petrelharp
commented
9 years ago Things to look at:
- start at coarse, exact solution (on 512x), try to push up to fine grid (256x or maye 128x)
- plot state after each update as that happens, and difference to true solution (still exactly solvable), on map, and one against the other (x vs y)
Possible issues:
- updates have conservation of mass, except near hole it's trying to hit so if it's off by a constant, mass has to propagate out from there.
- beware of being driven by high-hitting time locations
- shape of region trying to hit actually changes: trying to solve different problems
- near boundary pushing up/down from different grid sizes might not be very close to the right thing
Things to try:
- Jacobi updates instead of gradient-based
- separately fit overall scaling and shift constants
- add constraints to match known hitting times obtained from coarse grid, to help pin down solution and identify overall constant (solve interpolation problem rather than hitting time problem)
- hit squares instead of circles
There's a start of this in
multigrid-hitting-times.R, but it is (maybe?) having issues around convergence, possibly because the boundary of the set that's getting hit becomes jagged for the coarser grids.