SNESNRICHARDSON — PETSc 3.21.4 documentation

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# SNESNRICHARDSON

Richardson nonlinear solver that uses successive substitutions, also sometimes known as Picard iteration.

## Options Database Keys

- -snes_linesearch_type <l2,cp,basic> - Line search type.

- -snes_linesearch_damping<1.0> - Damping for the line search.

## Notes

If no inner nonlinear preconditioner is provided then solves F(x) - b = 0 using x^{n+1} = x^{n} - lambda (F(x^n) - b) where lambda is obtained either `SNESLineSearchSetDamping()`, -snes_damping or a line search. If an inner nonlinear preconditioner is provided (either with -npc_snes_type or `SNESSetNPC()`) then the inner solver is called an initial solution x^n and the nonlinear Richardson uses x^{n+1} = x^{n} + lambda d^{n} where d^{n} = \hat{x}^{n} - x^{n} where \hat{x}^{n} is the solution returned from the inner solver.

The update, especially without inner nonlinear preconditioner, may be ill-scaled. If using the basic linesearch, one may have to scale the update with -snes_linesearch_damping

This uses no derivative information thus will be much slower then Newton’s method obtained with -snes_type ls

Only supports left non-linear preconditioning.

## See Also

SNES: Nonlinear Solvers, `SNESCreate()`, `SNES`, `SNESSetType()`, `SNESNEWTONLS`, `SNESNEWTONTR`, `SNESNGMRES`, `SNESQN`, `SNESNCG`, `SNESLineSearchSetDamping()`

## Level

beginner

## Location

src/snes/impls/richardson/snesrichardson.c

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