#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 . 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, : $X_q = x_I \times (y_i + (y_{i+1} - y_i) x_q)$ , $W_q = w_I (y_{i+1} - y_i) w_q$ .

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, $x_I \in \mathbb{R}^{dim-1}$ .