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

[Gong Ding]

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