function direction.

Definition at line 828 of file quadrature_generator.h.

Constructor & Destructor Documentation

UpThroughDimensionCreator()

template<int dim, int spacedim>

NonMatching::internal::QuadratureGeneratorImplementation::UpThroughDimensionCreator< dim, spacedim >::UpThroughDimensionCreator	(	const hp::QCollection< 1 > &	q_collection1D,
		const AdditionalQGeneratorData &	additional_data
	)

Constructor. Takes the same parameters as QuadratureGenerator.

Definition at line 709 of file quadrature_generator.cc.

Member Function Documentation

generate()

template<int dim, int spacedim>

void NonMatching::internal::QuadratureGeneratorImplementation::UpThroughDimensionCreator< dim, spacedim >::generate	(	const std::vector< std::reference_wrapper< const Function< dim > > > &	level_sets,
		const BoundingBox< dim > &	box,
		const Quadrature< dim - 1 > &	low_dim_quadrature,
		const unsigned int	height_function_direction,
		QPartitioning< dim > &	q_partitioning
	)

Create \(dim\)-dimensional immersed quadratures from the incoming \((dim-1)\)-dimensional quadratures and add these to q_partitioning.

Definition at line 725 of file quadrature_generator.cc.

set_1D_quadrature()

template<int dim, int spacedim>

void NonMatching::internal::QuadratureGeneratorImplementation::UpThroughDimensionCreator< dim, spacedim >::set_1D_quadrature

(

const unsigned int

q_index

)

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

Definition at line 835 of file quadrature_generator.cc.

create_surface_point()

template<int dim, int spacedim>

void NonMatching::internal::QuadratureGeneratorImplementation::UpThroughDimensionCreator< dim, spacedim >::create_surface_point ( const Point< dim - 1 > &  point, const double  weight, const std::vector< std::reference_wrapper< const Function< dim > > > &  level_sets, const BoundingBox< dim > &  box, const unsigned int  height_function_direction, ImmersedSurfaceQuadrature< dim > &  surface_quadrature  )

private

Create a surface quadrature point from the lower-dimensional point and add it to surface_quadrature.

This function is only called when \(dim=spacedim\) and there is a single level set function. At this point there should only be a single root in the interval \([L, R]\)

Definition at line 781 of file quadrature_generator.cc.

Member Data Documentation

q_collection1D

template<int dim, int spacedim>

const SmartPointer<const hp::QCollection<1> > NonMatching::internal::QuadratureGeneratorImplementation::UpThroughDimensionCreator< dim, spacedim >::q_collection1D

private

One dimensional quadrature rules used to create the immersed quadratures.

Definition at line 881 of file quadrature_generator.h.

additional_data

template<int dim, int spacedim>

const AdditionalQGeneratorData NonMatching::internal::QuadratureGeneratorImplementation::UpThroughDimensionCreator< dim, spacedim >::additional_data

private

Stores options/settings for the algorithm.

Definition at line 886 of file quadrature_generator.h.

q_index

template<int dim, int spacedim>

unsigned int NonMatching::internal::QuadratureGeneratorImplementation::UpThroughDimensionCreator< dim, spacedim >::q_index

private

Which quadrature rule in the above collection that is used to create the immersed quadrature rules.

Definition at line 892 of file quadrature_generator.h.

point_restrictions

template<int dim, int spacedim>

std::vector<Functions::PointRestriction<dim - 1> > NonMatching::internal::QuadratureGeneratorImplementation::UpThroughDimensionCreator< dim, spacedim >::point_restrictions

private

1D-functions, that are restrictions of each dim-dimensional level set function passed to generate() to some \((dim-1)\)-dimensional point.

Definition at line 898 of file quadrature_generator.h.

root_finder

template<int dim, int spacedim>

RootFinder NonMatching::internal::QuadratureGeneratorImplementation::UpThroughDimensionCreator< dim, spacedim >::root_finder

private

Class used to find the roots of the above 1D-restictions.

Definition at line 903 of file quadrature_generator.h.

roots

template<int dim, int spacedim>

std::vector<double> NonMatching::internal::QuadratureGeneratorImplementation::UpThroughDimensionCreator< dim, spacedim >::roots

private

The roots of the functions in point_restrictions. This will be the values of the height functions, \(\{H_i(x_I)\}\) at some lower dimensional quadrature point, \(x_I \in \mathbb{R}^{dim-1}\).

Definition at line 911 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