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 | Private Member Functions | Private Attributes | List of all members
NonMatching::internal::QuadratureGeneratorImplementation::UpThroughDimensionCreator< dim, spacedim > Class Template Reference

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 896 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 732 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 748 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 858 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 804 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 949 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 954 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 960 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 966 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 971 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 979 of file quadrature_generator.h.


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