Geometry XY

The geometry folder contains a helper file geometry.hpp which provides shortcuts to the types needed to define the specific geometry. In this case the geometry is a simulation with 2 spatial dimensions (denoted X and Y).

In this geometry \(x\) and \(y\) are supposed periodic and the splines are supposed cubic.

The shortcuts defined in the geometry file represent:

  1. The continuous dimensions RDimX and RDimY.
  2. The type of coordinates of objects represented on the dimensions (CoordX, CoordY, CoordXY).
  3. The type of the B-Spline bases used on the spatial dimensions (BSplinesX and BSplinesY).
  4. The type which will describe the grid points on which the simulation will evolve (IDimX, IDimY).
  5. The type of the helper class which initialises grid points in space which are compatible with the defined splines (SplineInterpPointsX, SplineInterpPointsY).
  6. The type of the objects used to build splines (SplineXBuilder_XY, SplineYBuilder_XY).
  7. The type which describes the index of a grid point (e.g. IndexX).
  8. The type which describes a distance between grid points (e.g. IdxStepX).
  9. The type which describes the domain on which the grid points are defined (e.g. IdxRangeX).
  10. The templated type of a field memory block defined on each of the domains (e.g. FieldMemX<ElementType>). A field memory block allocates values at each grid point in the provided domain.
  11. The type of a field memory block of doubles defined on each of the domains (e.g. DFieldMemX).
  12. The templated type of a field defined on each of the domains (e.g. FieldX<ElementType>). A field is similar to a reference. It provides access to a field memory block or a sub-set of a field memory block, but does not own the data itself.
  13. The type of a field of doubles defined on each of the domains (e.g. DFieldX).
  14. The templated type of a constant field defined on each of the domains (e.g. ConstFieldX<ElementType>).
  15. The type of a constant field of doubles defined on each of the domains (e.g. DConstFieldX).
  16. The type of VectorField defined on the index range IdxRangeXY on the directions VectorIndexSet<RDimX, RDimY> (VectorFieldXY_XY).