Krylov Preconditioner
The Krylov Preconditioner node () is an attribute node that handles settings for Krylov-type methods. The settings are similar to the Iterative attribute node; the difference is that this node is an auxiliary attribute node, whereas Iterative handles settings for a main iterative solver.
Right-click an Iterative, Presmoother, Postsmoother, Coarse Solver, Schur Solver or Schur Source Solver attribute node to add a Krylov Preconditioner.
General
Select a linear system Solver: GMRES (the default), FGMRES, BiCGStab, TFQMR, or Conjugate gradients. See Iterative Solver Types for descriptions. The FGMRES option is not available when the Krylov Preconditioner subnode is added under a Schur Source Solver node.
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When GMRES or FGMRES is selected, enter a Number of iterations before restart to specify how many iterations the solver should take between each restart. A larger number increases robustness but also memory use and computational time.
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When GMRES, BiCGStab, TFQMR, or Conjugate gradients is selected, select an option from the Preconditioning list to specify whether to precondition the linear system matrix from the Left or from the Right. Normally, this setting does not significantly influence the convergence behavior of the selected solver. This setting is not available when the Krylov Preconditioner subnode is added under a Schur Source Solver node.
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When GMRES is selected, the Use GCRO-DR check box is available for the use of a GCRO-DR method. See The GCRO-DR Methods for Krylov Subspace Recycling (GMRES) for more information.
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For all Solver types, select a Termination technique:
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Fixed number of iterations to perform a fixed number of iterations each time the solver is used.
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Use tolerance to terminate the solver when a tolerance is fulfilled. Then enter a Relative tolerance and the Maximum number of iterations the solver is allowed to take. When this number of iterations has been performed without reaching the tolerance specified in the Relative tolerance field, the solver is automatically stopped with an error message.
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Iterations or tolerance to terminate when the estimated tolerance is smaller than a specified tolerance or after a specified number of iterations, whichever comes first. Then enter a Relative tolerance.
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For all Solver types, enter the Number of iterations. The default is 500.
Error
Select an option from the Validate error estimate list: Automatic (the default), Yes, or No. By choosing the appropriate option from the Validate error estimate list, the error estimate for left preconditioned solvers can be validated. No implies no error estimate validation, whereas Automatic or Yes does. By default, the validation is enabled with the Automatic option, meaning that it is performed, but preconditioner warnings are only issued if the iterative solver fails with an error. This setting is propagated recursively and applies to all children with left preconditioning.