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Yes, you can use a matrix-free approach on this matrix just like what you would do on the IJacobian matrix. Only the multTranspose operation needs to be overloaded for the adjoint.
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<div>Hong</div>
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<div class="">On Jul 30, 2020, at 6:52 PM, Salazar De Troya, Miguel via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov" class="">petsc-users@mcs.anl.gov</a>> wrote:</div>
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<span lang="ES" style="font-size: 11pt;" class="">Hi,<o:p class=""></o:p></span></div>
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<span lang="ES" style="font-size: 11pt;" class=""><o:p class=""> </o:p></span></div>
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<span style="font-size: 11pt;" class="">The jacobian of the RHS w.r.t. the parameter P is a matrix that will be multiplied by the adjoint solution within TSAdjoint(). I am interested in having access to that adjoint so I can calculate shape derivatives with
firedrake_adjoint. I will have to use that adjoint function, apply it to the residual and calculate the shape derivative from the resulting 0-form to obtain my RHSJacobianP*adjoint. This is the workaround done in pyadjoint:<span class="Apple-converted-space"> </span><a href="https://github.com/dolfin-adjoint/pyadjoint/blob/e6fbd13f8ac63290804852fa2f27307c44bdc9e3/dolfin_adjoint_common/blocks/solving.py#L204" style="color: rgb(5, 99, 193); text-decoration: underline;" class="">https://github.com/dolfin-adjoint/pyadjoint/blob/e6fbd13f8ac63290804852fa2f27307c44bdc9e3/dolfin_adjoint_common/blocks/solving.py#L204</a><span class="Apple-converted-space"> </span>Is
there another alternative within PETSc? Maybe using a matrix free approach?<o:p class=""></o:p></span></div>
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<span style="font-size: 11pt;" class=""><o:p class=""> </o:p></span></div>
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<span style="font-size: 11pt;" class="">Thanks<o:p class=""></o:p></span></div>
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<span style="font-size: 11pt;" class="">Miguel<o:p class=""></o:p></span></div>
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<span style="font-size: 11pt;" class=""><o:p class=""> </o:p></span></div>
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<span lang="ES" style="font-size: 9pt; font-family: Consolas;" class="">Miguel A. Salazar de Troya</span><span lang="ES" style="font-size: 10.5pt;" class=""><o:p class=""></o:p></span></div>
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<span style="font-size: 9pt; font-family: Consolas;" class="">Postdoctoral Researcher, Lawrence Livermore National Laboratory</span><span style="font-size: 10.5pt;" class=""><o:p class=""></o:p></span></div>
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<span style="font-size: 9pt; font-family: Consolas;" class="">B141</span><span style="font-size: 10.5pt;" class=""><o:p class=""></o:p></span></div>
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<span style="font-size: 9pt; font-family: Consolas;" class="">Rm: 1085-5</span><span style="font-size: 10.5pt;" class=""><o:p class=""></o:p></span></div>
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<span style="font-size: 9pt; font-family: Consolas;" class="">Ph: 1(925) 422-6411</span></div>
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