[petsc-users] about finite difference jacobian approximations

[Jed Brown]

On Sat, 1 May 2010 15:35:25 +0800, "=?gb2312?B?s8LA1sa9o6hMZXBpbmcgQ2hlbqOp?=" <chenleping at yahoo.cn> wrote:
> hello, petsc teams,
> 
> When I use finite difference jacobian approximations, I only find the
> computation methods and results of jacobian matrix cannot influence
> iterative process of snes.

I don't know what you're asking.  The accuracy of the Jacobian certainly
can affect the convergence rate; for simple or well-conditioned
problems, finite difference Jacobians are usually reliable.  Analytic
Jacobians, or Jacobians from automatic differentiation (AD) are usually
better when available and not too expensive to compute.  Another common
thing is to assemble a "cheap" preconditioning matrix (dropping terms,
or with a lower order discretization) for use with a matrix-free
(usually finite difference or AD) operator.

Jed