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Are there other alternative methods that might be easier to implement? Miguel On Mon, Jul 8, 2024 at 1: 43 PM Matthew Knepley <knepley@ gmail. com> wrote: On Mon, Jul 8, 2024 at 6: 14 AM Miguel Angel Salazar de Troya <miguel. salazar@ corintis. com>
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<div dir="ltr">Are there other alternative methods that might be easier to implement?<div><br></div><div>Miguel</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, Jul 8, 2024 at 1:43 PM Matthew Knepley <<a href="mailto:knepley@gmail.com">knepley@gmail.com</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">On Mon, Jul 8, 2024 at 6:14 AM Miguel Angel Salazar de Troya <<a href="mailto:miguel.salazar@corintis.com" target="_blank">miguel.salazar@corintis.com</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">Thanks Adam and Matt,<div><br></div><div>Matt, can I get away with just using PCFIELDSPLIT? Or do I need the SNESFIELDSPLIT? Though it looks like the block Gauss-Seidel is only implemented in serial (<a href="https://urldefense.us/v3/__https://petsc.org/main/manual/ksp/*block-jacobi-and-overlapping-additive-schwarz-preconditioners__;Iw!!G_uCfscf7eWS!bSoUE_2lViJzEHKf5CEFph-9dqm5ZtOB6QjWVEk4zIyGBukbkcoEGiVzHu84pF637kvsxFyFQoUPYjIUFM5eZZ51NH3TTKGi$" target="_blank">https://petsc.org/main/manual/ksp/#block-jacobi-and-overlapping-additive-schwarz-preconditioners</a>)</div></div></blockquote><div><br></div><div>You can do what you want for the linear problem, but that will probably not help. The best thing I know of for this kind of nonlinear coupling is</div><div>now called primal-dual Newton, a name which I am not wild about. It is discussed here (<a href="https://urldefense.us/v3/__https://core.ac.uk/download/pdf/211337815.pdf__;!!G_uCfscf7eWS!bSoUE_2lViJzEHKf5CEFph-9dqm5ZtOB6QjWVEk4zIyGBukbkcoEGiVzHu84pF637kvsxFyFQoUPYjIUFM5eZZ51NFSFi9w1$" target="_blank">https://core.ac.uk/download/pdf/211337815.pdf</a>) and</div><div>originated in reference [33] from that thesis. My aim was to allow these kinds of solvers with that branch.</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>On a more theoretical note, I have the impression that the convergence failures of the Newton-Raphson method for this kind of problem is ultimately due to a lack of a diagonally dominant Jacobian. I have not found any reference so I might be wrong.</div></div></blockquote><div><br></div><div>I would say that the dominant direction for momentum hides the direction for improvement of the coefficient.</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>Best,</div><div>Miguel</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sat, Jul 6, 2024 at 3:33 PM Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</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">On Fri, Jul 5, 2024 at 3:29 AM Miguel Angel Salazar de Troya <<a href="mailto:miguel.salazar@corintis.com" target="_blank">miguel.salazar@corintis.com</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>
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Hello, I have the Navier-Stokes equation coupled with a convection-diffusion equation for the temperature. It is a two-way coupling because the viscosity depends on the temperature. One way to solve this is with some kind of fixed point iteration
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<div dir="ltr">Hello,<div><br></div><div>I have the Navier-Stokes equation coupled with a convection-diffusion equation for the temperature. It is a two-way coupling because the viscosity depends on the temperature. One way to solve this is with some kind of fixed point iteration scheme, where I solve each equation separately in a loop until I see convergence. I am aware this is not possible directly at the SNES level. Is there something that one can do using PCFIELDSPLIT? I would like to assemble my fully coupled system and play with the solver options to get some kind of fixed-point iteration scheme. I would like to avoid having to build two separate SNES solvers, one per equation. Any reference on techniques to solve this type of coupled system is welcome.</div></div></div></blockquote><div><br></div><div>Hi Miguel,</div><div><br></div><div>I have a branch</div><div><br></div><div> <a href="https://urldefense.us/v3/__https://gitlab.com/petsc/petsc/-/tree/knepley/feature-snes-fieldsplit?ref_type=heads__;!!G_uCfscf7eWS!bSoUE_2lViJzEHKf5CEFph-9dqm5ZtOB6QjWVEk4zIyGBukbkcoEGiVzHu84pF637kvsxFyFQoUPYjIUFM5eZZ51NA5DeA9R$" target="_blank">https://gitlab.com/petsc/petsc/-/tree/knepley/feature-snes-fieldsplit?ref_type=heads</a></div><div><br></div><div>that will allow you to do exactly what you want to do. However, there are caveats. In order to have SNES do this, it needs a way to selectively</div><div>reassemble subproblems. I assume you are using Firedrake, so this will not work. I would definitely be willing to work with those guys to get</div><div>this going, introducing callbacks, just as we did on the FieldSplit case.</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div><div dir="ltr"><div>Best,</div><div>Miguel</div></div>
</div></blockquote></div><br clear="all"><div><br></div><span class="gmail_signature_prefix">-- </span><br><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div><div><br></div><div><a href="https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!bSoUE_2lViJzEHKf5CEFph-9dqm5ZtOB6QjWVEk4zIyGBukbkcoEGiVzHu84pF637kvsxFyFQoUPYjIUFM5eZZ51NMU5f6M8$" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div></div></div></div>
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</blockquote></div><br clear="all"><div><br></div><span class="gmail_signature_prefix">-- </span><br><div dir="ltr" class="gmail_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="https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!bSoUE_2lViJzEHKf5CEFph-9dqm5ZtOB6QjWVEk4zIyGBukbkcoEGiVzHu84pF637kvsxFyFQoUPYjIUFM5eZZ51NMU5f6M8$" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div></div></div></div>
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