zoomy_core.symsolver.numpy_backend.assembly

`zoomy_core.symsolver.numpy_backend.assembly`#

Assembly of a cell operator by colouring and the host AMG solve, shared by the numpy and JAX runtimes (pure numpy / scipy / pyamg).

References

Griewank, Walther 2008, https://doi.org/10.1137/1.9780898717761
Bell, Olson, Schroder 2022, https://doi.org/10.21105/joss.04142

Module Contents#

Functions#

`cell_pattern`	Sparsity of a cell operator on `k = n / nc` cell-major unknowns: each couples to those of the cells in its LSQ stencil.
`cell_colors`	Distance-2 colouring of the stencil pairs `(c, d)` by speculative parallel greedy (a clash with a heavier random-weight neighbour retries).
`host_amg_solve`	GMRES preconditioned by a smoothed-aggregation AMG hierarchy of the cell-block-scaled matrix; the hierarchy in `cache` is lagged: rebuilt every `ls['amg_rebuild']` solves, or once the iterations exceed `ls['amg_growth']` times those after the last rebuild.

API#

zoomy_core.symsolver.numpy_backend.assembly.cell_pattern(n, nc, nbrs, n_rows=None)#

Sparsity of a cell operator on k = n / nc cell-major unknowns: each couples to those of the cells in its LSQ stencil.

Returns

rows, cols in CSR order and a colour per column such that columns sharing a row differ.

zoomy_core.symsolver.numpy_backend.assembly.cell_colors(c, d, nc, seed=0)#: Distance-2 colouring of the stencil pairs (c, d) by speculative parallel greedy (a clash with a heavier random-weight neighbour retries).

zoomy_core.symsolver.numpy_backend.assembly.host_amg_solve(vals, rhs, rows, cols, n, k, ls, pyamg, cache, transpose=False)#

GMRES preconditioned by a smoothed-aggregation AMG hierarchy of the cell-block-scaled matrix; the hierarchy in cache is lagged: rebuilt every ls['amg_rebuild'] solves, or once the iterations exceed ls['amg_growth'] times those after the last rebuild.

Args

vals, rows, cols: the (n, n) matrix in COO form, k x k blocks per cell
ls: tol, restart, maxiter, amg_rebuild, amg_growth
cache: a dict kept between the solves of one operator