PCGAMG#

Geometric algebraic multigrid (AMG) preconditioner

Options Database Keys#

-pc_gamg_type <type,default=agg> - one of agg, geo, or classical (only smoothed aggregation, agg, supported)
-pc_gamg_repartition <bool,default=false> - repartition the degrees of freedom across the coarse grids as they are determined
-pc_gamg_asm_use_agg <bool,default=false> - use the aggregates from the coasening process to defined the subdomains on each level for the PCASM smoother
-pc_gamg_process_eq_limit <limit, default=50> - PCGAMG will reduce the number of MPI ranks used directly on the coarse grids so that there are around equations on each process that has degrees of freedom
-pc_gamg_coarse_eq_limit <limit, default=50> - Set maximum number of equations on coarsest grid to aim for.
-pc_gamg_reuse_interpolation <bool,default=true> - when rebuilding the algebraic multigrid preconditioner reuse the previously computed interpolations (should always be true)
-pc_gamg_threshold[] <thresh,default=[- 1,…]> - Before aggregating the graph PCGAMG will remove small values from the graph on each level (< 0 does no filtering)
-pc_gamg_threshold_scale <scale,default=1> - Scaling of threshold on each coarser grid if not specified

Options Database Keys for Aggregation#

-pc_gamg_agg_nsmooths <nsmooth, default=1> - number of smoothing steps to use with smooth aggregation to construct prolongation
-pc_gamg_aggressive_coarsening <n,default=1> - number of aggressive coarsening (MIS-2) levels from finest.
-pc_gamg_aggressive_square_graph <bool,default=false> - Use square graph (A’A) or MIS-k (k=2) for aggressive coarsening
-pc_gamg_mis_k_minimum_degree_ordering <bool,default=true> - Use minimum degree ordering in greedy MIS algorithm
-pc_gamg_pc_gamg_asm_hem_aggs <n,default=0> - Number of HEM aggregation steps for ASM smoother
-pc_gamg_aggressive_mis_k <n,default=2> - Number (k) distance in MIS coarsening (>2 is ‘aggressive’)

Options Database Keys for Multigrid#

-pc_mg_cycle_type - v or w, see PCMGSetCycleType()
-pc_mg_distinct_smoothup - configure the up and down (pre and post) smoothers separately, see PCMGSetDistinctSmoothUp()
-pc_mg_type - (one of) additive multiplicative full kascade
-pc_mg_levels - Number of levels of multigrid to use. GAMG has a heuristic so pc_mg_levels is not usually used with GAMG

Notes#

To obtain good performance for PCGAMG for vector valued problems you must call MatSetBlockSize() to indicate the number of degrees of freedom per grid point call MatSetNearNullSpace() (or PCSetCoordinates() if solving the equations of elasticity) to indicate the near null space of the operator

The many options for PCMG also work directly for PCGAMG such as controlling the smoothers on each level etc.