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</o:shapelayout></xml><![endif]--></head><body lang=DE link=blue vlink=purple style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal><span style='mso-fareast-language:EN-US'>Hello everyone,<o:p></o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>I have a follow up on my question. I noticed the following behavior. Let’s assume I have 5 fields which I want to group with the following options:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>-ksp_type fgmres<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>-ksp_max_it 1<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>-ksp_monitor_true_residual<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>-ksp_view<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>-pc_type fieldsplit<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>-pc_fieldsplit_type multiplicative<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>-pc_fieldsplit_0_fields 0,1<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>-pc_fieldsplit_1_fields 2<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>-pc_fieldsplit_2_fields 3,4<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>-fieldsplit_0_ksp_type preonly<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>-fieldsplit_0_pc_type jacobi<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>-fieldsplit_2_ksp_type preonly<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>-fieldsplit_2_pc_type jacobi<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>Then, the first split is fine, but both the second and third splits get the same prefix, i.e., “fieldsplit_2”. This is shown in the output of the ksp_view, which I attach below.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>The first one gets the prefix as there is only a single split (and I choose as name the index) and the third split gets the name as it groups two other fields, so the “outer” name is taken. Is there any way to circumvent this, other than using custom names for the splits which are unique?<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>Thanks for your time and best regards,<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>Sebastian Blauth<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>The output of “ksp_view” is the following<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>KSP Object: 1 MPI process<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> type: fgmres<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> happy breakdown tolerance 1e-30<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> maximum iterations=1, initial guess is zero<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> right preconditioning<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> using UNPRECONDITIONED norm type for convergence test<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>PC Object: 1 MPI process<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> type: fieldsplit<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> FieldSplit with MULTIPLICATIVE composition: total splits = 3<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> Solver info for each split is in the following KSP objects:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> Split number 0 Defined by IS<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> KSP Object: (fieldsplit_0_) 1 MPI process<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> type: preonly<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> maximum iterations=10000, initial guess is zero<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> left preconditioning<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> using NONE norm type for convergence test<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> PC Object: (fieldsplit_0_) 1 MPI process<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> type: jacobi<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> type DIAGONAL<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> linear system matrix = precond matrix:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> Mat Object: (fieldsplit_0_) 1 MPI process<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> type: seqaij<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> rows=243, cols=243<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> total: nonzeros=4473, allocated nonzeros=4473<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> total number of mallocs used during MatSetValues calls=0<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> using I-node routines: found 86 nodes, limit used is 5<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> Split number 1 Defined by IS<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> KSP Object: (fieldsplit_2_) 1 MPI process<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> type: preonly<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> maximum iterations=10000, initial guess is zero<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> left preconditioning<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> using NONE norm type for convergence test<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> PC Object: (fieldsplit_2_) 1 MPI process<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> type: jacobi<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> type DIAGONAL<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> linear system matrix = precond matrix:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> Mat Object: (fieldsplit_2_) 1 MPI process<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> type: seqaij<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> rows=81, cols=81<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> total: nonzeros=497, allocated nonzeros=497<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> total number of mallocs used during MatSetValues calls=0<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> not using I-node routines<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> Split number 2 Defined by IS<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> KSP Object: (fieldsplit_2_) 1 MPI process<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> type: preonly<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> maximum iterations=10000, initial guess is zero<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> left preconditioning<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> using NONE norm type for convergence test<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> PC Object: (fieldsplit_2_) 1 MPI process<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> type: jacobi<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> type DIAGONAL<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> linear system matrix = precond matrix:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> Mat Object: (fieldsplit_2_) 1 MPI process<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> type: seqaij<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> rows=243, cols=243<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> total: nonzeros=4473, allocated nonzeros=4473<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> total number of mallocs used during MatSetValues calls=0<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> using I-node routines: found 85 nodes, limit used is 5<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> linear system matrix = precond matrix:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> Mat Object: 1 MPI process<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> type: seqaij<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> rows=567, cols=567<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> total: nonzeros=24353, allocated nonzeros=24353<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> total number of mallocs used during MatSetValues calls=0<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'> using I-node routines: found 173 nodes, limit used is 5<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><div><p class=MsoNormal>--<o:p></o:p></p><p class=MsoNormal>Dr. Sebastian Blauth<o:p></o:p></p><p class=MsoNormal>Fraunhofer-Institut für<o:p></o:p></p><p class=MsoNormal>Techno- und Wirtschaftsmathematik ITWM<o:p></o:p></p><p class=MsoNormal>Abteilung Transportvorgänge<o:p></o:p></p><p class=MsoNormal>Fraunhofer-Platz 1, 67663 Kaiserslautern<o:p></o:p></p><p class=MsoNormal>Telefon: +49 631 31600-4968<o:p></o:p></p><p class=MsoNormal><a href="mailto:sebastian.blauth@itwm.fraunhofer.de">sebastian.blauth@itwm.fraunhofer.de</a><o:p></o:p></p><p class=MsoNormal><a href="https://www.itwm.fraunhofer.de">https://www.itwm.fraunhofer.de</a><o:p></o:p></p></div><p class=MsoNormal><span style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><div style='border:none;border-left:solid blue 1.5pt;padding:0cm 0cm 0cm 4.0pt'><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0cm 0cm 0cm'><p class=MsoNormal><b><span lang=EN-US>From:</span></b><span lang=EN-US> petsc-users <petsc-users-bounces@mcs.anl.gov> <b>On Behalf Of </b>Blauth, Sebastian<br><b>Sent:</b> Tuesday, July 2, 2024 11:47 AM<br><b>To:</b> Matthew Knepley <knepley@gmail.com><br><b>Cc:</b> petsc-users@mcs.anl.gov<br><b>Subject:</b> Re: [petsc-users] Question regarding naming of fieldsplit splits<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span style='mso-fareast-language:EN-US'>Hi Matt,<o:p></o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>thanks fort he answer and clarification. Then I’ll work around this issue in python, where I set the options.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>Best,<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'>Sebastian<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal>--<o:p></o:p></p><p class=MsoNormal>Dr. Sebastian Blauth<o:p></o:p></p><p class=MsoNormal>Fraunhofer-Institut für<o:p></o:p></p><p class=MsoNormal>Techno- und Wirtschaftsmathematik ITWM<o:p></o:p></p><p class=MsoNormal>Abteilung Transportvorgänge<o:p></o:p></p><p class=MsoNormal>Fraunhofer-Platz 1, 67663 Kaiserslautern<o:p></o:p></p><p class=MsoNormal>Telefon: +49 631 31600-4968<o:p></o:p></p><p class=MsoNormal><a href="mailto:sebastian.blauth@itwm.fraunhofer.de">sebastian.blauth@itwm.fraunhofer.de</a><o:p></o:p></p><p class=MsoNormal><a href="https://www.itwm.fraunhofer.de">https://www.itwm.fraunhofer.de</a><o:p></o:p></p><p class=MsoNormal><span style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><div style='border:none;border-left:solid blue 1.5pt;padding:0cm 0cm 0cm 4.0pt'><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0cm 0cm 0cm'><p class=MsoNormal><b><span lang=EN-US>From:</span></b><span lang=EN-US> Matthew Knepley <<a href="mailto:knepley@gmail.com">knepley@gmail.com</a>> <br><b>Sent:</b> Monday, July 1, 2024 4:30 PM<br><b>To:</b> Blauth, Sebastian <<a href="mailto:sebastian.blauth@itwm.fraunhofer.de">sebastian.blauth@itwm.fraunhofer.de</a>><br><b>Cc:</b> <a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a><br><b>Subject:</b> Re: [petsc-users] Question regarding naming of fieldsplit splits<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal>On Mon, Jul 1, 2024 at 9:48 AM Blauth, Sebastian <<a href="mailto:sebastian.blauth@itwm.fraunhofer.de">sebastian.blauth@itwm.fraunhofer.de</a>> wrote:<o:p></o:p></p></div><div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt'><div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Dear Matt,<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>thanks a lot for your help. Unfortunately, for me these extra options do not have any effect, I still get the “u” and “p” fieldnames. Also, this would not help me to get rid of the “c” fieldname – on that level of the fieldsplit I am basically using your approach already, and still it does show up. The output of the -ksp_view is unchanged, so that I do not attach it here again. Maybe I misunderstood you?</span><o:p></o:p></p></div></div></div></blockquote><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Oh, we make an exception for single fields, since we think you would want to use the name. I have to make an extra option to shut off naming.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal> Thanks,<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal> Matt<o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt'><div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>Thanks for the help and best regards,</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>Sebastian</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>--<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Dr. Sebastian Blauth<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Fraunhofer-Institut für<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Techno- und Wirtschaftsmathematik ITWM<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Abteilung Transportvorgänge<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Fraunhofer-Platz 1, 67663 Kaiserslautern<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Telefon: +49 631 31600-4968<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a href="mailto:sebastian.blauth@itwm.fraunhofer.de" target="_blank">sebastian.blauth@itwm.fraunhofer.de</a><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a href="https://www.itwm.fraunhofer.de" target="_blank">https://www.itwm.fraunhofer.de</a><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div style='border:none;border-left:solid blue 1.5pt;padding:0cm 0cm 0cm 4.0pt'><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0cm 0cm 0cm'><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b><span lang=EN-US>From:</span></b><span lang=EN-US> Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>> <br><b>Sent:</b> Monday, July 1, 2024 2:27 PM<br><b>To:</b> Blauth, Sebastian <<a href="mailto:sebastian.blauth@itwm.fraunhofer.de" target="_blank">sebastian.blauth@itwm.fraunhofer.de</a>><br><b>Cc:</b> <a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a><br><b>Subject:</b> Re: [petsc-users] Question regarding naming of fieldsplit splits</span><o:p></o:p></p></div></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>On Fri, Jun 28, 2024 at 4:05 AM Blauth, Sebastian <<a href="mailto:sebastian.blauth@itwm.fraunhofer.de" target="_blank">sebastian.blauth@itwm.fraunhofer.de</a>> wrote:<o:p></o:p></p></div><div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt'><div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Hello everyone,<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>I have a question regarding the naming convention using PETSc’s PCFieldsplit. I have been following <a href="https://lists.mcs.anl.gov/pipermail/petsc-users/2019-January/037262.html" target="_blank">https://lists.mcs.anl.gov/pipermail/petsc-users/2019-January/037262.html</a> to create a DMShell with FEniCS in order to customize PCFieldsplit for my application. </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>I am using the following options, which work nicely for me:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-ksp_type fgmres</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-pc_type fieldsplit</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-pc_fieldsplit_0_fields 0, 1</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-pc_fieldsplit_1_fields 2</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-pc_fieldsplit_type additive</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-fieldsplit_0_ksp_type fgmres</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-fieldsplit_0_pc_type fieldsplit</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-fieldsplit_0_pc_fieldsplit_type schur</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-fieldsplit_0_pc_fieldsplit_schur_fact_type full</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-fieldsplit_0_pc_fieldsplit_schur_precondition selfp</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-fieldsplit_0_fieldsplit_u_ksp_type preonly</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-fieldsplit_0_fieldsplit_u_pc_type lu</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-fieldsplit_0_fieldsplit_p_ksp_type cg</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-fieldsplit_0_fieldsplit_p_ksp_rtol 1e-14</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-fieldsplit_0_fieldsplit_p_ksp_atol 1e-30</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-fieldsplit_0_fieldsplit_p_pc_type icc</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-fieldsplit_0_ksp_rtol 1e-14</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-fieldsplit_0_ksp_atol 1e-30</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-fieldsplit_0_ksp_monitor_true_residual</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-fieldsplit_c_ksp_type preonly</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-fieldsplit_c_pc_type lu</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>-ksp_view</span><o:p></o:p></p></div></div></div></blockquote><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>By default, we use the field names, but you can prevent this by specifying the fields by hand, so<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>-fieldsplit_0_pc_fieldsplit_0_fields 0<br>-fieldsplit_0_pc_fieldsplit_1_fields 1<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>should remove the 'u' and 'p' fieldnames. It is somewhat hacky, but I think easier to remember than<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>some extra option.<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> Thanks,<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> Matt<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt'><div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>Note that this is just an academic example (sorry for the low solver tolerances) to test the approach, consisting of a Stokes equation and some concentration equation (which is not even coupled to Stokes, just for testing).</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>Completely analogous to <a href="https://lists.mcs.anl.gov/pipermail/petsc-users/2019-January/037262.html" target="_blank">https://lists.mcs.anl.gov/pipermail/petsc-users/2019-January/037262.html</a>, I translate my IS’s to a PETSc Section, which is then supplied to a DMShell and assigned to a KSP. I am not so familiar with the code or how / why this works, but it seems to do so perfectly. I name my sections with petsc4py using</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>section.setFieldName(0, "u")</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>section.setFieldName(1, "p")</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>section.setFieldName(2, "c")</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>However, this is also reflected in the way I can access the fieldsplit options from the command line. My question is: Is there any way of not using the FieldNames specified in python but use the index of the field as defined with “-pc_fieldsplit_0_fields 0, 1” and “-pc_fieldsplit_1_fields 2”, i.e., instead of the prefix “fieldsplit_0_fieldsplit_u” I want to write “fieldsplit_0_fieldsplit_0”, instead of “fieldsplit_0_fieldsplit_p” I want to use “fieldsplit_0_fieldsplit_1”, and instead of “fieldsplit_c” I want to use “fieldsplit_1”. Just changing the names of the fields to</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>section.setFieldName(0, "0")</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>section.setFieldName(1, "1")</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>section.setFieldName(2, "2")</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>does obviously not work as expected, as it works for velocity and pressure, but not for the concentration – the prefix there is then “fieldsplit_2” and not “fieldsplit_1”. In the docs, I have found <a href="https://petsc.org/main/manualpages/PC/PCFieldSplitSetFields/" target="_blank">https://petsc.org/main/manualpages/PC/PCFieldSplitSetFields/</a> which seems to suggest that the fieldname can potentially be supplied, but I don’t see how to do so from the command line. Also, for the sake of completeness, I attach the output of the solve with “-ksp_view” below. </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>Thanks a lot in advance and best regards,</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>Sebastian</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>The output of ksp_view is the following:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>KSP Object: 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: fgmres</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> happy breakdown tolerance 1e-30</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> maximum iterations=10000, initial guess is zero</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> tolerances: relative=1e-05, absolute=1e-11, divergence=10000.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> right preconditioning</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> using UNPRECONDITIONED norm type for convergence test</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>PC Object: 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: fieldsplit</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> FieldSplit with ADDITIVE composition: total splits = 2</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Solver info for each split is in the following KSP objects:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Split number 0 Defined by IS</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> KSP Object: (fieldsplit_0_) 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: fgmres</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> happy breakdown tolerance 1e-30</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> maximum iterations=10000, initial guess is zero</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> tolerances: relative=1e-14, absolute=1e-30, divergence=10000.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> right preconditioning</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> using UNPRECONDITIONED norm type for convergence test</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> PC Object: (fieldsplit_0_) 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: fieldsplit</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> FieldSplit with Schur preconditioner, factorization FULL</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Preconditioner for the Schur complement formed from Sp, an assembled approximation to S, which uses A00's diagonal's inverse</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Split info:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Split number 0 Defined by IS</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Split number 1 Defined by IS</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> KSP solver for A00 block</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> KSP Object: (fieldsplit_0_fieldsplit_u_) 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: preonly</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> maximum iterations=10000, initial guess is zero</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> left preconditioning</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> using NONE norm type for convergence test</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> PC Object: (fieldsplit_0_fieldsplit_u_) 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: lu</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> out-of-place factorization</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> tolerance for zero pivot 2.22045e-14</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> matrix ordering: nd</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> factor fill ratio given 5., needed 3.92639</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Factored matrix follows:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Mat Object: 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: seqaij</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> rows=4290, cols=4290</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> package used to perform factorization: petsc</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total: nonzeros=375944, allocated nonzeros=375944</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> using I-node routines: found 2548 nodes, limit used is 5</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> linear system matrix = precond matrix:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Mat Object: (fieldsplit_0_fieldsplit_u_) 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: seqaij</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> rows=4290, cols=4290</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total: nonzeros=95748, allocated nonzeros=95748</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total number of mallocs used during MatSetValues calls=0</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> using I-node routines: found 3287 nodes, limit used is 5</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> KSP solver for S = A11 - A10 inv(A00) A01 </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> KSP Object: (fieldsplit_0_fieldsplit_p_) 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: cg</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> maximum iterations=10000, initial guess is zero</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> tolerances: relative=1e-14, absolute=1e-30, divergence=10000.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> left preconditioning</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> using PRECONDITIONED norm type for convergence test</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> PC Object: (fieldsplit_0_fieldsplit_p_) 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: icc</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> out-of-place factorization</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> 0 levels of fill</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> tolerance for zero pivot 2.22045e-14</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> using Manteuffel shift [POSITIVE_DEFINITE]</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> matrix ordering: natural</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> factor fill ratio given 1., needed 1.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Factored matrix follows:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Mat Object: 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: seqsbaij</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> rows=561, cols=561</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> package used to perform factorization: petsc</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total: nonzeros=5120, allocated nonzeros=5120</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> block size is 1</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> linear system matrix followed by preconditioner matrix:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Mat Object: (fieldsplit_0_fieldsplit_p_) 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: schurcomplement</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> rows=561, cols=561</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Schur complement A11 - A10 inv(A00) A01</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> A11</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Mat Object: (fieldsplit_0_fieldsplit_p_) 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: seqaij</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> rows=561, cols=561</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total: nonzeros=3729, allocated nonzeros=3729</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total number of mallocs used during MatSetValues calls=0</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> not using I-node routines</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> A10</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Mat Object: 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: seqaij</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> rows=561, cols=4290</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total: nonzeros=19938, allocated nonzeros=19938</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total number of mallocs used during MatSetValues calls=0</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> not using I-node routines</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> KSP of A00</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> KSP Object: (fieldsplit_0_fieldsplit_u_) 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: preonly</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> maximum iterations=10000, initial guess is zero</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> left preconditioning</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> using NONE norm type for convergence test</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> PC Object: (fieldsplit_0_fieldsplit_u_) 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: lu</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> out-of-place factorization</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> tolerance for zero pivot 2.22045e-14</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> matrix ordering: nd</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> factor fill ratio given 5., needed 3.92639</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Factored matrix follows:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Mat Object: 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: seqaij</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> rows=4290, cols=4290</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> package used to perform factorization: petsc</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total: nonzeros=375944, allocated nonzeros=375944</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> using I-node routines: found 2548 nodes, limit used is 5</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> linear system matrix = precond matrix:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Mat Object: (fieldsplit_0_fieldsplit_u_) 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: seqaij</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> rows=4290, cols=4290</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total: nonzeros=95748, allocated nonzeros=95748</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total number of mallocs used during MatSetValues calls=0</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> using I-node routines: found 3287 nodes, limit used is 5</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> A01</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Mat Object: 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: seqaij</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> rows=4290, cols=561</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total: nonzeros=19938, allocated nonzeros=19938</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total number of mallocs used during MatSetValues calls=0</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> using I-node routines: found 3287 nodes, limit used is 5</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Mat Object: 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: seqaij</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> rows=561, cols=561</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total: nonzeros=9679, allocated nonzeros=9679</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total number of mallocs used during MatSetValues calls=0</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> not using I-node routines</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> linear system matrix = precond matrix:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Mat Object: (fieldsplit_0_) 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: seqaij</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> rows=4851, cols=4851</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total: nonzeros=139353, allocated nonzeros=139353</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total number of mallocs used during MatSetValues calls=0</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> using I-node routines: found 3830 nodes, limit used is 5</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Split number 1 Defined by IS</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> KSP Object: (fieldsplit_c_) 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: preonly</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> maximum iterations=10000, initial guess is zero</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> left preconditioning</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> using NONE norm type for convergence test</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> PC Object: (fieldsplit_c_) 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: lu</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> out-of-place factorization</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> tolerance for zero pivot 2.22045e-14</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> matrix ordering: nd</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> factor fill ratio given 5., needed 4.24323</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Factored matrix follows:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Mat Object: 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: seqaij</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> rows=561, cols=561</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> package used to perform factorization: petsc</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total: nonzeros=15823, allocated nonzeros=15823</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> not using I-node routines</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> linear system matrix = precond matrix:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Mat Object: (fieldsplit_c_) 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: seqaij</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> rows=561, cols=561</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total: nonzeros=3729, allocated nonzeros=3729</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total number of mallocs used during MatSetValues calls=0</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> not using I-node routines</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> linear system matrix = precond matrix:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> Mat Object: 1 MPI processes</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> type: seqaij</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> rows=5412, cols=5412</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total: nonzeros=190416, allocated nonzeros=190416</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> total number of mallocs used during MatSetValues calls=0</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> using I-node routines: found 3833 nodes, limit used is 5</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>--<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Dr. Sebastian Blauth<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Fraunhofer-Institut für<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Techno- und Wirtschaftsmathematik ITWM<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Abteilung Transportvorgänge<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Fraunhofer-Platz 1, 67663 Kaiserslautern<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Telefon: +49 631 31600-4968<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a href="mailto:sebastian.blauth@itwm.fraunhofer.de" target="_blank">sebastian.blauth@itwm.fraunhofer.de</a><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a href="https://www.itwm.fraunhofer.de" target="_blank">https://www.itwm.fraunhofer.de</a><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div></div></div></blockquote></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><br clear=all><o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span class=m-552471448270057200gmailsignatureprefix>-- </span><o:p></o:p></p><div><div><div><div><div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>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<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><o:p></o:p></p></div></div></div></div></div></div></div></div></div></div></div></div></blockquote></div><p class=MsoNormal><br clear=all><o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p></div><p class=MsoNormal><span class=gmailsignatureprefix>-- </span><o:p></o:p></p><div><div><div><div><div><div><div><p class=MsoNormal>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<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><o:p></o:p></p></div></div></div></div></div></div></div></div></div></div></div></body></html>