petsc-3.7.1 2016-05-15
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# SNESSetPicard

Use SNES to solve the semilinear-system A(x) x = b(x) via a Picard type iteration (Picard linearization)

### Synopsis

    #include "petscsnes.h"
    PetscErrorCode  SNESSetPicard(SNES snes,Vec r,PetscErrorCode (*b)(SNES,Vec,Vec,void*),Mat Amat, Mat Pmat, PetscErrorCode (*J)(SNES,Vec,Mat,Mat,void*),void *ctx)

Logically Collective on SNES Many br

### Input Parameters

| snes | - the SNES context Many br
| r | - vector to store function value Many br
| b | - function evaluation routine Many br
| Amat | - matrix with which A(x) x - b(x) is to be computed Many br
| Pmat | - matrix from which preconditioner is computed (usually the same as Amat) Many br
| J | - function to compute matrix value, see SNESJacobianFunction for details on its calling sequence Many br
| ctx | - [optional] user-defined context for private data for the Many brfunction evaluation routine (may be NULL) Many br

### Notes

We do not recomemend using this routine. It is far better to provide the nonlinear function F() and some approximation to the Jacobian and use Many bran approximate Newton solver. This interface is provided to allow porting/testing a previous Picard based code in PETSc before converting it to approximate Newton. Many br

One can call SNESSetPicard() or SNESSetFunction() (and possibly SNESSetJacobian()) but cannot call both Many br

        Solves the equation A(x) x = b(x) via the defect correction algorithm A(x^{n}) (x^{n+1} - x^{n}) = b(x^{n}) - A(x^{n})x^{n}

        Note that when an exact solver is used this corresponds to the "classic" Picard A(x^{n}) x^{n+1} = b(x^{n}) iteration.

Run with -snes_mf_operator to solve the system with Newton's method using A(x^{n}) to construct the preconditioner. Many br

We implement the defect correction form of the Picard iteration because it converges much more generally when inexact linear solvers are used then Many brthe direct Picard iteration A(x^n) x^{n+1} = b(x^n) Many br

There is some controversity over the definition of a Picard iteration for nonlinear systems but almost everyone agrees that it involves a linear solve and some Many brbelieve it is the iteration A(x^{n}) x^{n+1} = b(x^{n}) hence we use the name Picard. If anyone has an authoritative reference that defines the Picard iteration Many brdifferent please contact us at petsc-dev@mcs.anl.gov and we'll have an entirely new argument :-). Many br

Many br

### Keywords

SNES, nonlinear, set, function

### See Also

SNESGetFunction(), SNESSetFunction(), SNESComputeFunction(), SNESSetJacobian(), SNESGetPicard(), SNESLineSearchPreCheckPicard(), SNESJacobianFunction

Level:intermediate
Location:src/snes/interface/snes.c
Index of all SNES routines
Table of Contents for all manual pages
Index of all manual pages