The physical problem itself is ill-conditioned since there are floating
regions in the simulation domain.
I use MUMPS as 64 bit LU solver, and a special improved SuperLU as 128
bit LU solver (https://github.com/cogenda/superlu, added float128 support).
Although 128 bit solver works, it is 10x slower.
I'd like to try, if jacobian can be processed under 64 bit precision
while keeps the Newton iteration convergence.
Method 1:
Use a block inversion of the main diagonal of jacobian as
preconditioner (or ILU? ). Then factorize M*J.
Both the precondition matrix and jacobian matrix are 64 bit.
Method 2:
Do a 64 bit LU factorization of jacobian matrix, and use the
factorization result as a preconditioner for higher precision krylov
solver (such as iterative refinement)
On 2023/9/14 23:05, Zhang, Hong wrote:
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 <[email protected]> on behalf of
Mark Adams <[email protected]>
*Sent:* Thursday, September 14, 2023 5:35 AM
*To:* Gong Ding <[email protected]>
*Cc:* [email protected] <[email protected]>
*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 <[email protected]> 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
