GAMG Solver

Table of Contents

Properties

  • symmetric or asymmetric matrices
  • run-time selectable smoother
  • efficient transport of information across the solution domain
  • moderate parallel scaling

Usage

Many of the GAMG solver inputs can be omitted and left to their default values such that the basic usage comprises: 

solver                  GAMG;
smoother                <smoother>;
relTol                  <relative tolerance>;
tolerance               <absolute tolerance>;

For more complete control, the full set of input entries includes: 

// Mandatory entries
solver                  GAMG;
smoother                <smoother>;
relTol                  <relative tolerance>;
tolerance               <absolute tolerance>;


// Optional entries and associated default values

// Agglomeration
cacheAgglomeration      yes;
nCellsInCoarsestLevel   10;
processorAgglomerator   <processor agglomeration method>;

// Solver
nPreSweeps              0;
preSweepsLevelMultiplier 1;
maxPreSweeps            4;
nPostSweeps             2;
postSweepsLevelMultiplier 1;
maxPostSweeps           4;
nFinestSweeps           2;
interpolateCorrection   no;
scaleCorrection         yes;  // Yes: symmetric No: Asymmetric
directSolveCoarsest     no;

Details

Operation

Coarsens using agglomeration

  • face area pair (geometric)
  • algebraic pair (numerical coefficients)

Agglomeration - number of levels depends on

  • number of cells at coarsest level
  • hard-limit of a maximum of 50 levels

V-cycle

  • optional pre- and post- solve smoothing at each level
  • optional smoothing at finest level

Data exchange between levels:

  • restriction: fine-to-coarse (summation)
  • prolongation: coarse-to-fine (injection)

Coarsest level solved using either:

  • direct solver
  • PCG (symmetric matrices)
  • PBiCGStab (asymmetric matrices)
Note
The system becomes more difficult to solve with increasing coarse levels due to the increasing amount of (explicit) processor contributions. This requires an efficient pre-conditioner, which are generally not parallel-aware

Computation cost

Start-up:

  • construction of agglomeration levels
  • 1 matrix-vector multiply
  • 1 parallel reduction

Per iteration:

  • 1 matrix-vector multiply per level
  • 1 parallel reduction per level
  • 1 matrix-vector multiply per V-cycle per iteration (finest level)
  • 1 parallel reduction per V-cycle per iteration (finest level)
  • + cost of coarsest level solution, e.g. using the PCG solver

Further information

Source code:

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