Gong Ding, When you use a LU solver, the preconditioner M = inv(LU) = inv (J) on theory. I suspect your jacobian evaluation by 64bit might be inaccurate. What LU solver did you use? Run your code with option '-snes_view -snes_monitor -ksp_monitor' and compare the displays. Hong ________________________________ From: petsc-users <petsc-users-boun...@mcs.anl.gov> on behalf of Mark Adams <mfad...@lbl.gov> Sent: Thursday, September 14, 2023 5:35 AM To: Gong Ding <gongd...@cn.cogenda.com> Cc: petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov> Subject: Re: [petsc-users] Is precondition works for ill-conditioned jacobian matrix
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 <gongd...@cn.cogenda.com<mailto:gongd...@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
