KSPRICHARDSON — PETSc 3.21.4 documentation

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# KSPRICHARDSON

The preconditioned Richardson iterative method [Ric11]

## Options Database Key

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

## Notes

\( x^{n+1} = x^{n} + scale*B(b - A x^{n})\)

Here B is the application of the preconditioner

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

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

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

Supports only left preconditioning

If using direct solvers such as `PCLU` and `PCCHOLESKY` one generally uses `KSPPREONLY` instead of this which uses exactly one iteration

`-ksp_type richardson -pc_type jacobi` gives one classical Jacobi preconditioning

## References

[Ric11]

Lewis Fry Richardson. The approximate arithmetical solution by finite differences of physical problems including differential equations, with an application to the stresses in a masonry dam. Philosophical Transactions of the Royal Society A, 210(459–470):307–357, 1911. doi:10.1098/rsta.1911.0009.

## See Also

KSP: Linear System Solvers, `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPRichardsonSetScale()`, `KSPPREONLY`, `KSPRichardsonSetSelfScale()`

## Level

beginner

## Location

src/ksp/ksp/impls/rich/rich.c

## Examples

src/ksp/ksp/tutorials/ex71.c

Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages