[petsc-users] Is precondition works for ill-conditioned jacobian matrix

[Mark Adams]

I would first verify that you are happy with the solution that works.

Next, I would worry about losing accuracy in computing M*J, but you could
try it and search for any related work. There may be some tricks.

And MUMPS is good at high accuracy, you might try that and if it fails look
at the MUMPS docs for any flags for high-accuracy.

Good luck,
Mark

On Thu, Sep 14, 2023 at 5:35 AM Gong Ding <gongding at cn.cogenda.com> wrote:

> Hi all
>
> I find such a nonlinear problem, the jacobian matrix is ill conditioned.
>
> Solve the jacobian matrix by 64bit LU  solver, the Newton method failed
> to convergence.
>
> However, when solve the jacobian matrix by 128bit LU solver , Newton
> iteration will convergence.
>
> I think this phenomena indicate that , the jacobian matrix is ill
> conditioned.
>
>
> The question is, if I do a precondition as M*J*dx = -M*f(x), here M is
> the precondition matrix, . then I solve the matrix A=M*J by a LU solver.
>
> Can I expect that solve A=M*J has a better precision result that help
> the convergence of Newton iteration?
>
> Gong Ding
>
>
>
>
>
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