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<p class="MsoNormal">Hi Art,<br>
<br>
Here is a TS example that uses MatShell for implicit time integration and adjoint sensitivity calculation:
<br>
src/ts/tutorials/advection-diffusion-reaction/ex5adj_mf.c<o:p></o:p></p>
<p class="MsoNormal"><br>
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.<br>
<br>
Hong<br>
<br>
<o:p></o:p></p>
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<p class="MsoNormal"><b><span style="font-family:"Calibri",sans-serif;color:black">From:
</span></b><span style="font-family:"Calibri",sans-serif;color:black">petsc-users <petsc-users-bounces@mcs.anl.gov> on behalf of Art <mac3bar@gmail.com><br>
<b>Date: </b>Monday, July 7, 2025 at 9:33 AM<br>
<b>To: </b>"petsc-users@mcs.anl.gov" <petsc-users@mcs.anl.gov><br>
<b>Subject: </b>[petsc-users] Matrix-Free J*v in PETSc<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Hi all,<br>
<br>
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<br>
<br>
Is there a way to do something similar in PETSc TS (for BDF or other implicit schemes)?<br>
<br>
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.<br>
<br>
Best regards,<br>
<br>
Art<o:p></o:p></p>
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