[petsc-users] Store and reuse the factor of matrix

[Jinlei Shen]

​Hi,

I'm trying to implement modified newton method to solve the nonlinear
finite element using petsc.

As well known,  the advantage of modified newton is the Jacobian matrix is
always same during the iteration, which means once the J is factorized at
the first iteration, we can store the factors and avoid the factorization
for next iteration if we use direct solver, e.g. super_lu. Therefore, the
option FACTORED in SUPER_LU is quite useful.

However, it looks like the option FACTORED is not available in
SUPER_LU_DIST in petsc. I tried, and it shows 'unknown option'.

Is there alternative way to use the same idea of FACTORED in petsc for
super_lu?

Also, I'm wondering whether iterative solver in PETSC is also able to apply
the same strategy.

In other words, in the problem where Jacobian is constant, only residue and
solution vectors need to be updated, is there any way to take advantage of
such same Jacobian pattern to expedite the computation using iterative
solver?

Thank you

BTW, though using modified newton will increase the iteration number,
however, in the case which is much more expensive to factorize the
jacobian, more iterations will probably be worthwhile.

Bests,
Jinlei
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