SpECTRE Documentation Coverage Report
Current view: top level - NumericalAlgorithms/Spectral - Projection.hpp Hit Total Coverage
Commit: 2ae2b99409ac582030d56a4560a92a3e066a7e54 Lines: 6 9 66.7 %
Date: 2022-01-15 08:40:38
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          Line data    Source code
       1           0 : // Distributed under the MIT License.
       2             : // See LICENSE.txt for details.
       3             : 
       4             : #pragma once
       5             : 
       6             : #include <array>
       7             : #include <cstddef>
       8             : #include <functional>
       9             : #include <ostream>
      10             : 
      11             : /// \cond
      12             : class Matrix;
      13             : template <size_t Dim>
      14             : class Mesh;
      15             : /// \endcond
      16             : 
      17             : namespace Spectral {
      18             : 
      19             : /// The portion of a mesh covered by a child mesh.
      20           0 : enum class ChildSize { Full, UpperHalf, LowerHalf };
      21             : 
      22             : /// The portion of an element covered by a mortar.
      23           1 : using MortarSize = ChildSize;
      24             : 
      25           0 : std::ostream& operator<<(std::ostream& os, ChildSize mortar_size);
      26             : 
      27             : /// Determine whether data needs to be projected between a child mesh and its
      28             : /// parent mesh. If no projection is necessary the data may be used as-is.
      29             : /// Projection is necessary if the child is either p-refined or h-refined
      30             : /// relative to its parent, or both. This operation is symmetric, i.e. it is
      31             : /// irrelevant in which order the child and the parent mesh are passed in.
      32             : template <size_t Dim>
      33           1 : bool needs_projection(const Mesh<Dim>& mesh1, const Mesh<Dim>& mesh2,
      34             :                       const std::array<ChildSize, Dim>& child_sizes);
      35             : 
      36             : /*!
      37             :  * \brief The projection matrix from a child mesh to its parent.
      38             :  *
      39             :  * The projection matrices returned by this function (and by
      40             :  * projection_matrix_parent_to_child()) define orthogonal projection operators
      41             :  * between the spaces of functions on a parent mesh and its children. These
      42             :  * projections are usually the correct way to transfer data between meshes in
      43             :  * a mesh-refinement hierarchy, as well as between an element face and its
      44             :  * adjacent mortars.
      45             :  *
      46             :  * These functions assume that the `child_mesh` is at least as fine as the
      47             :  * `parent_mesh`, i.e. functions on the `parent_mesh` can be represented exactly
      48             :  * on the `child_mesh`. In practice this means that functions can be projected
      49             :  * to a mortar (the `child_mesh`) from both adjacent element faces (the
      50             :  * `parent_mesh`) without losing accuracy. Similarly, functions in a
      51             :  * mesh-refinement hierarchy don't lose accuracy when an element is split
      52             :  * (h-refined). For this reason, the `projection_matrix_child_to_parent` is
      53             :  * sometimes referred to as a "restriction operator" and the
      54             :  * `projection_matrix_parent_to_child` as a "prolongation operator".
      55             :  *
      56             :  * \par Massive quantities
      57             :  * If the quantity that should be projected is not a function over the
      58             :  * computational grid but a "massive" residual, i.e. a quantity
      59             :  * \f$\int_{\Omega_k} f(x) \psi_p(x) \mathrm{d}V\f$ where \f$\psi_p\f$ are the
      60             :  * basis functions on the mesh, then pass `true` for the parameter
      61             :  * `operand_is_massive` (default is `false`). The restriction operator for this
      62             :  * case is just the transpose of the prolongation operator, i.e. just an
      63             :  * interpolation matrix transpose. Note that the "massive" residual already
      64             :  * takes the difference in element size between parent and children into account
      65             :  * by including a Jacobian in the volume element of the integral.
      66             :  *
      67             :  * \par Implementation details
      68             :  * The half-interval projections are based on an equation derived by
      69             :  * Saul.  This shows that the projection from the spectral basis for
      70             :  * the entire interval to the spectral basis for the upper half
      71             :  * interval is
      72             :  * \f{equation*}
      73             :  * T_{jk} = \frac{2 j + 1}{2} 2^j \sum_{n=0}^{j-k} \binom{j}{k+n}
      74             :  * \binom{(j + k + n - 1)/2}{j} \frac{(k + n)!^2}{(2 k + n + 1)! n!}
      75             :  * \f}
      76             :  */
      77           1 : const Matrix& projection_matrix_child_to_parent(
      78             :     const Mesh<1>& child_mesh, const Mesh<1>& parent_mesh, ChildSize size,
      79             :     bool operand_is_massive = false);
      80             : 
      81             : /// The projection matrix from a child mesh to its parent, in `Dim` dimensions.
      82             : template <size_t Dim>
      83             : std::array<std::reference_wrapper<const Matrix>, Dim>
      84           1 : projection_matrix_child_to_parent(const Mesh<Dim>& child_mesh,
      85             :                                   const Mesh<Dim>& parent_mesh,
      86             :                                   const std::array<ChildSize, Dim>& child_sizes,
      87             :                                   bool operand_is_massive = false);
      88             : 
      89             : /// The projection matrix from a parent mesh to one of its children.
      90             : ///
      91             : /// \see projection_matrix_child_to_parent()
      92           1 : const Matrix& projection_matrix_parent_to_child(const Mesh<1>& parent_mesh,
      93             :                                                 const Mesh<1>& child_mesh,
      94             :                                                 ChildSize size);
      95             : 
      96             : /// The projection matrix from a parent mesh to one of its children, in `Dim`
      97             : /// dimensions
      98             : template <size_t Dim>
      99             : std::array<std::reference_wrapper<const Matrix>, Dim>
     100           1 : projection_matrix_parent_to_child(
     101             :     const Mesh<Dim>& parent_mesh, const Mesh<Dim>& child_mesh,
     102             :     const std::array<ChildSize, Dim>& child_sizes);
     103             : 
     104             : }  // namespace Spectral

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