Reuse extrapolation weights for multiple variables

[trhille]

This merge calculates IDW weights during the first extrapolation of a variable across the MPAS domain when converting from a Albany exodus file and then reuses those weights for the extrapolation of subsequent variables. This eliminates the repeated wave-front search that can be slow on large meshes, replacing an effectively O(N^1.5) operation with O(N) operation.

[trhille]

Using these changes on a fairly small 4–40km GIS mesh (nCells = 55928), I get:

Time taken for extrapolation and smoothing muFriction: 15.169 seconds
Time taken for extrapolation and smoothing stiffnessFactor: 0.974 seconds

Without these changes:

Time taken for extrapolation and smoothing muFriction: 8.124 seconds
Time taken for extrapolation and smoothing stiffnessFactor: 14.412 seconds

(I ran this three times for each configuration. Times varied within about ±1.5s compared with those reported above.)
So, that's a large fractional savings, but a small absolute savings. However, as we go to larger meshes, this savings should become considerable. Here is Claude's estimate:

"The key is the algorithmic complexity of each approach:

Original (per variable): O(N × R), where R is the number of wave-front rings needed to fill all empty cells. For a 2D mesh, R ≈ √N (the "radius" of the extrapolation region in cells). So effectively O(N^1.5) — each of the 24 iterations scans all remaining empty cells (O(N)), and there are O(√N) such iterations.

Cached replay: A single ordered pass over all filled cells — O(N).

So the savings ratio grows as O(√N). Concretely:

For typical large Antarctic meshes (hundreds of thousands to millions of cells), the cache turns a multi-hour extrapolation into minutes for the second and third variables. The first variable still pays full cost — which itself grows as O(N^1.5) — so on very large meshes, the pattern-building step will also become a bottleneck."

[trhille]

Testing

These changes yields BFB behavior with the current behavior in master for variables with min extrapolation (i.e., muFriction):

There are roundoff-level differences with the stiffnessFactor field, which uses IDW extrapolation, but these can be ignored: