<div dir="ltr"><div dir="ltr"><br></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, Mar 20, 2019 at 8:30 AM Yingjie Wu via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div dir="ltr">Thank you very much for your reply. </div><div dir="ltr">I think my statement may not be very clear. I want to know why the linear residual increases at gmres restart. </div></div></blockquote><div><br></div><div>GMRES combines the functions in the Krylov subspace that minimize the residual, by design (and this is provable). With restart you are not doing pure GMRES and the proof is gone. So if you have restart of 50 and do 51 iterations then the residual can not be lower than if you did 51 iterations of GMRES. I don't think you can prove anything about what the residual will do after a restart other than it will not go down more than it would without restart.</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div dir="ltr">I think I should have no problem with the residual evaluation function, because after setting a large gmres restart, the results are also in line with expectations. <br></div><div>Thanks,</div><div>Yingjie</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>> 于2019年3月20日周三 下午8:00写道：<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div dir="ltr">On Wed, Mar 20, 2019 at 6:53 AM Yingjie Wu via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>> wrote:<br></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div dir="ltr">Dear PETSc developers:<div>Hi,</div><div>Recently, I used PETSc to solve a non-linear PDEs for thermodynamic problems. In the process of solving, I found the following two phenomena, hoping to get some help and suggestions. </div><div><br></div><div>1. Because my problem involves a lot of physical parameters, it needs to call a series of functions, and can not analytically construct Jacobian matrix, so I use - snes_mf_operator to solve it, and give an approximate Jacobian matrix as a preconditioner. Because of the large dimension of the problem and the magnitude difference of the physical variables involved, it is found that the linear step residuals will increase at each restart (default 30th linear step) . This problem can be solved by setting a large number of restart steps. I would like to ask the reasons for this phenomenon? What knowledge or articles should I learn if I want to find out this problem? </div></div></div></blockquote><div><br></div><div>Make sure you non-dimensionalize the problem first, so that any scale differences are real and not the result of units.</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div dir="ltr"><div>2. In my problem model, there are many physical fields (variables are realized by finite difference method), and the magnitude of variables varies greatly. Is there any Scaling interface or function in Petsc? </div></div></div></blockquote><div><br></div><div>That is what Jacobi does.</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div dir="ltr"><div>Thanks,</div><div>Yingjie</div></div></div>
</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr" class="gmail-m_-7489483547758710013gmail-m_2219456166318611923gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><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><div><br></div><div><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div></div></div></div>
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