lagrangegridcreator.hh 13.7 KB
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#pragma once

#include <cassert>
#include <cstdint>
#include <limits>
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#include <optional>
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#include <vector>

#include <dune/common/exceptions.hh>
#include <dune/common/hybridutilities.hh>
#include <dune/geometry/utility/typefromvertexcount.hh>
#include <dune/localfunctions/lagrange.hh>
#include <dune/grid/common/gridfactory.hh>

#include <dune/vtk/forward.hh>
#include <dune/vtk/vtktypes.hh>
#include <dune/vtk/gridcreatorinterface.hh>
#include <dune/vtk/utility/lagrangepoints.hh>

namespace Dune
{
  // \brief Create a grid from data that represents higher (lagrange) cells.
  /**
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   * The grid is created from the first nodes of a cell parametrization, representing
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   * the  corner vertices. Thus a piecewise "flat" grid is constructed. The
   * parametrization is 1. passed as a local element parametrization to the
   * `insertElement()` function of a gridFactory to allow the grid itself to handle the
   * parametrization and 2. is stored internally that can be accessed by using this
   * GridCreator object as a grid function, or by extracting locally the parametrization
   * on each existing grid element after creation of the grid.
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   *
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   * So, the LagrangeGridCreator models both, a `GridCreator` and a `GridFunction`.
   **/
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  template <class GridType>
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  struct LagrangeGridCreator
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      : public GridCreatorInterface<GridType, LagrangeGridCreator<GridType>>
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  {
    using Self = LagrangeGridCreator;
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    using Super = GridCreatorInterface<GridType, Self>;
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    using GlobalCoordinate = typename Super::GlobalCoordinate;

    using Nodes = std::vector<GlobalCoordinate>;

    struct ElementParametrization
    {
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      GeometryType type;                  //< Geometry type of the element
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      std::vector<std::int64_t> nodes;    //< Indices of the w.r.t. `nodes_` vector
      std::vector<unsigned int> corners;  //< Insertion-indices of the element corner nodes
    };

    using Parametrization = std::vector<ElementParametrization>;
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    using Element = typename GridType::template Codim<0>::Entity;
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    using LocalCoordinate = typename Element::Geometry::LocalCoordinate;

    class LocalParametrization;
    class LocalFunction;

  public:
    using Super::factory;

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    LagrangeGridCreator (GridFactory<GridType>& factory)
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      : Super(factory)
    {}

    /// Implementation of the interface function `insertVertices()`
    void insertVerticesImpl (std::vector<GlobalCoordinate> const& points,
                             std::vector<std::uint64_t> const& /*point_ids*/)
    {
      // store point coordinates in member variable
      nodes_ = points;
    }

    template <class F>
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    using HasParametrizedElements = decltype(std::declval<F>().insertElement(std::declval<GeometryType>(),
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      std::declval<std::vector<unsigned int> const&>(), std::declval<std::function<GlobalCoordinate(LocalCoordinate)>>()));

    /// Implementation of the interface function `insertElements()`
    void insertElementsImpl (std::vector<std::uint8_t> const& types,
                             std::vector<std::int64_t> const& offsets,
                             std::vector<std::int64_t> const& connectivity)
    {
      assert(nodes_.size() > 0);

      // mapping of node index to element-vertex index
      std::vector<std::int64_t> elementVertices(nodes_.size(), -1);
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      parametrization_.reserve(types.size());
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      std::int64_t vertexIndex = 0;
      for (std::size_t i = 0; i < types.size(); ++i) {
        auto type = Vtk::to_geometry(types[i]);
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        if (type.dim() != GridType::dimension)
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          continue;

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        Vtk::CellType cellType{type};
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        auto refElem = referenceElement<double,GridType::dimension>(type);
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        std::int64_t shift = (i == 0 ? 0 : offsets[i-1]);
        int nNodes = offsets[i] - shift;
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        int nVertices = refElem.size(GridType::dimension);
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        // insert vertices into grid and construct element vertices
        std::vector<unsigned int> element(nVertices);
        for (int j = 0; j < nVertices; ++j) {
          auto index = connectivity.at(shift + j);
          auto& vertex = elementVertices.at(index);
          if (vertex < 0) {
            factory().insertVertex(nodes_.at(index));
            vertex = vertexIndex++;
          }
          element[j] = vertex;
        }

        // permute element indices
        if (!cellType.noPermutation()) {
          // apply index permutation
          std::vector<unsigned int> cell(element.size());
          for (int j = 0; j < element.size(); ++j)
            cell[j] = element[cellType.permutation(j)];
          std::swap(element, cell);
        }

        // fill vector of element parametrizations
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        parametrization_.push_back(ElementParametrization{type});
        auto& param = parametrization_.back();

        param.nodes.resize(nNodes);
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        for (int j = 0; j < nNodes; ++j)
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          param.nodes[j] = connectivity.at(shift + j);
        param.corners = element;
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        // try to create element with parametrization
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        if constexpr (Std::is_detected_v<HasParametrizedElements, GridFactory<GridType>>) {
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          try {
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            factory().insertElement(type, element, localParametrization(parametrization_.size()-1));
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          } catch (Dune::GridError const& /* notImplemented */) {
            factory().insertElement(type, element);
          }
        } else {
          factory().insertElement(type, element);
        }
      }
    }

    /// \brief Construct an element parametrization
    /**
     * The returned LocalParametrization is a mapping `GlobalCoordinate(LocalCoordinate)`
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     * where `LocalCoordinate is w.r.t. the local coordinate system in an element with
     * given `insertionIndex` (defined by the inserted corner vertices) and
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     * `GlobalCoordinate` a world coordinate in the parametrized grid.
     **/
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    LocalParametrization localParametrization (unsigned int insertionIndex) const
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    {
      assert(!nodes_.empty() && !parametrization_.empty());
      auto const& localParam = parametrization_.at(insertionIndex);
      return LocalParametrization{nodes_, localParam, order(localParam)};
    }

    /// \brief Construct an element parametrization
    /**
     * The returned LocalParametrization is a mapping `GlobalCoordinate(LocalCoordinate)`
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     * where `LocalCoordinate is w.r.t. the local coordinate system in the passed element
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     * and `GlobalCoordinate` a world coordinate in the parametrized grid.
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     *
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     * Note, when an element is passed, it might have a different local coordinate system
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     * than the coordinate system used to defined the element parametrization. Thus
     * coordinate transform is internally chained to the evaluation of the local
     * parametrization. This local geometry transform is obtained by figuring out the
     * permutation of corners in the element corresponding to the inserted corner
     * vertices.
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     **/
    LocalParametrization localParametrization (Element const& element) const
    {
      assert(!nodes_.empty() && !parametrization_.empty());

      unsigned int insertionIndex = factory().insertionIndex(element);
      auto const& localParam = parametrization_.at(insertionIndex);
      assert(element.type() == localParam.type);

      // collect indices of vertices
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      std::vector<unsigned int> indices(element.subEntities(GridType::dimension));
      for (unsigned int i = 0; i < element.subEntities(GridType::dimension); ++i)
        indices[i] = factory().insertionIndex(element.template subEntity<GridType::dimension>(i));
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      // calculate permutation vector
      std::vector<unsigned int> permutation(indices.size());
      for (std::size_t i = 0; i < indices.size(); ++i) {
        auto it = std::find(localParam.corners.begin(), localParam.corners.end(), indices[i]);
        assert(it != localParam.corners.end());
        permutation[i] = std::distance(localParam.corners.begin(), it);
      }

      return LocalParametrization{nodes_, localParam, order(localParam), permutation};
    }

    /// Determine lagrange order from number of points
    template <class LocalParam>
    unsigned int order (LocalParam const& localParam) const
    {
      GeometryType type = localParam.type;
      std::size_t nNodes = localParam.nodes.size();
      for (unsigned int o = 1; o <= nNodes; ++o)
        if (numLagrangePoints(type.id(), type.dim(), o) == nNodes)
          return o;

      return 1;
    }

    /// Determine lagrange order from number of points from the first element parametrization
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    unsigned int order () const
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    {
      assert(!parametrization_.empty());
      return order(parametrization_.front());
    }

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  public:
    /// \brief Local function representing the parametrization of the grid.
    /**
     * The returned object models Functions::Concept::LocalFunction
     * and can thus be bound to an element of the created grid and evaluated in
     * the local coordinates of the bound element.
     *
     * It is implemented in terms of the \ref LocalParametrization function
     * returned by the method \ref localParametrization(element). See comments
     * there for further details.
     *
     * Note, this methods requires the GridCreator to be based by
     * lvalue-reference. This is necessary, since we want to guarantee that all
     * internal storage is preserved while evaluating the local function.
     **/
    friend LocalFunction localFunction (LagrangeGridCreator& gridCreator)
    {
      return LocalFunction{gridCreator};
    }

    struct EntitySet
    {
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      using Grid = GridType;
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    };

    /// Dummy function returning a placeholder entityset
    EntitySet entitySet () const
    {
      assert(false && "Should not be used!");
      return EntitySet{};
    }

    /// Dummy function returning a placeholder entityset
    GlobalCoordinate operator() (GlobalCoordinate const&) const
    {
      assert(false && "Should not be used!");
      return GlobalCoordinate{};
    }

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  private:
    /// All point coordinates inclusing the higher-order lagrange points
    Nodes nodes_;

    /// Parametrization for all elements
    Parametrization parametrization_;
  };


  template <class Grid>
  class LagrangeGridCreator<Grid>::LocalParametrization
  {
    using ctype = typename Grid::ctype;
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    using GlobalCoordinate = typename Grid::template Codim<0>::Entity::Geometry::GlobalCoordinate;
    using LocalCoordinate = typename Grid::template Codim<0>::Entity::Geometry::LocalCoordinate;
    using LocalGeometry = MultiLinearGeometry<ctype,Grid::dimension,Grid::dimension>;

    using LocalFE = LagrangeLocalFiniteElement<VtkLagrangePointSet, Grid::dimension, ctype, ctype>;
    using LocalBasis = typename LocalFE::Traits::LocalBasisType;
    using LocalBasisTraits = typename LocalBasis::Traits;

  public:
    /// Construct a local element parametrization
    template <class Nodes, class LocalParam>
    LocalParametrization (Nodes const& nodes, LocalParam const& param, unsigned int order)
      : localFE_(param.type, order)
      , localNodes_(param.nodes.size())
    {
      for (std::size_t i = 0; i < localNodes_.size(); ++i)
        localNodes_[i] = nodes[param.nodes[i]];
    }

    /// Construct a local element parametrization for elements with permuted corners
    template <class Nodes, class LocalParam, class Permutation>
    LocalParametrization (Nodes const& nodes, LocalParam const& param, unsigned int order, Permutation const& permutation)
      : LocalParametrization(nodes, param, order)
    {
      auto refElem = referenceElement<ctype,Grid::dimension>(param.type);
      std::vector<LocalCoordinate> corners(permutation.size());
      for (std::size_t i = 0; i < permutation.size(); ++i)
        corners[i] = refElem.position(permutation[i], Grid::dimension);

      localGeometry_.emplace(param.type, corners);
    }

    /// Evaluate the local parametrization in local coordinates
    template <class LocalCoordinate>
    GlobalCoordinate operator() (LocalCoordinate const& local) const
    {
      // map coordinates if element corners are permuted
      LocalCoordinate x = localGeometry_ ? localGeometry_->global(local) : local;

      LocalBasis const& localBasis = localFE_.localBasis();
      localBasis.evaluateFunction(x, shapeValues_);
      assert(shapeValues_.size() == localNodes_.size());

      GlobalCoordinate out(0);
      for (std::size_t i = 0; i < shapeValues_.size(); ++i)
        out.axpy(shapeValues_[i], localNodes_[i]);

      return out;
    }

  private:
    LocalFE localFE_;
    std::vector<GlobalCoordinate> localNodes_;
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    std::optional<LocalGeometry> localGeometry_;
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    mutable std::vector<typename LocalBasisTraits::RangeType> shapeValues_;
  };


  template <class Grid>
  class LagrangeGridCreator<Grid>::LocalFunction
  {
    using ctype = typename Grid::ctype;
    using LocalContext = typename Grid::template Codim<0>::Entity;
    using GlobalCoordinate = typename LocalContext::Geometry::GlobalCoordinate;
    using LocalCoordinate = typename LocalContext::Geometry::LocalCoordinate;
    using LocalParametrization = typename LagrangeGridCreator::LocalParametrization;

  public:
    explicit LocalFunction (LagrangeGridCreator& gridCreator)
      : gridCreator_(&gridCreator)
    {}

    /// Collect a local parametrization on the element
    void bind (LocalContext const& element)
    {
      localContext_ = element;
      localParametrization_.emplace(gridCreator_->localParametrization(element));
    }

    void unbind () { /* do nothing */ }

    /// Evaluate the local parametrization in local coordinates
    GlobalCoordinate operator() (LocalCoordinate const& local) const
    {
      assert(!!localParametrization_);
      return (*localParametrization_)(local);
    }

    /// Return the bound element
    LocalContext const& localContext () const
    {
      return localContext_;
    }

  private:
    LagrangeGridCreator const* gridCreator_;

    LocalContext localContext_;
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    std::optional<LocalParametrization> localParametrization_;
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  };

} // end namespace Dune