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Hi Matt,</div>
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please ignore my previous email. it was a silly question. <br>
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Thanks,</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
Feng<br>
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<div id="divRplyFwdMsg" dir="ltr"><font style="font-size:11pt" face="Calibri, sans-serif" color="#000000"><b>From:</b> petsc-users <petsc-users-bounces@mcs.anl.gov> on behalf of feng wang <snailsoar@hotmail.com><br>
<b>Sent:</b> 12 March 2021 17:12<br>
<b>To:</b> Matthew Knepley <knepley@gmail.com><br>
<b>Cc:</b> petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov><br>
<b>Subject:</b> Re: [petsc-users] Questions on matrix-free GMRES implementation</font>
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Hi Matt,</div>
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Thanks for your reply. I've checked my math, it is correct. I did not intend to reset the base point within a Newton iteration. what criteria is used in petsc to decide if it needs to automatically re-compute the basepoint?
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Thanks,</div>
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Feng<br>
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<div id="x_divRplyFwdMsg" dir="ltr"><font style="font-size:11pt" face="Calibri, sans-serif" color="#000000"><b>From:</b> Matthew Knepley <knepley@gmail.com><br>
<b>Sent:</b> 12 March 2021 15:40<br>
<b>To:</b> feng wang <snailsoar@hotmail.com><br>
<b>Cc:</b> Barry Smith <bsmith@petsc.dev>; petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov><br>
<b>Subject:</b> Re: [petsc-users] Questions on matrix-free GMRES implementation</font>
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<div dir="ltr">On Fri, Mar 12, 2021 at 10:37 AM feng wang <<a href="mailto:snailsoar@hotmail.com">snailsoar@hotmail.com</a>> wrote:<br>
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Hi Matt,</div>
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<br>
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Thanks for your prompt response. <br>
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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.
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?</div>
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<div>If you reset the base point, we need to recompute F(b), so you get two function calls. Normally, you do not reset the base point</div>
<div>within a Newton iteration. Maybe you should write out mathematically what you are doing. I cannot understand it right now.</div>
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<div> Thanks,</div>
<div><br>
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<div> Matt</div>
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Thanks,</div>
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Feng<br>
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<b>//This does not work</b><br>
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<div style="font-family:Calibri,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0)">
fld->cnsv( iqs,iqe, q, aux, csv );
<div> //add contribution of time-stepping</div>
<div> for(iv=0; iv<nv; iv++)</div>
<div> {</div>
<div> for(iq=0; iq<nq; iq++)</div>
<div> {</div>
<div> //use conservative variables here</div>
<div> rhs[iv][iq] = -rhs[iv][iq] + csv[iv][iq]*lhsa[nlhs-1][iq]/cfl;</div>
<div> }</div>
<div> }</div>
<div> ierr = petsc_setcsv(petsc_csv); CHKERRQ(ierr);</div>
<div> ierr = petsc_setrhs(petsc_baserhs); CHKERRQ(ierr);</div>
<div> ierr = MatMFFDSetBase(petsc_A_mf, petsc_csv, petsc_baserhs); CHKERRQ(ierr);</div>
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<b>//This works</b><br>
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fld->cnsv( iqs,iqe, q, aux, csv );
<div> ierr = petsc_setcsv(petsc_csv); CHKERRQ(ierr);</div>
<div> ierr = FormFunction_mf(this, petsc_csv, petsc_baserhs); //this is my callback function, now call it manually<br>
</div>
<div> ierr = MatMFFDSetBase(petsc_A_mf, petsc_csv, petsc_baserhs); CHKERRQ(ierr);</div>
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<div id="x_x_gmail-m_-4578071130681336893divRplyFwdMsg" dir="ltr"><font style="font-size:11pt" face="Calibri, sans-serif" color="#000000"><b>From:</b> Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
<b>Sent:</b> 12 March 2021 15:08<br>
<b>To:</b> feng wang <<a href="mailto:snailsoar@hotmail.com" target="_blank">snailsoar@hotmail.com</a>><br>
<b>Cc:</b> Barry Smith <<a href="mailto:bsmith@petsc.dev" target="_blank">bsmith@petsc.dev</a>>;
<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a> <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:</b> Re: [petsc-users] Questions on matrix-free GMRES implementation</font>
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<div dir="ltr">On Fri, Mar 12, 2021 at 9:55 AM feng wang <<a href="mailto:snailsoar@hotmail.com" target="_blank">snailsoar@hotmail.com</a>> wrote:<br>
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Hi Mat,</div>
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Thanks for your reply. I will try the parallel implementation.</div>
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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>
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<div>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>
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<div> Thanks,</div>
<div><br>
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<div> Matt</div>
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Thanks,</div>
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Feng<br>
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<font style="font-size:11pt" face="Calibri, sans-serif" color="#000000"><b>From:</b> Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
<b>Sent:</b> 12 March 2021 12:05<br>
<b>To:</b> feng wang <<a href="mailto:snailsoar@hotmail.com" target="_blank">snailsoar@hotmail.com</a>><br>
<b>Cc:</b> Barry Smith <<a href="mailto:bsmith@petsc.dev" target="_blank">bsmith@petsc.dev</a>>;
<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a> <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:</b> Re: [petsc-users] Questions on matrix-free GMRES implementation</font>
<div> </div>
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<div dir="ltr">On Fri, Mar 12, 2021 at 6:02 AM feng wang <<a href="mailto:snailsoar@hotmail.com" target="_blank">snailsoar@hotmail.com</a>> wrote:<br>
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Hi Barry,</div>
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Thanks for your advice.</div>
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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>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.
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In my previous buggy version, I only compute RHS twice. If possible, could you elaborate on your comments "<font face="Calibri, Helvetica, sans-serif">Also be careful about </font><span style="font-family:Calibri,Helvetica,sans-serif"> </span><span style="font-family:Calibri,Helvetica,sans-serif">petsc_baserhs</span>",
so I may possibly understand what was going on with my buggy version.</div>
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<div>Our FD implementation is simple. It approximates the action of the Jacobian as</div>
<div><br>
</div>
<div> J(b) v = (F(b + h v) - F(b)) / h ||v||</div>
<div><br>
</div>
<div>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>and v is the proposed solution update.</div>
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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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<div>Sure</div>
<div><br>
</div>
<div> <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSetSizes.html" target="_blank">https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSetSizes.html</a></div>
<div><br>
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<div> Thanks,</div>
<div><br>
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<div> Matt</div>
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Many thanks,</div>
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Feng<br>
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<font style="font-size:11pt" face="Calibri, sans-serif" color="#000000"><b>From:</b> Barry Smith <<a href="mailto:bsmith@petsc.dev" target="_blank">bsmith@petsc.dev</a>><br>
<b>Sent:</b> 11 March 2021 22:15<br>
<b>To:</b> feng wang <<a href="mailto:snailsoar@hotmail.com" target="_blank">snailsoar@hotmail.com</a>><br>
<b>Cc:</b> <a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a> <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:</b> Re: [petsc-users] Questions on matrix-free GMRES implementation</font>
<div> </div>
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<div><br>
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Feng,
<div><br>
</div>
<div> 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><br>
</div>
<div>The easiest way is to call <font face="Calibri, Helvetica, sans-serif">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"> </span><span style="font-family:Calibri,Helvetica,sans-serif">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">petsc_baserhs values to the function evaluation at that point.</span></div>
<div><span style="font-family:Calibri,Helvetica,sans-serif"><br>
</span></div>
<div><span style="font-family:Calibri,Helvetica,sans-serif">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><br>
</div>
<div>Barry</div>
<div><br>
</div>
<div>
<div><br>
<blockquote type="cite">
<div>On Mar 11, 2021, at 7:35 AM, feng wang <<a href="mailto:snailsoar@hotmail.com" target="_blank">snailsoar@hotmail.com</a>> wrote:</div>
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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">
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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">
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the matrix-free matrix is created as:</div>
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ierr = MatCreateMFFD(*A_COMM_WORLD, iqe*blocksize, iqe*blocksize, PETSC_DETERMINE, PETSC_DETERMINE, &petsc_A_mf); CHKERRQ(ierr);
<div> ierr = MatMFFDSetFunction(petsc_A_mf, FormFunction_mf, this); CHKERRQ(ierr);</div>
<div></div>
<div><br>
</div>
<div>KSP linear operator is set up as:</div>
<div><br>
</div>
<div> ierr = KSPSetOperators(petsc_ksp, petsc_A_mf, petsc_A_pre); CHKERRQ(ierr); //petsc_A_pre is my assembled pre-conditioning matrix<br>
</div>
<div><br>
</div>
<div>Before calling KSPSolve, I do:</div>
<div><br>
</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>
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The call back function is defined as:</div>
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PetscErrorCode cFdDomain::FormFunction_mf(void *ctx, Vec in_vec, Vec out_vec)
<div> {</div>
<div> PetscErrorCode ierr;</div>
<div> cFdDomain *user_ctx;</div>
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<div> cout << "FormFunction_mf called\n";</div>
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<div> //in_vec: flow states</div>
<div> //out_vec: right hand side + diagonal contributions from CFL number</div>
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<div> user_ctx = (cFdDomain*)ctx;</div>
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<div> //get perturbed conservative variables from petsc</div>
<div> user_ctx->petsc_getcsv(in_vec);</div>
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<div> //get new right side</div>
<div> user_ctx->petsc_fd_rhs();</div>
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<div> //set new right hand side to the output vector</div>
<div> user_ctx->petsc_setrhs(out_vec);</div>
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<div> ierr = 0;</div>
<div> return ierr;</div>
<div> }</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> </span><br>
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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> </span></div>
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<div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>
-- Norbert Wiener</div>
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<div><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br>
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<div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>
-- Norbert Wiener</div>
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<div><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br>
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<div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>
-- Norbert Wiener</div>
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<div><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br>
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