Add extended cubed-sphere dual halo with a correct alpha-beta projection.

[odlomax]

This is PRs 86 and 87 from JCSCA-internal, merged into one. The functionality added is as follows:

PR 86

This PR add functionality to the dual mesh halo. Now, the halo size can be set to any value < N-1, where N is the grid-size of a cubed sphere tile. This allows arbitrary-sized stencil operations to work on the cubed-sphere dual mesh.

An example of a cubed sphere dual mesh partition (8 PEs, default partitioner) with a halo of 3 is shown below.

xy projection of an N48 partition with a halo of 3.

xyz projection of an N48 partition with a halo of 3.

I've updated several of the existing cubed sphere dual mesh tests to use larger halo sizes.

PR 87

This PR predominantly adds an (x, y) to (alpha, beta) projection for tile t. Here, (alpha, beta) is defined strictly as the angular coordinates described by Ronchi et al., (1996).

In practice, the transform is a simple shift and rotate for xy coordinates internal to tile t. A non-linear stretch is applied for external points (i.e. halo xy coordinates).

The following example considers tile t=0 of the LFRic cubed sphere dual mesh, with halo = 3. The first image shows the xy projection. The second image gives the (alpha, beta) projection.

This required changes to several classes, summarised as follows:

• grid::Tiles added tileCenter and tileJacobian which return the xy centre and d_xy/d_alphabeta Jacobian for each tile.
• meshgenerator::detail::cubedsphere::Jacobian2 removed class and added equivalent to util namespace.
• Refactored several classes to use the projection::detail::ProjectionImpl::Jacobian class.
• meshgenerator::detail::cubedsphere::NeighbourJacobian updated this class to use the new Tiles methods. This minor refactoring therefore serves as a test for the changes.
• CubedSphereGrid added method to return a reference to the stored CubedSphereProjectionBase
• redistribution::detail::RedistributionGeneric removed rank <= 3 constraint. Not related to projection, but it was an easy fix.

This transform is currently only implemented for the equiangular cubedsphere projection. It is also likely that I've introduced some unnecessary redundancy to the CubedSphereProjectionBase and Tiles classes. However, given that we intend to refactor the cubed sphere grid at some point, we'll eventually need to refactor these classes too.

[codecov-commenter]

Codecov Report

Merging #95 (e3f40ea) into develop (0eb1d5f) will increase coverage by 0.06%.
The diff coverage is 96.62%.

@@             Coverage Diff             @@
##           develop      #95      +/-   ##
===========================================
+ Coverage    77.94%   78.01%   +0.06%     
===========================================
  Files          773      773              
  Lines        52917    53094     +177     
===========================================
+ Hits         41245    41419     +174     
- Misses       11672    11675       +3     

Impacted Files	Coverage Δ
src/atlas/functionspace/CubedSphereColumns.h	100.00% <ø> (ø)
.../atlas/functionspace/detail/CubedSphereStructure.h	100.00% <ø> (ø)
src/atlas/grid/Tiles.h	100.00% <ø> (ø)
src/atlas/grid/detail/tiles/FV3Tiles.cc	93.63% <0.00%> (-1.74%)	⬇️
src/atlas/grid/detail/tiles/FV3Tiles.h	100.00% <ø> (ø)
src/atlas/grid/detail/tiles/LFRicTiles.h	100.00% <ø> (ø)
src/atlas/grid/detail/tiles/Tiles.cc	62.50% <ø> (ø)
src/atlas/grid/detail/tiles/Tiles.h	100.00% <ø> (ø)
...eshgenerator/detail/CubedSphereDualMeshGenerator.h	50.00% <ø> (ø)
...hgenerator/detail/cubedsphere/CubedSphereUtility.h	100.00% <ø> (ø)
... and 22 more

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[wdeconinck]

Looking good! Thanks for this @odlomax .

[odlomax]

Looking good! Thanks for this @odlomax .

Thanks for taking the time to give it a look, @wdeconinck 😀

[wdeconinck]

All merged in develop with commit 8133262