PCGAMG#

Geometric algebraic multigrid (AMG) preconditioner

Options Database Keys#

-pc_gamg_type type (agg|geo|classical) - see PCGAMGType
-pc_gamg_repartition (true|false) - repartition the degrees of freedom across the coarse grids as they are determined
-pc_gamg_asm_use_agg (true|false) - use the aggregates from the coarsening process to define the subdomains on each level for the PCASM smoother, this also forces using -mg_levels_pc_type asm
-pc_gamg_process_eq_limit limit - PCGAMG will reduce the number of MPI processes used directly on the coarse grids so that there are around limit equations on each process that has degrees of freedom
-pc_gamg_coarse_eq_limit limit - set maximum number of equations on coarsest grid to aim for
-pc_gamg_reuse_interpolation (true|false) - when rebuilding the algebraic multigrid preconditioner reuse the previously computed interpolations (should always be true)
-pc_gamg_threshold l0,l1,… - before aggregating the graph PCGAMG will remove small values from the graph on each level (< 0 does no filtering)
-pc_gamg_threshold_scale scale - scaling of threshold on each coarser grid if not specified

Options Database Keys for Aggregation#

-pc_gamg_agg_nsmooths nsmooth - number of smoothing steps to use with smooth aggregation to construct prolongation
-pc_gamg_aggressive_coarsening n - number of aggressive coarsening (MIS-2 or square graph) levels from finest.
-pc_gamg_aggressive_square_graph (true|false) - use square graph (\(A^T A\)) for coarsening. Otherwise, MIS-k (k=2) is used, see PCGAMGMISkSetAggressive()
-pc_gamg_square[_i]_mat_product_algorithm algorithm - MatProductAlgorithm to use when squaring the matrix for aggressive coarsening (on level i < n)
-pc_gamg_mis_k_minimum_degree_ordering (true|false) - use minimum degree ordering in greedy MIS algorithm
-pc_gamg_asm_hem_aggs n - number of HEM aggregation steps for PCASM smoother
-pc_gamg_aggressive_mis_k n - number (k) distance in MIS coarsening (>2 is ‘aggressive’)

Options Database Keys for Multigrid#

-pc_mg_cycle_type (v|w) - see PCMGSetCycleType()
-pc_mg_distinct_smoothup - configure the up and down (pre and post) smoothers separately, see PCMGSetDistinctSmoothUp()
-pc_mg_type (additive|multiplicative|full|kaskade) - see PCMGType
-pc_mg_levels levels - number of levels of multigrid to use; PCGAMG has a heuristic to determine the number of levels so this is not usually used with PCGAMG

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.