Distinguish between vertices, edges, faces & cells in the discretization #45
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Description
See https://gitlab.maisondelasimulation.fr/gysela-developpers/voicexx/-/issues/34
Currently and according to Voice++#26 , we only discretize points (vertices).
I would like to introduce edges discretization also.
For example, in 3D, this could look like so:
using IDimX = ×DiscretizationOf<RDimX>;
using IDimY = ×DiscretizationOf<RDimY>;
using IDimZ = ×DiscretizationOf<RDimZ>;
using IVerticesSpace = DiscreteSpace<IDimX, IDimY, IDimZ>;
using IXEdgesSpace = DiscreteSpace<IDimX::Edges, IDimY, IDimZ>;
using IYEdgesSpace = DiscreteSpace<IDimX, IDimY::Edges, IDimZ>;
using IXFacesSpace = DiscreteSpace<IDimX, IDimY::Edges, IDimZ::Edges>;
using IYFacesSpace = DiscreteSpace<IDimX::Edges, IDimY, IDimZ::Edges>;
using ICellsSpace = DiscreteSpace<IDimX::Edges, IDimY::Edges, IDimZ::Edges>;
The real type would be a tensor product that would combine either Point<RDim> or Interval<RDim>
using RVertex = VectorElement<Point<RDimX>, Point<RDimY>, Point<RDimZ>>;
using RXEdge = VectorElement<Interval<RDimX>, Point<RDimY>, Point<RDimZ>>;
using RYEdge = VectorElement<Point<RDimX>, Interval<RDimY>, Point<RDimZ>>;
using RXFace = VectorElement<Point<RDimX>, Interval<RDimY>, Interval<RDimZ>>;
using RYFace = VectorElement<Interval<RDimX>, Point<RDimY>, Interval<RDimZ>>;
using RCell = VectorElement<Interval<RDimX>, Interval<RDimY>, Interval<RDimZ>>;
The to_real() function would yield a type that depends on the discrete space:
IVerticesSpace vertices_space = /*[...]*/;
ICellsSpace cell_space = /*[...]*/;
RVertex = vertices_space.to_real(/*[...]*/);
RCell = cell_space.to_real(/*[...]*/);