Cleanup of boundary conditions

Add documentation to boundary conditions
Correct DirichletBC::fillBC to use column basis for solution

amdis/BoundaryCondition.hpp

 #pragma once
 
+#include <list>
 #include <memory>
 
-#include <amdis/Boundary.hpp>
-#include <amdis/BoundaryManager.hpp>
+#include <amdis/typetree/TreeData.hpp>
 
 namespace AMDiS
 {
+  /// \brief Interface class for boundary conditions
+  /**
+   * Stores a boundary subset related to the boundary condition. See \ref BoundarySubset.
+   * \relates DirichletBoundaryCondition
+   * \relates PeriodicBoundaryCondition
+   * \tparam Mat  Matrix
+   * \tparam Sol  Vector of solution
+   * \tparam Rhs  Vector of rhs
+   **/
+  template <class Mat, class Sol, class Rhs>
   class BoundaryCondition
   {
   public:
+    /// Default constructor.
     BoundaryCondition() = default;
-    BoundaryCondition(std::shared_ptr<BoundaryManagerBase const> const& boundaryManager, BoundaryType id)
-      : boundaryManager_(boundaryManager)
-      , id_(id)
-    {}
-
-    /// Return true if intersection is on boundary with id
-    template <class Intersection>
-    bool onBoundary(Intersection const& is) const
-    {
-      return is.boundary() && (!boundaryManager_  || boundaryManager_->boundaryId(is) == id_);
-    }
-
-    template <class RowBasis, class ColBasis>
-    void init(RowBasis const& rowBasis, ColBasis const& colBasis) { /* do nothing */ }
-
-    template <class Matrix, class X, class B, class RN, class RTP, class CN, class CTP>
-    void fillBoundaryCondition(Matrix& A, X& x, B& b, RN const& rowNode, RTP rowTreePath, CN const& colNode, CTP colTreePath) { /* do nothing */ }
-
-  protected:
-    std::shared_ptr<BoundaryManagerBase const> boundaryManager_{nullptr};
-    BoundaryType id_{0};
+
+    /// \brief Initialize the boundary condition.
+    /**
+     * This performs setup before starting the matrix and vector assembly independantly of the
+     * matrix, rhs or solution.
+     **/
+    virtual void init() = 0;
+
+    /// \brief Apply the boundary condition to matrix and vector.
+    /**
+     * This is called after the matrix `A` and rhs `b` are assembled.
+     * Implementations may alter values or change the structure of `A`, `x` or `b`.
+     **/
+    virtual void apply(Mat& A, Sol& x, Rhs& b) = 0;
   };
 
+  template <class Mat, class Sol, class Rhs>
+  struct BCData
+  {
+    template <class RN, class CN>
+    using type = std::list<std::shared_ptr<BoundaryCondition<Mat, Sol, Rhs>>>;
+  };
+
+  /// Container for storing shared pointers to boundary conditions indexed by their position in
+  /// the basis tree, see \ref MatrixData.
+  template <class Mat, class Sol, class Rhs, class RB, class CB>
+  using BoundaryConditions = MatrixData<RB, CB, BCData<Mat, Sol, Rhs>::template type>;
+
 } // end namespace AMDiS

amdis/BoundarySubset.hpp

+#pragma once
+
+#include <functional>
+
+#include <amdis/Boundary.hpp>
+#include <amdis/BoundaryManager.hpp>
+#include <amdis/common/Concepts.hpp>
+#include <amdis/common/ConceptsBase.hpp>
+
+namespace AMDiS
+{
+  /// \brief Class defining a subset of a domain boundary.
+  /**
+   * Stores a predicate identifying boundary segments. This may be given as
+   *  - a boundary manager and a boundary ID, see \ref BoundaryManager,
+   *  - a functor of the form bool(GlobalCoordinate)
+   *  - no argument in which case the whole boundary is used.
+   *
+   *  \tparam IS  Type of the intersection of the elements with the boundary
+   **/
+  template <class IS>
+  class BoundarySubset
+  {
+    using Domain = typename IS::GlobalCoordinate;
+
+  public:
+    using Intersection = IS;
+
+    /// Default constructor. Uses a predicate that returns true on the complete boundary.
+    BoundarySubset()
+      : predicate_([](Intersection const& is) -> bool { return is.boundary(); })
+    {}
+
+    /// Use a boundary manager and id to determine a subset.
+    BoundarySubset(BoundaryManagerBase& boundaryManager, BoundaryType id)
+      : predicate_([&boundaryManager, id](Intersection const& is) -> bool {
+                     return is.boundary() && boundaryManager.boundaryId(is) == id;
+                     })
+    {}
+
+    /// Use a predicate of the form bool(GlobalCoordinate) to determine a subset.
+    template <class Predicate,
+      REQUIRES(Concepts::Functor<Predicate, bool(Domain)>)>
+    BoundarySubset(Predicate&& predicate)
+      : predicate_([predicate](Intersection const& is) -> bool {
+                     return predicate(is.geometry().center());
+                     })
+    {}
+
+    /// Return true if intersection is on boundary segment
+    bool operator()(Intersection const& is) const
+    {
+      return predicate_(is);
+    }
+
+  protected:
+    std::shared_ptr<BoundaryManagerBase const> boundaryManager_;
+    BoundaryType id_{0};
+    std::function<bool(Intersection const&)> predicate_;
+  };
+
+} // end namespace AMDiS

amdis/CMakeLists.txt

@@ -29,6 +29,7 @@ install(FILES
     Boundary.hpp
     BoundaryCondition.hpp
     BoundaryManager.hpp
+    BoundarySubset.hpp
     ContextGeometry.hpp
     CreatorInterface.hpp
     CreatorMap.hpp

amdis/DirichletBC.hpp

 #pragma once
 
 #include <functional>
-#include <list>
-#include <memory>
+#include <utility>
 #include <vector>
 
-#include <dune/common/std/optional.hh>
+#include <dune/common/concept.hh>
+#include <dune/functions/functionspacebases/concepts.hh>
+#include <dune/functions/functionspacebases/subspacebasis.hh>
 
 #include <amdis/Boundary.hpp>
 #include <amdis/BoundaryCondition.hpp>
+#include <amdis/BoundarySubset.hpp>
 #include <amdis/common/Concepts.hpp>
+#include <amdis/common/TypeTraits.hpp>
 #include <amdis/typetree/RangeType.hpp>
-#include <amdis/typetree/Traversal.hpp>
-#include <amdis/typetree/TreeData.hpp>
+#include <amdis/typetree/TreePath.hpp>
 
 namespace AMDiS
 {
   /// Implements a boundary condition of Dirichlet-type.
   /**
-   * By calling the methods \ref init() and \ref finish before and after
+   * By calling the methods \ref init and \ref finish before and after
    * assembling the system-matrix, respectively, dirichlet boundary conditions
    * can be applied to the matrix and system vector. Therefore, a predicate
    * functions indicates the DOFs where values should be enforced and a second
    * functor provided in the constructor is responsible for determining the
    * values to be set at the DOFs.
    *
-   * In the \ref finish method the matrix is called with \ref applyDirichletBC
+   * In the \ref finish method the matrix is called with \ref apply
    * to erase the corresponding rows and columns for the DOF indices. This
    * application of boundary conditions can be symmetric if the matrix does
-   * support this symmetric modification. As a result, this method returns a list
-   * of columns values, that should be subtracted from the rhs.
+   * support this symmetric modification.
+   *
+   * \tparam Mat  Matrix
+   * \tparam Sol  Vector of solution
+   * \tparam Rhs  Vector of rhs
+   * \tparam RB   Basis of the row FE space
+   * \tparam RTP  Treepath to the row node this constraint applies to
+   * \tparam CB   Basis of the column FE space
+   * \tparam CTP  Treepath to the column node this constraint applies to
    **/
-  template <class Domain, class Range = double>
+  template <class Mat, class Sol, class Rhs, class RB, class RTP, class CB, class CTP>
   class DirichletBC
-      : public BoundaryCondition
+      : public BoundaryCondition<Mat, Sol, Rhs>
   {
-    using Super = BoundaryCondition;
+    using Super = BoundaryCondition<Mat, Sol, Rhs>;
+    using RowSubBasis = Dune::Functions::SubspaceBasis<RB, RTP>;
+    using ColSubBasis = Dune::Functions::SubspaceBasis<CB, CTP>;
+    // We assume CB's GridView to be the same as RB's
+    using Domain = typename RB::GridView::template Codim<0>::Geometry::GlobalCoordinate;
+    using Intersection = typename RB::GridView::Intersection;
+    using Range = RangeType_t<typename ColSubBasis::LocalView::Tree>;
 
   public:
-    template <class BM, class Values,
-      REQUIRES(Concepts::Functor<Values, Range(Domain)>) >
-    DirichletBC(BM&& boundaryManager, BoundaryType id, Values&& values)
-      : Super(FWD(boundaryManager), id)
+    /// Constructor accepting subspacebases.
+    template <class Values,
+      REQUIRES(Concepts::Functor<Values, Range(Domain)>)>
+    DirichletBC(RowSubBasis rowBasis, ColSubBasis colBasis,
+                BoundarySubset<Intersection> boundarySubset, Values&& values)
+      : rowBasis_(std::move(rowBasis))
+      , colBasis_(std::move(colBasis))
+      , boundarySubset_(std::move(boundarySubset))
       , values_(FWD(values))
     {}
 
-    template <class Predicate, class Values,
-      REQUIRES(Concepts::Functor<Predicate, bool(Domain)>),
+    /// Constructor accepting global bases and treepaths.
+    template <class Values,
       REQUIRES(Concepts::Functor<Values, Range(Domain)>)>
-    DirichletBC(Predicate&& predicate, Values&& values)
-      : predicate_(FWD(predicate))
-      , values_(FWD(values))
+    DirichletBC(RB const& rowBasis, RTP const& rowTreePath,
+                CB const& colBasis, CTP const& colTreePath,
+                BoundarySubset<Intersection> boundarySubset, Values&& values)
+      : DirichletBC(Dune::Functions::subspaceBasis(rowBasis, rowTreePath),
+                    Dune::Functions::subspaceBasis(colBasis, colTreePath),
+                    std::move(boundarySubset), FWD(values))
     {}
 
-    template <class IS>
-    bool onBoundary(IS const& intersection) const
-    {
-      return predicate_ ? (*predicate_)(intersection.geometry().center())
-                        : Super::onBoundary(intersection);
-    }
-
     // fill \ref dirichletNodes_ with 1 or 0 whether DOF corresponds to the boundary or not.
-    template <class RB, class CB>
-    void init(RB const& rowBasis, CB const& colBasis);
+    /**
+     * \see BoundaryCondition::init
+     **/
+    void init() override;
 
-    /// \brief Apply dirichlet BC to matrix and vector, i.e., add a unit-row
-    /// to the matrix and optionally delete the corresponding matrix-column.
+    /// \brief Apply dirichlet BC to matrix and vector
     /**
-     * \tparam Mat  Matrix
-     * \tparam Sol  Vector type of solution
-     * \tparam Rhs  Vector type of rhs
-     * \tparam RN   RowNode
-     * \tparam CN   ColNode
+     * Add a unit-row to the matrix and optionally delete the corresponding matrix-column.
+     * Uses a backend-specific implementation.
      **/
-    template <class Mat, class Sol, class Rhs, class RN, class RTP, class CN, class CTP>
-    void fillBoundaryCondition(Mat& matrix, Sol& solution, Rhs& rhs, RN const& rowNode, RTP rowTreePath, CN const& colNode, CTP colTreePath);
+    void apply(Mat& matrix, Sol& solution, Rhs& rhs) override;
 
   private:
-    Dune::Std::optional<std::function<bool(Domain)>> predicate_;
+    RowSubBasis rowBasis_;
+    ColSubBasis colBasis_;
+    BoundarySubset<Intersection> boundarySubset_;
     std::function<Range(Domain)> values_;
     std::vector<bool> dirichletNodes_;
   };
 
 
-  template <class Basis>
-  struct DirichletData
+  /// Make a DirichletBC from subspacebases
+  template <class Mat, class Sol, class Rhs, class RB, class RTP, class CB, class CTP, class Values>
+  auto makeDirichletBC(Dune::Functions::SubspaceBasis<RB, RTP> rowBasis,
+                       Dune::Functions::SubspaceBasis<CB, CTP> colBasis,
+                       BoundarySubset<typename RB::GridView::Intersection> boundarySubset,
+                       Values&& values)
   {
-    using WorldVector = typename Basis::GridView::template Codim<0>::Geometry::GlobalCoordinate;
-
-    template <class RN, class CN>
-    using type = std::list< std::shared_ptr<DirichletBC<WorldVector, RangeType_t<RN>>> >;
-  };
-
-  template <class RowBasis, class ColBasis>
-  using DirichletBCs = MatrixData<RowBasis, ColBasis, DirichletData<RowBasis>::template type>;
+    using BcType = DirichletBC<Mat, Sol, Rhs, RB, RTP, CB, CTP>;
+    return BcType(std::move(rowBasis), std::move(colBasis), std::move(boundarySubset), FWD(values));
+  }
+
+  /// Make a DirichletBC from a row- and colbasis with treepath arguments
+  template <class Mat, class Sol, class Rhs, class RB, class RTP, class CB, class CTP, class Values,
+    REQUIRES(Dune::models<Dune::Functions::Concept::GlobalBasis<typename RB::GridView>, RB>()),
+    REQUIRES(Dune::models<Dune::Functions::Concept::GlobalBasis<typename CB::GridView>, CB>())>
+  auto makeDirichletBC(RB const& rowBasis, RTP const& rowTreePath,
+                       CB const& colBasis, CTP const& colTreePath,
+                       BoundarySubset<typename RB::GridView::Intersection> boundarySubset,
+                       Values&& values)
+  {
+    using BcType = DirichletBC<Mat, Sol, Rhs, RB, RTP, CB, CTP>;
+    return BcType(rowBasis, rowTreePath, colBasis, colTreePath,
+                  std::move(boundarySubset), FWD(values));
+  }
+
+  /// Make a DirichletBC from a global row- and colbasis
+  template <class Mat, class Sol, class Rhs, class RB, class CB, class Values,
+    REQUIRES(Dune::models<Dune::Functions::Concept::GlobalBasis<typename RB::GridView>, RB>()),
+    REQUIRES(Dune::models<Dune::Functions::Concept::GlobalBasis<typename CB::GridView>, CB>())>
+  auto makeDirichletBC(RB const& rowBasis, CB const& colBasis,
+                       BoundarySubset<typename RB::GridView::Intersection> boundarySubset,
+                       Values&& values)
+  {
+    return makeDirichletBC<Mat, Sol, Rhs>(rowBasis, treepath(), colBasis, treepath(),
+                                          std::move(boundarySubset), FWD(values));
+  }
 
 } // end namespace AMDiS
 

amdis/DirichletBC.inc.hpp

@@ -2,18 +2,17 @@
 
 #include <type_traits>
 
-#include <dune/common/hybridutilities.hh>
 #include <dune/functions/functionspacebases/subentitydofs.hh>
 
-#include <amdis/LinearAlgebra.hpp>
 #include <amdis/functions/Interpolate.hpp>
-#include <amdis/gridfunctions/GridFunction.hpp>
+#include <amdis/LinearAlgebra.hpp>
 
 namespace AMDiS {
 namespace Impl {
 
 /// Traverse all interior boundary DOFs and apply the functor f.
-/// The Functor must have the signature `void(int, typename Basis::LocalView, typename Basis::GridView::Intersection)`
+/// The Functor must have the signature
+/// `void(int, typename Basis::LocalView, typename Basis::GridView::Intersection)`
 template <class Basis, class F>
 void forEachInteriorBoundaryDOF(Basis const& basis, F&& f)
 {
@@ -34,31 +33,26 @@ void forEachInteriorBoundaryDOF(Basis const& basis, F&& f)
 } // end namespace Impl
 
 
-template <class D, class R>
-  template <class RB, class CB>
-void DirichletBC<D,R>::
-init(RB const& rowBasis, CB const& colBasis)
+template <class Mat, class Sol, class Rhs, class RB, class RTP, class CB, class CTP>
+void DirichletBC<Mat, Sol, Rhs, RB, RTP, CB, CTP>::
+init()
 {
-  using LV = typename CB::LocalView;
-  using IS = typename CB::GridView::Intersection;
-  dirichletNodes_.resize(colBasis.dimension());
-  dirichletNodes_.assign(dirichletNodes_.size(), false);
-  Impl::forEachInteriorBoundaryDOF(colBasis, [&](int localIndex, LV const& localView, IS const& intersection) {
-    dirichletNodes_[localView.index(localIndex)] = dirichletNodes_[localView.index(localIndex)] || onBoundary(intersection);
+  using LV = typename ColSubBasis::LocalView;
+  dirichletNodes_.assign(colBasis_.dimension(), false);
+  Impl::forEachInteriorBoundaryDOF(colBasis_,
+    [&](int localIndex, LV const& localView, Intersection const& intersection) {
+      dirichletNodes_[localView.index(localIndex)] = dirichletNodes_[localView.index(localIndex)]
+                                                     || boundarySubset_(intersection);
   });
 }
 
 
-template <class D, class R>
-  template <class Mat, class Sol, class Rhs, class RN, class RTP, class CN, class CTP>
-void DirichletBC<D,R>::
-fillBoundaryCondition(Mat& matrix, Sol& solution, Rhs& rhs, RN const& rowNode, RTP rowTreePath, CN const& colNode, CTP colTreePath)
+template <class Mat, class Sol, class Rhs, class RB, class RTP, class CB, class CTP>
+void DirichletBC<Mat, Sol, Rhs, RB, RTP, CB, CTP>::
+apply(Mat& matrix, Sol& solution, Rhs& rhs)
 {
-  Dune::Hybrid::ifElse(std::is_same<RangeType_t<RN>, R>{},
-    [&](auto id) {
-      auto&& gf = makeGridFunction(values_, solution.basis()->gridView());
-      AMDiS::interpolate(*solution.basis(), id(solution), gf, rowTreePath, tag::defaulted{}, dirichletNodes_);
-    });
+  auto&& gf = makeGridFunction(values_, colBasis_.gridView());
+  AMDiS::interpolate(colBasis_, solution, gf, tag::defaulted{}, tag::defaulted{}, dirichletNodes_);
 
   dirichletBC(matrix, solution, rhs, dirichletNodes_);
 }

amdis/OperatorList.hpp

@@ -3,7 +3,7 @@
 #include <list>
 #include <memory>
 
-#include <amdis/BoundaryCondition.hpp>
+#include <amdis/BoundarySubset.hpp>
 #include <amdis/AssemblerInterface.hpp>
 #include <amdis/typetree/TreeData.hpp>
 
@@ -13,10 +13,10 @@ namespace AMDiS
   {
     template <class E> struct element_operator { using type = E; };
     template <class I> struct intersection_operator { using type = I; };
-    template <class I> struct boundary_operator : public BoundaryCondition
+    template <class I> struct boundary_operator : public BoundarySubset<I>
     {
       using type = I;
-      using BoundaryCondition::BoundaryCondition;
+      using BoundarySubset<I>::BoundarySubset;
     };
   }
 
@@ -30,7 +30,7 @@ namespace AMDiS
     struct DataElement
     {
       std::shared_ptr<Op> op;
-      BoundaryCondition bc;
+      BoundarySubset<Intersection> bs;
     };
 
     /// Lists of \ref DataElement on the Element, BoundaryIntersction, and InteriorIntersections

amdis/PeriodicBC.hpp

 #pragma once
 
-#include <functional>
-#include <list>
 #include <map>
-#include <type_traits>
+#include <utility>
 #include <vector>
 
-#include <amdis/Output.hpp>
+#include <dune/common/concept.hh>
+#include <dune/common/std/optional.hh>
+#include <dune/functions/functionspacebases/concepts.hh>
+#include <dune/functions/functionspacebases/subspacebasis.hh>
+
+#include <amdis/BoundaryCondition.hpp>
+#include <amdis/BoundarySubset.hpp>
 #include <amdis/common/ConceptsBase.hpp>
 #include <amdis/common/FieldMatVec.hpp>
+#include <amdis/common/TypeTraits.hpp>
+#include <amdis/typetree/TreePath.hpp>
 
 
 namespace AMDiS
 {
+  /// \brief Affine transformation x := A*x + b
   template <class ct, int dow>
   struct FaceTransformation
   {
     using WorldMatrix = FieldMatrix<ct, dow, dow>;
     using WorldVector = FieldVector<ct, dow>;
 
-    WorldMatrix matrix_; // Note: We assume the matrix to be orthogonal, here
+    /// orthogonal (rotation) matrix
+    WorldMatrix matrix_;
+
+    /// Shift vector
     WorldVector shift_;
 
     WorldVector evaluate(WorldVector const& x) const
@@ -41,55 +51,73 @@ namespace AMDiS
 
   /// Implements a periodic boundary condition
   /**
-   * \tparam D  Domain
-   * \tparam MI Type of the MultiIndex
+   * \tparam Mat    Matrix
+   * \tparam Sol    Vector of solution
+   * \tparam Rhs    Vector of rhs
+   * \tparam Basis  RowBasis, must be the same as ColBasis
+   * \tparam TP     Treepath to the node this constraint applies to
    **/
-  template <class D, class MI>
+  template <class Mat, class Sol, class Rhs, class Basis, class TP>
   class PeriodicBC
-      : public BoundaryCondition
+      : public BoundaryCondition<Mat, Sol, Rhs>
   {
-    using Super = BoundaryCondition;
+    using Super = BoundaryCondition<Mat, Sol, Rhs>;
+    using SubspaceBasis = Dune::Functions::SubspaceBasis<Basis, TP>;
 
   public:
-    using Domain = D;
-    using MultiIndex = MI;
-    using FaceTrafo = FaceTransformation<typename D::field_type, D::dimension>;
+    using Domain = typename SubspaceBasis::GridView::template Codim<0>::Geometry::GlobalCoordinate;
+    using MultiIndex = typename SubspaceBasis::MultiIndex;
+    using FaceTrafo = FaceTransformation<typename Domain::field_type, Domain::dimension>;
+    using Intersection = typename SubspaceBasis::GridView::Intersection;
 
   public:
-    template <class BM>
-    PeriodicBC(BM&& boundaryManager, BoundaryType id, FaceTrafo faceTrafo)
-      : Super(FWD(boundaryManager), id)
+    /// Create the BoundaryCondition and store the face transformation in a local variable.
+    PeriodicBC(SubspaceBasis basis, BoundarySubset<Intersection> boundarySubset,
+               FaceTrafo faceTrafo)
+      : basis_(std::move(basis))
+      , boundarySubset_(std::move(boundarySubset))
       , faceTrafo_(std::move(faceTrafo))
     {}
 
-    template <class RB, class CB>
-    void init(RB const& rowBasis, CB const& colBasis);
-
-    template <class Mat, class Sol, class Rhs, class RN, class RTP, class CN, class CTP>
-    void fillBoundaryCondition(Mat& A, Sol& x, Rhs& b, RN const& rowNode, RTP rowTreePath, CN const& colNode, CTP colTreePath);
-
+    /// Compute the pairs of associated boundary DOFs
+    /**
+     * After leaving the function the vector used by periodicNodes() is initialized and its value is
+     * true for all DOFs on the periodic boundary. Furthermode associations() is initialized and
+     * contains the index of the DOF associated to a DOF on the periodic boundary.
+     **/
+    void init() override;
+
+    /// Move matrix rows (and columns) of dependant DOFs to the corresponding master DOFs
+    /**
+     * Add rows (and columns) of dependant DOFs to rows (and columns) master DOFs and set rows (and
+     * columns) of dependant DOFs to unit-rows[columns] with entries of -1 at master DOF indices.
+     * Uses a backend-specific implementation.
+     **/
+    void apply(Mat& matrix, Sol& solution, Rhs& rhs) override;
+
+    /// Return the map of DOF associations
     auto const& associations() const
     {
       return associations_;
     }
 
+    /// Return the boolean boundary indicator
     auto const& periodicNodes() const
     {
       return periodicNodes_;
     }
 
   protected:
-    template <class Basis>
-    void initAssociations(Basis const& basis);
-
-    template <class Basis>
-    void initAssociations2(Basis const& basis);
+    void initAssociations();
+    void initAssociations2();
 
     // Get the coordinates of the DOFs
     template <class Node>
-    std::vector<Domain> coords(Node const& node, std::vector<std::size_t> const& localIndices) const;
+    auto coords(Node const& node, std::vector<std::size_t> const& localIndices) const;
 
   private:
+    SubspaceBasis basis_;
+    BoundarySubset<Intersection> boundarySubset_;
     FaceTrafo faceTrafo_;
 
     std::vector<bool> periodicNodes_;
@@ -97,18 +125,45 @@ namespace AMDiS
     Dune::Std::optional<bool> hasConnectedIntersections_;
   };
 
+  namespace Impl {
+    template <class Basis>
+    using FaceTrafo = FaceTransformation<
+      typename Basis::GridView::template Codim<0>::Geometry::GlobalCoordinate::field_type,
+      Basis::GridView::template Codim<0>::Geometry::GlobalCoordinate::dimension>;
+  }
 
-  template <class Basis>
-  struct PeriodicData
-  {
-    using WorldVector = typename Basis::GridView::template Codim<0>::Geometry::GlobalCoordinate;
-
-    template <class RowNode, class ColNode>
-    using type = std::list< std::shared_ptr<PeriodicBC<WorldVector, typename Basis::MultiIndex>> >;
-  };
 
-  template <class RowBasis, class ColBasis>
-  using PeriodicBCs = MatrixData<RowBasis, ColBasis, PeriodicData<RowBasis>::template type>;
+  /// Make a PeriodicBC from a subspacebasis
+  template <class Mat, class Sol, class Rhs, class B, class TP>
+  auto makePeriodicBC(Dune::Functions::SubspaceBasis<B, TP> basis,
+                      BoundarySubset<typename B::GridView::Intersection> boundarySubset,
+                      Impl::FaceTrafo<B> trafo)
+  {
+    using BcType = PeriodicBC<Mat, Sol, Rhs, B, TP>;