PETSc version 3.17.4
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# SNESFAS

Full Approximation Scheme nonlinear multigrid solver. The nonlinear problem is solved by correction using coarse versions of the nonlinear problem. This problem is perturbed so that a projected solution of the fine problem elicits no correction from the coarse problem.

### Options Database

| -snes_fas_levels | - The number of levels
| -snes_fas_cycles<1> | - The number of cycles -- 1 for V, 2 for W
| -snes_fas_type<additive,multiplicative,full,kaskade> | - Additive or multiplicative cycle
| -snes_fas_galerkin<PETSC_FALSE> | - Form coarse problems by projection back upon the fine problem
| -snes_fas_smoothup<1> | - The number of iterations of the post-smoother
| -snes_fas_smoothdown<1> | - The number of iterations of the pre-smoother
| -snes_fas_monitor | - Monitor progress of all of the levels
| -snes_fas_full_downsweep<PETSC_FALSE> | - call the downsmooth on the initial downsweep of full FAS
| -fas_levels_snes_ | - SNES options for all smoothers
| -fas_levels_cycle_snes_ | - SNES options for all cycles
| -fas_levels_i_snes_ | - SNES options for the smoothers on level i
| -fas_levels_i_cycle_snes_ | - SNES options for the cycle on level i
| -fas_coarse_snes_ | - SNES options for the coarsest smoother

### Notes

The organization of the FAS solver is slightly different from the organization of PCMG As each level has smoother SNES instances(down and potentially up) and a cycle SNES instance. The cycle SNES instance may be used for monitoring convergence on a particular level.

### References

| * | - Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu, "Composing Scalable Nonlinear Algebraic Solvers", SIAM Review, 57(4), 2015

### See Also

PCMG, SNESCreate(), SNES, SNESSetType(), SNESType (for list of available types)

### Level

beginner

### Location

src/snes/impls/fas/fas.c
Index of all SNESFAS routines
Table of Contents for all manual pages
Index of all manual pages