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 with 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 on the 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 provided with SNESSetJacobian() thus it 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

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