[petsc-users] Matrix-Free J*v in PETSc

[Art]

Hi all,

I am integrating a stiff system of ODEs/PDEs using PETSc TS (typically with
BDF or other implicit time-stepping schemes), and I would like to exploit
the fact that I can efficiently compute the action of the Jacobian on a
vector (Jv) without assembling the full Jacobian matrix. Since for a large
system it becomes expensive to assemble the Jacobian in each iteration.  In
scikits.odes (SUNDIALS/CVODE), there is a native API for passing only a J*v
routine to the time integrator. In my experience, when I use only a
Jacobian-vector product routine (without assembling the full matrix), the
performance improves significantly for large systems. However, in PETSc TS,
the workflow seems more matrix-centric, and I have only found the
possibility to use MatShell for the Jacobian

Is there a way to do something similar in PETSc TS (for BDF or other
implicit schemes)?

Currently, I use the matrix-free Newton-Krylov method to approximate the
Jacobian and have adjusted the tolerances to achieve convergence, as
recommended by Barry. In that case, I obtain similar integration times
with scikits.odes CVODE without using the Jacobian times vector.

Best regards,

Art
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