Hi Art, Here is a TS example that uses MatShell for implicit time integration and adjoint sensitivity calculation: src/ts/tutorials/advection-diffusion-reaction/ex5adj_mf.c
You will need to provide a (jvp) routine like MyIMatMult() in this example. Adjoints require vjp (vector-Jacobian product) routines that are also included in this example. Hong From: petsc-users <petsc-users-boun...@mcs.anl.gov> on behalf of Art <mac3...@gmail.com> Date: Monday, July 7, 2025 at 9:33 AM To: "petsc-users@mcs.anl.gov" <petsc-users@mcs.anl.gov> Subject: [petsc-users] Matrix-Free J*v in PETSc 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
