<html><head><meta http-equiv="Content-Type" content="text/html; charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Mar 12, 2021, at 9:37 AM, feng wang <<a href="mailto:snailsoar@hotmail.com" class="">snailsoar@hotmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class="">
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Hi Matt,</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
<br class="">
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<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
Thanks for your prompt response. <br class="">
</div>
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Below are my two versions. one is buggy and the 2nd one is working. For the first one, I add the diagonal contribution to the true RHS (variable: rhs) and then set the base point, the callback function is somehow called twice afterwards to compute Jacobian.
</div></div></div></blockquote><div><br class=""></div> Do you mean "to compute the Jacobian matrix-vector product?"</div><div><br class=""></div><div> Is it only in the first computation of the product (for the given base vector) that it calls it twice or every matrix-vector product?</div><div><br class=""></div><div> It is possible there is a bug in our logic; run in the debugger with a break point in <font face="Calibri, Helvetica, sans-serif" class="">FormFunction_mf and each time the function is hit in the debugger type where or bt to get the stack frames from the calls. Send this. From this we can all see if it is being called excessively and why.</font></div><div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">For the 2nd one, I just call the callback function manually to recompute everything, the callback function is then called once as expected to compute the Jacobian. For me, both versions should do the same things. but I don't know why in the first one the callback
function is called twice after I set the base point. what could possibly go wrong?<br class=""></div></div></div></blockquote><div><br class=""></div> The logic of how it is suppose to work is shown below.<br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
<br class="">
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<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
Thanks,</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
Feng<br class="">
</div>
<div class="">
<div id="appendonsend" class=""></div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
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<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
<b class="">//This does not work</b><br class="">
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
fld->cnsv( iqs,iqe, q, aux, csv );
<div class=""> //add contribution of time-stepping</div>
<div class=""> for(iv=0; iv<nv; iv++)</div>
<div class=""> {</div>
<div class=""> for(iq=0; iq<nq; iq++)</div>
<div class=""> {</div>
<div class=""> //use conservative variables here</div>
<div class=""> rhs[iv][iq] = -rhs[iv][iq] + csv[iv][iq]*lhsa[nlhs-1][iq]/cfl;</div>
<div class=""> }</div>
<div class=""> }</div>
<div class=""> ierr = petsc_setcsv(petsc_csv); CHKERRQ(ierr);</div>
<div class=""> ierr = petsc_setrhs(petsc_baserhs); CHKERRQ(ierr);</div>
<div class=""> ierr = MatMFFDSetBase(petsc_A_mf, petsc_csv, petsc_baserhs); CHKERRQ(ierr);</div>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
<br class="">
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
<b class="">//This works</b><br class="">
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
fld->cnsv( iqs,iqe, q, aux, csv );
<div class=""> ierr = petsc_setcsv(petsc_csv); CHKERRQ(ierr);</div>
<div class=""> ierr = FormFunction_mf(this, petsc_csv, petsc_baserhs); //this is my callback function, now call it manually<br class="">
</div>
<div class=""> ierr = MatMFFDSetBase(petsc_A_mf, petsc_csv, petsc_baserhs); CHKERRQ(ierr);</div>
<div class=""><br class="">
</div>
<br class=""></div></div></div></div></blockquote><div> Since you provide <span style="font-family: Calibri, Helvetica, sans-serif;" class="">petsc_baserhs MatMFFD assumes (naturally) that you will keep the correct values in it. Hence for each new base value YOU need to compute the new values in </span><span style="font-family: Calibri, Helvetica, sans-serif;" class="">petsc_baserhs. This approach gives you a bit more control over reusing the information in </span><span style="font-family: Calibri, Helvetica, sans-serif;" class="">petsc_baserhs. </span></div><div><span style="font-family: Calibri, Helvetica, sans-serif;" class=""><br class=""></span></div><div><span style="font-family: Calibri, Helvetica, sans-serif;" class=""> If you would prefer that </span><span style="font-family: Calibri, Helvetica, sans-serif;" class="">MatMFFD recomputes the base values, as needed, then you call </span><span style="font-family: Calibri, Helvetica, sans-serif;" class="">FormFunction_mf(this, petsc_csv, NULL); and PETSc will allocate a vector and fill it up as needed by calling your </span><span style="font-family: Calibri, Helvetica, sans-serif;" class="">FormFunction_mf() But you need to call MatAssemblyBegin/End each time you the base input vector </span><span style="font-family: Calibri, Helvetica, sans-serif;" class="">this, petsc_csv values change. For </span><font face="Calibri, Helvetica, sans-serif" class="">example</font></div><div><font face="Calibri, Helvetica, sans-serif" class=""><br class=""></font></div><div><font face="Calibri, Helvetica, sans-serif" class=""> MatAssemblyBegin(</font><span style="font-family: Calibri, Helvetica, sans-serif;" class="">petsc_A_mf,...)</span></div><div><span style="font-family: Calibri, Helvetica, sans-serif;" class=""> </span><font face="Calibri, Helvetica, sans-serif" class="">MatAssemblyEnd(</font><span style="font-family: Calibri, Helvetica, sans-serif;" class="">petsc_A_mf,...)</span></div><div><span style="font-family: Calibri, Helvetica, sans-serif;" class=""> KSPSolve()</span></div><div><span style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class=""><br class=""></span></div><div><span style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class=""><br class=""></span></div><div><br class=""></div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class=""><div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
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<div id="divRplyFwdMsg" dir="ltr" class=""><font style="font-size:11pt" face="Calibri, sans-serif" class=""><b class="">From:</b> Matthew Knepley <<a href="mailto:knepley@gmail.com" class="">knepley@gmail.com</a>><br class="">
<b class="">Sent:</b> 12 March 2021 15:08<br class="">
<b class="">To:</b> feng wang <<a href="mailto:snailsoar@hotmail.com" class="">snailsoar@hotmail.com</a>><br class="">
<b class="">Cc:</b> Barry Smith <<a href="mailto:bsmith@petsc.dev" class="">bsmith@petsc.dev</a>>; <a href="mailto:petsc-users@mcs.anl.gov" class="">petsc-users@mcs.anl.gov</a> <<a href="mailto:petsc-users@mcs.anl.gov" class="">petsc-users@mcs.anl.gov</a>><br class="">
<b class="">Subject:</b> Re: [petsc-users] Questions on matrix-free GMRES implementation</font>
<div class=""> </div>
</div>
<div class="">
<div dir="ltr" class="">
<div dir="ltr" class="">On Fri, Mar 12, 2021 at 9:55 AM feng wang <<a href="mailto:snailsoar@hotmail.com" class="">snailsoar@hotmail.com</a>> wrote:<br class="">
</div>
<div class="x_gmail_quote">
<blockquote class="x_gmail_quote" style="margin:0px 0px 0px 0.8ex; border-left:1px solid rgb(204,204,204); padding-left:1ex">
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<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
Hi Mat,</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
<br class="">
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
Thanks for your reply. I will try the parallel implementation.</div>
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<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
I've got a serial matrix-free GMRES working, but I would like to know why my initial version of matrix-free implementation does not work and there is still something I don't understand. I did some debugging and find that the callback function to compute the
RHS for the matrix-free matrix is called twice by Petsc when it computes the finite difference Jacobian, but it should only be called once. I don't know why, could you please give some advice?</div>
</div>
</blockquote>
<div class=""><br class="">
</div>
<div class="">F is called once to calculate the base point and once to get the perturbation. The base point is not recalculated, so if you do many iterates, it is amortized.</div>
<div class=""><br class="">
</div>
<div class=""> Thanks,</div>
<div class=""><br class="">
</div>
<div class=""> Matt</div>
<div class=""> </div>
<blockquote class="x_gmail_quote" style="margin:0px 0px 0px 0.8ex; border-left:1px solid rgb(204,204,204); padding-left:1ex">
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<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
Thanks,</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
Feng<br class="">
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
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<div id="x_gmail-m_-6641396561494424030divRplyFwdMsg" dir="ltr" class=""><font style="font-size:11pt" face="Calibri, sans-serif" class=""><b class="">From:</b> Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank" class="">knepley@gmail.com</a>><br class="">
<b class="">Sent:</b> 12 March 2021 12:05<br class="">
<b class="">To:</b> feng wang <<a href="mailto:snailsoar@hotmail.com" target="_blank" class="">snailsoar@hotmail.com</a>><br class="">
<b class="">Cc:</b> Barry Smith <<a href="mailto:bsmith@petsc.dev" target="_blank" class="">bsmith@petsc.dev</a>>;
<a href="mailto:petsc-users@mcs.anl.gov" target="_blank" class="">petsc-users@mcs.anl.gov</a> <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank" class="">petsc-users@mcs.anl.gov</a>><br class="">
<b class="">Subject:</b> Re: [petsc-users] Questions on matrix-free GMRES implementation</font>
<div class=""> </div>
</div>
<div class="">
<div dir="ltr" class="">
<div dir="ltr" class="">On Fri, Mar 12, 2021 at 6:02 AM feng wang <<a href="mailto:snailsoar@hotmail.com" target="_blank" class="">snailsoar@hotmail.com</a>> wrote:<br class="">
</div>
<div class="">
<blockquote style="margin:0px 0px 0px 0.8ex; border-left:1px solid rgb(204,204,204); padding-left:1ex" class="">
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<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
Hi Barry,</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
<br class="">
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
Thanks for your advice.</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
<br class="">
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
You are right on this. somehow there is some inconsistency when I compute the right hand side (true RHS + time-stepping contribution to the diagonal matrix) to compute the finite difference Jacobian. If I just use the call back function to recompute my RHS
before I call <b class="">MatMFFDSetBase</b>, then it works like a charm. But now I end up with computing my RHS three times. 1st time is to compute the true RHS, the rest two is for computing finite difference Jacobian.
<br class="">
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
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</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
In my previous buggy version, I only compute RHS twice. If possible, could you elaborate on your comments "<font face="Calibri, Helvetica, sans-serif" class="">Also be careful about </font><span style="font-family:Calibri,Helvetica,sans-serif" class=""> </span><span style="font-family:Calibri,Helvetica,sans-serif" class="">petsc_baserhs</span>",
so I may possibly understand what was going on with my buggy version.</div>
</div>
</blockquote>
<div class=""><br class="">
</div>
<div class="">Our FD implementation is simple. It approximates the action of the Jacobian as</div>
<div class=""><br class="">
</div>
<div class=""> J(b) v = (F(b + h v) - F(b)) / h ||v||</div>
<div class=""><br class="">
</div>
<div class="">where h is some small parameter and b is the base vector, namely the one that you are linearizing around. In a Newton step, b is the previous solution</div>
<div class="">and v is the proposed solution update.</div>
<div class=""> </div>
<blockquote style="margin:0px 0px 0px 0.8ex; border-left:1px solid rgb(204,204,204); padding-left:1ex" class="">
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<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
Besides, for a parallel implementation, my code already has its own partition method, is it possible to allow petsc read in a user-defined partition? if not what is a better way to do this?</div>
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</blockquote>
<div class=""><br class="">
</div>
<div class="">Sure</div>
<div class=""><br class="">
</div>
<div class=""> <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSetSizes.html" target="_blank" class="">https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSetSizes.html</a></div>
<div class=""><br class="">
</div>
<div class=""> Thanks,</div>
<div class=""><br class="">
</div>
<div class=""> Matt</div>
<div class=""> </div>
<blockquote style="margin:0px 0px 0px 0.8ex; border-left:1px solid rgb(204,204,204); padding-left:1ex" class="">
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<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
Many thanks,</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
Feng<br class="">
</div>
<div class="">
<div id="x_gmail-m_-6641396561494424030x_gmail-m_-4210113834389506889appendonsend" class="">
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">
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<div id="x_gmail-m_-6641396561494424030x_gmail-m_-4210113834389506889divRplyFwdMsg" dir="ltr" class="">
<font style="font-size:11pt" face="Calibri, sans-serif" class=""><b class="">From:</b> Barry Smith <<a href="mailto:bsmith@petsc.dev" target="_blank" class="">bsmith@petsc.dev</a>><br class="">
<b class="">Sent:</b> 11 March 2021 22:15<br class="">
<b class="">To:</b> feng wang <<a href="mailto:snailsoar@hotmail.com" target="_blank" class="">snailsoar@hotmail.com</a>><br class="">
<b class="">Cc:</b> <a href="mailto:petsc-users@mcs.anl.gov" target="_blank" class="">petsc-users@mcs.anl.gov</a> <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank" class="">petsc-users@mcs.anl.gov</a>><br class="">
<b class="">Subject:</b> Re: [petsc-users] Questions on matrix-free GMRES implementation</font>
<div class=""> </div>
</div>
<div class="">
<div class=""><br class="">
</div>
Feng,
<div class=""><br class="">
</div>
<div class=""> The first thing to check is that for each linear solve that involves a new operator (values in the base vector) the MFFD matrix knows it is using a new operator. </div>
<div class=""><br class="">
</div>
<div class="">The easiest way is to call <font face="Calibri, Helvetica, sans-serif" class="">MatMFFDSetBase() before each solve that involves a new operator (new values in the base vector). Also be careful about </font><span style="font-family:Calibri,Helvetica,sans-serif" class=""> </span><span style="font-family:Calibri,Helvetica,sans-serif" class="">petsc_baserhs,
when you change the base vector's values you also need to change the </span><span style="font-family:Calibri,Helvetica,sans-serif" class="">petsc_baserhs values to the function evaluation at that point.</span></div>
<div class=""><span style="font-family:Calibri,Helvetica,sans-serif" class=""><br class="">
</span></div>
<div class=""><span style="font-family:Calibri,Helvetica,sans-serif" class="">If that is correct I would check with a trivial function evaluator to make sure the infrastructure is all set up correctly. For examples use for the matrix free a 1 4 1 operator applied matrix free. </span></div>
<div class=""><br class="">
</div>
<div class="">Barry</div>
<div class=""><br class="">
</div>
<div class="">
<div class=""><br class="">
<blockquote type="cite" class="">
<div class="">On Mar 11, 2021, at 7:35 AM, feng wang <<a href="mailto:snailsoar@hotmail.com" target="_blank" class="">snailsoar@hotmail.com</a>> wrote:</div>
<br class="">
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<div style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt" class="">
Dear All,</div>
<div style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt" class="">
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I am new to petsc and trying to implement a matrix-free GMRES. I have assembled an approximate Jacobian matrix just for preconditioning. After reading some previous questions on this topic, my approach is:</div>
<div style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt" class="">
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<div style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt" class="">
the matrix-free matrix is created as:</div>
<div style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt" class="">
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</div>
<div style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt" class="">
ierr = MatCreateMFFD(*A_COMM_WORLD, iqe*blocksize, iqe*blocksize, PETSC_DETERMINE, PETSC_DETERMINE, &petsc_A_mf); CHKERRQ(ierr);
<div class=""> ierr = MatMFFDSetFunction(petsc_A_mf, FormFunction_mf, this); CHKERRQ(ierr);</div>
<div class=""></div>
<div class=""><br class="">
</div>
<div class="">KSP linear operator is set up as:</div>
<div class=""><br class="">
</div>
<div class=""> ierr = KSPSetOperators(petsc_ksp, petsc_A_mf, petsc_A_pre); CHKERRQ(ierr); //petsc_A_pre is my assembled pre-conditioning matrix<br class="">
</div>
<div class=""><br class="">
</div>
<div class="">Before calling KSPSolve, I do:</div>
<div class=""><br class="">
</div>
ierr = MatMFFDSetBase(petsc_A_mf, petsc_csv, petsc_baserhs); CHKERRQ(ierr); //petsc_csv is the flow states, petsc_baserhs is the pre-computed right hand side</div>
<div style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt" class="">
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</div>
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The call back function is defined as:</div>
<div style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt" class="">
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<div style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt" class="">
PetscErrorCode cFdDomain::FormFunction_mf(void *ctx, Vec in_vec, Vec out_vec)
<div class=""> {</div>
<div class=""> PetscErrorCode ierr;</div>
<div class=""> cFdDomain *user_ctx;</div>
<div class=""><br class="">
</div>
<div class=""> cout << "FormFunction_mf called\n";</div>
<div class=""><br class="">
</div>
<div class=""> //in_vec: flow states</div>
<div class=""> //out_vec: right hand side + diagonal contributions from CFL number</div>
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<div class=""> user_ctx = (cFdDomain*)ctx;</div>
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<div class=""> //get perturbed conservative variables from petsc</div>
<div class=""> user_ctx->petsc_getcsv(in_vec);</div>
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<div class=""> //get new right side</div>
<div class=""> user_ctx->petsc_fd_rhs();</div>
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<div class=""> //set new right hand side to the output vector</div>
<div class=""> user_ctx->petsc_setrhs(out_vec);</div>
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<div class=""> ierr = 0;</div>
<div class=""> return ierr;</div>
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The linear system I am solving is (J+D)x=RHS. J is the Jacobian matrix. D is a diagonal matrix and it is used to stabilise the solution at the start but reduced gradually when the solution moves on to recover Newton's method. I add D*x to the true right side
when non-linear function is computed to work out finite difference Jacobian, so when finite difference is used, it actually computes (J+D)*dx.<span class=""> </span><br class="">
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The code runs but diverges in the end. If I don't do matrix-free and use my approximate Jacobian matrix, GMRES works. So something is wrong with my matrix-free implementation. Have I missed something in my implementation? Besides, is there a way to check
if the finite difference Jacobian matrix is computed correctly in a matrix-free implementation?</div>
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Thanks for your help in advance.</div>
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Feng <span class=""> </span></div>
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<div class="">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br class="">
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<div class=""><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank" class="">https://www.cse.buffalo.edu/~knepley/</a><br class="">
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<div class="">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br class="">
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