AMG Linear Solver Reference

In finite volume computations, the algebraic multigrid methods solve the discrete linear system iteratively. The AMG Linear Solver node contains the objects that you would use for Multigrid Cycling Strategies.

Theory See Algebraic Multigrid.
Example Node Path Solvers > Multiphase Segregated Flow > Phase Coupled Velocity > AMG Linear Solver
Properties Key properties are: Cycle Type and Convergence Tolerance.

See AMG Linear Solver Properties.

AMG Linear Solver Properties

Max Cycles
Specifies the maximum number of multigrid cycles to run in case the residuals of the linear system remain above Epsilon and the Convergence Tolerance is not met.
Verbosity

Specifies the amount of feedback (directed to the console window) by the AMG Linear Solver.

  • None

    The AMG Linear Solver runs silently. There is no feedback.

  • Low

    Residuals of the linear system are printed at the completion of each multigrid cycle.

  • High

    Same as Low, plus the number of multigrid levels and number of equations at each level are printed once all multigrid cycles are complete.

  • Diagnostics

    Provides the highest degree of information regarding performance of the AMG system. This option can affect performance, and therefore is not recommended for normal iteration.

Convergence Tolerance
Factor by which residuals of the linear system (that are above the value of Epsilon) must be reduced before multigrid cycling stops (provided Max. cycles have not been reached). For example, a convergence tolerance of 0.01 requires that cycling continue until residuals of the linear system have dropped by two orders of magnitude. A tolerance of 0.001 requires a drop of three orders of magnitude, and so on.
Cycle Type

Specifies the multigrid cycling strategy. See Multigrid Cycling.

  • F Cycle

    After restriction one W-cycle is applied on the next coarsest level, followed by one V-cycle (also on the next coarsest level).

  • V Cycle

    After restriction one cycle (also a V-cycle) is applied on the next coarsest level.

  • W Cycle

    After restriction two cycles (also W-Cycles) are applied on the next coarsest level.

    The three Fixed Cycle nodes have the following properties:

    Pre-Sweeps
    Number of smoothing sweeps at the start of each cycle.
    Post-Sweeps
    Number of smoothing sweeps at the end of each cycle.
    Max Levels
    Maximum number of coarse levels in the sequence.
  • Flex Cycle

    Rather than using all multigrid levels in a regular pattern, the residuals are monitored after every sweep on a given grid level. If the ratio of the residuals exceeds a given threshold, the solution continues on a coarser level. If the residual on a given level is reduced more than a specified tolerance, the solution moves to a finer level. A limit is further imposed on the number of sweeps that are allowed at any level.

    This type of cycle is a more economical cycling strategy for linear systems that are not stiff.

    The Flex Cycle node has the following properties:

    Restriction Tolerance
    Ratio of two successive residuals of the linear system below which progression to the next coarsest level is suspended.
    Prolongation Tolerance
    Specifies the amount by which the residuals of the linear system must be reduced before the solution is stopped on any given level.
    Sweeps
    Number of smoothing sweeps at the start of each cycle.
Enable Direct Solver
Controls whether to use the direct solver for AMG coarse levels.
Maximum Direct Solver Equations
Sets the maximum number of equations for the direct solver.
Epsilon
Cutoff value for residuals of the linear system below which convergence is considered complete and multigrid cycling stops, regardless of the Convergence Tolerance setting. For example, an Epsilon value of 1.e-08 implies that cycling stops when residuals of the linear system drop below 1.e-08.
Group Size Control

Specifies how the group size must be set.

  • Auto

    The group size is set automatically to 2 in two-dimensional cases and 4 in three-dimensional cases.

  • Specified

    Allows a user-specified group size. Adds a Group Size sub-node to this node.

Group Size
The number of equations on a given multigrid level that are agglomerated to form one equation on the next coarsest level. This value is read-only and reports the current group size being used, as determined by the Auto setting or from the Group Size sub-node when Specified.
Relaxation Scheme

Specifies the method for iteratively correcting (relaxing) the linear equation that is set during multigrid cycling. See AMG Solver.

  • Jacobi

    A slow, simple method.

  • Gauss-Seidel

    Provides better convergence. The default option.

  • ILU

    A more efficient but more expensive method.

Acceleration Method

Specifies the acceleration type for the AMG solver.

  • None

    No acceleration method used.

  • Conjugate Gradient

    Uses the Conjugate-Gradient Method with the AMG solver as the preconditioner. This method is available with the Constant Density and Segregated Flow models only. It is accessed through the Expert Properties of the AMG Linear Solver sub-node of the Segregated Flow > Pressure solver node.

  • Bi-Conjugate Gradient Stabilized

    Uses the Bi-Conjugate Gradient Stabilized Method to solve nonsymmetric (general) linear systems.

  • Generalized Minimal Residuals

    Uses the Generalized Minimal Residual Method (GMRes) method to solve general, not necessarily symmetric, linear systems.

Scaling

Controls the manner in which corrections are prolongated from the next coarsest level. Scaling is only appropriate when the linear system matrix A (Eqn. (984)) is symmetric positive-definite.

  • Auto

    Scaling is automatically applied to the coarse level corrections to achieve optimal convergence.

  • Disabled

    Coarse level corrections are prolongated without any scaling applied (the default).