# KSPConvergedDefault#

Default code to determine convergence of the linear iterative solvers

## Synopsis#

#include "petscksp.h"
PetscErrorCode KSPConvergedDefault(KSP ksp, PetscInt n, PetscReal rnorm, KSPConvergedReason *reason, void *ctx)


Collective

## Input Parameters#

• ksp - iterative context

• n - iteration number

• rnorm - residual norm (may be estimated, depending on the method may be the preconditioned residual norm)

• ctx - convergence context which must be created by KSPConvergedDefaultCreate()

## Output Parameter#

• reason - the convergence reason; it is positive if the iteration has converged, negative if the iteration has diverged, and KSP_CONVERGED_ITERATING otherwise

## Options Database Keys#

• -ksp_max_it - maximum number of linear iterations

• -ksp_rtol rtol - relative tolerance used in default determination of convergence, i.e. if residual norm decreases by this factor than convergence is declared

• -ksp_atol abstol - absolute tolerance used in default convergence test, i.e. if residual norm is less than this then convergence is declared

• -ksp_divtol tol - if residual norm increases by this factor than divergence is declared

• -ksp_converged_use_initial_residual_norm - see KSPConvergedDefaultSetUIRNorm()

• -ksp_converged_use_min_initial_residual_norm - see KSPConvergedDefaultSetUMIRNorm()

• -ksp_converged_maxits - see KSPConvergedDefaultSetConvergedMaxits()

## Notes#

KSPConvergedDefault() reaches convergence when rnorm < MAX (rtol * rnorm_0, abstol); Divergence is detected if rnorm > dtol * rnorm_0, or when failures are detected throughout the iteration. By default, reaching the maximum number of iterations is considered divergence (i.e. KSP_DIVERGED_ITS). In order to have PETSc declaring convergence in such a case (i.e. KSP_CONVERGED_ITS), users can use KSPConvergedDefaultSetConvergedMaxits()

## where#

• rtol - relative tolerance,

• abstol - absolute tolerance.

• dtol - divergence tolerance,

• rnorm_0 - the two norm of the right hand side (or the preconditioned norm, depending on what was set with KSPSetNormType(). When initial guess is non-zero you can call KSPConvergedDefaultSetUIRNorm() to use the norm of (b - A*(initial guess)) as the starting point for relative norm convergence testing, that is as rnorm_0. Call KSPConvergedDefaultSetUMIRNorm() to use the minimum of the norm of (b - A*(initial guess)) and the norm of b as the starting point.

Use KSPSetTolerances() to alter the defaults for rtol, abstol, dtol.

Use KSPSetNormType() (or -ksp_norm_type <none,preconditioned,unpreconditioned,natural>) to change the norm used for computing rnorm

The precise values of reason are macros such as KSP_CONVERGED_RTOL, which are defined in petscksp.h.

This routine is used by KSP by default so the user generally never needs call it directly.

Use KSPSetConvergenceTest() to provide your own test instead of using this one.

Call KSPSetConvergenceTest() with the ctx, as created above and the destruction function KSPConvergedDefaultDestroy()

KSP: Linear System Solvers, KSP, KSPSetConvergenceTest(), KSPSetTolerances(), KSPConvergedSkip(), KSPConvergedReason, KSPGetConvergedReason(), KSPConvergedDefaultSetUIRNorm(), KSPConvergedDefaultSetUMIRNorm(), KSPConvergedDefaultSetConvergedMaxits(), KSPConvergedDefaultCreate(), KSPConvergedDefaultDestroy()