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Reference documentation for deal.II version 9.6.0
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Reference documentation for deal.II version 9.6.0
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#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 |
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.
| 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.
| 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.
| 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.
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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.
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private |
One dimensional quadrature rules used to create the immersed quadratures.
Definition at line 949 of file quadrature_generator.h.
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Stores options/settings for the algorithm.
Definition at line 954 of file quadrature_generator.h.
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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.
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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.
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Class used to find the roots of the above 1d-restictions.
Definition at line 971 of file quadrature_generator.h.
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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.
1.11.0