Using MatShell is the standard method. Note that MatShell allows exposing other "matrix operations", such as producing a diagonal or other preconditioning ingredients.
Art <mac3...@gmail.com> writes: > 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
