petsc-3.7.1 2016-05-15
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# KSPRICHARDSON

The preconditioned Richardson iterative method

### Options Database Keys

-ksp_richardson_scale -damping factor on the correction (defaults to 1.0) Many br

Many br

Notes: x^{n+1} = x^{n} + scale*B(b - A x^{n}) Many br

Here B is the application of the preconditioner Many br

This method often (usually) will not converge unless scale is very small. Many br

Notes: For some preconditioners, currently SOR, the convergence test is skipped to improve speed, Many brthus it always iterates the maximum number of iterations you've selected. When -ksp_monitor Many br(or any other monitor) is turned on, the norm is computed at each iteration and so the convergence test is run unless Many bryou specifically call KSPSetNormType(ksp,KSP_NORM_NONE); Many br

For some preconditioners, currently PCMG and PCHYPRE with BoomerAMG if -ksp_monitor (and also Many brany other monitor) is not turned on then the convergence test is done by the preconditioner itself and Many brso the solver may run more or fewer iterations then if -ksp_monitor is selected. Many br

Supports only left preconditioning Many br

### References

1. -L. F. Richardson, "The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Many brDifferential Equations, with an Application to the Stresses in a Masonry Dam", Many brPhilosophical Transactions of the Royal Society of London. Series A, Many brContaining Papers of a Mathematical or Physical Character, Vol. 210, 1911 (1911). Many br

### See Also

KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
KSPRichardsonSetScale() Many br

Level:beginner
Location:src/ksp/ksp/impls/rich/rich.c
Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages