[petsc-users] Errors encountered with KSPsolver with MATNEST and VECNEST
Matthew Knepley
knepley at gmail.com
Thu Jul 16 04:55:37 CDT 2020
On Thu, Jul 16, 2020 at 5:43 AM Karl Yang <y.juntao at hotmail.com> wrote:
> Hi, Matt,
>
> Sorry for the confusion. The error shows as below without SetIS().
>
I see the problem now. It is about the interface for MatNest.
MatNest is intended _only_ as an optimization. I think you should never
have MatNest in user code. Here the
problem is that MatNest only supports extraction using the ISes it was
created with, whereas detection is
finding a different IS. I recommend getting everything working with AIJ,
and then use MatSetType() or
-mat_type at the end to try out Nest. The interfaces are the same.
Thanks,
Matt
> [0]PETSC ERROR: --------------------- Error Message
> --------------------------------------------------------------
> [0]PETSC ERROR: Arguments are incompatible
> [0]PETSC ERROR: Could not find index set
> [0]PETSC ERROR: See https://www.mcs.anl.gov/petsc/documentation/faq.html
> for trouble shooting.
> [0]PETSC ERROR: Petsc Release Version 3.12.5, Mar, 29, 2020
> [0]PETSC ERROR: ./testSolve on a arch-linux2-c-debug named ae3f0ab5a8c4 by
> Unknown Thu Jul 16 17:36:52 2020
> [0]PETSC ERROR: Configure options --with-cc=gcc --with-cxx=g++
> --with-fc=gfortran --download-mpich --download-fblaslapack --with-cuda
> [0]PETSC ERROR: #1 MatNestFindIS() line 365 in
> /usr/local/petsc/petsc-3.12.5/src/mat/impls/nest/matnest.c
> [0]PETSC ERROR: #2 MatNestFindSubMat() line 425 in
> /usr/local/petsc/petsc-3.12.5/src/mat/impls/nest/matnest.c
> [0]PETSC ERROR: #3 MatCreateSubMatrix_Nest() line 456 in
> /usr/local/petsc/petsc-3.12.5/src/mat/impls/nest/matnest.c
> [0]PETSC ERROR: #4 MatCreateSubMatrix() line 7859 in
> /usr/local/petsc/petsc-3.12.5/src/mat/interface/matrix.c
> [0]PETSC ERROR: #5 PCSetUp_FieldSplit() line 676 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/pc/impls/fieldsplit/fieldsplit.c
> [0]PETSC ERROR: #6 PCSetUp() line 894 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/pc/interface/precon.c
> [0]PETSC ERROR: --------------------- Error Message
> --------------------------------------------------------------
> [0]PETSC ERROR: Corrupt argument:
> https://www.mcs.anl.gov/petsc/documentation/faq.html#valgrind
> [0]PETSC ERROR: Invalid Pointer to Object: Parameter # 1
> [0]PETSC ERROR: See https://www.mcs.anl.gov/petsc/documentation/faq.html
> for trouble shooting.
> [0]PETSC ERROR: Petsc Release Version 3.12.5, Mar, 29, 2020
> [0]PETSC ERROR: ./testSolve on a arch-linux2-c-debug named ae3f0ab5a8c4 by
> Unknown Thu Jul 16 17:36:52 2020
> [0]PETSC ERROR: Configure options --with-cc=gcc --with-cxx=g++
> --with-fc=gfortran --download-mpich --download-fblaslapack --with-cuda
> [0]PETSC ERROR: #7 MatDestroy() line 1266 in
> /usr/local/petsc/petsc-3.12.5/src/mat/interface/matrix.c
> [0]PETSC ERROR: #8 PCSetUp_FieldSplit() line 697 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/pc/impls/fieldsplit/fieldsplit.c
> [0]PETSC ERROR: #9 PCSetUp() line 894 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/pc/interface/precon.c
> [0]PETSC ERROR: #10 KSPSetUp() line 376 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/ksp/interface/itfunc.c
> KSP Object: 1 MPI processes
> type: fgmres
> restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
> happy breakdown tolerance 1e-30
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> right preconditioning
> using UNPRECONDITIONED norm type for convergence test
> PC Object: 1 MPI processes
> type: fieldsplit
> PC has not been set up so information may be incomplete
> FieldSplit with Schur preconditioner, blocksize = 1, factorization FULL
> Preconditioner for the Schur complement formed from S itself
> Split info:
> Split number 0 Defined by IS
> Split number 1 Defined by IS
> KSP solver for A00 block
> KSP Object: (fieldsplit_0_) 1 MPI processes
> type: preonly
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> left preconditioning
> using DEFAULT norm type for convergence test
> PC Object: (fieldsplit_0_) 1 MPI processes
> type not yet set
> PC has not been set up so information may be incomplete
> KSP solver for upper A00 in upper triangular factor
> not yet available
> KSP solver for S = A11 - A10 inv(A00) A01
> not yet available
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: nest
> rows=15, cols=15
> Matrix object:
> type=nest, rows=3, cols=3
> MatNest structure:
> (0,0) : type=seqaij, rows=5, cols=5
> (0,1) : NULL
> (0,2) : type=seqaij, rows=5, cols=5
> (1,0) : NULL
> (1,1) : type=seqaij, rows=5, cols=5
> (1,2) : type=seqaij, rows=5, cols=5
> (2,0) : type=seqaij, rows=5, cols=5
> (2,1) : type=seqaij, rows=5, cols=5
> (2,2) : NULL
> Segmentation fault (core dumped)
>
>
> Attached is the test code.
>
> Regards
> JT
>
>
>
>
> On Jul 16 2020, at 5:30 pm, Matthew Knepley <knepley at gmail.com> wrote:
>
> On Thu, Jul 16, 2020 at 1:23 AM Karl Yang <y.juntao at hotmail.com
> <https://link.getmailspring.com/link/1D2D2990-B215-4510-B196-F29BD06D4684@getmailspring.com/0?redirect=mailto%3Ay.juntao%40hotmail.com&recipient=a25lcGxleUBnbWFpbC5jb20%3D>>
> wrote:
> [image: Sent from Mailspring]
>
> Hi, Junchao,
>
> Thank you. It works. :)
>
> May I ask some follow up question regarding the same example about
> fieldsplit. I am trying to learn about matnest with fieldsplit
> preconditioner on manual page 94. But I get a bit lost trying to understand
> fields, ISs once it is not eactly the same on the manual.
>
> In this same example, I tried to use PCFIELDSPLIT and
> PCFieldSplitSetDetectSaddlePoint as follows.
>
>
> You cannot mix DetectSaddlePoint() with SetIS() since the detection tries
> to make the proper ISes. Maybe we should check that.
>
> Thanks,
>
> Matt
>
>
> IS rows[3];
> IS cols[3];
> MatNestGetISs(testMesh->system, rows, cols);
>
> KSP ksp;
> PC pc;
> KSPCreate(PETSC_COMM_WORLD, &ksp);
> KSPSetType(ksp, KSPFGMRES);
> KSPSetOperators(ksp, testMesh->system, testMesh->system);
> KSPGetPC(ksp, &pc);
> PCFieldSplitSetIS(pc, "u", rows[0]);
> PCFieldSplitSetIS(pc, "v", rows[1]);
> PCFieldSplitSetIS(pc, "p", rows[2]);
> PCSetType(pc, PCFIELDSPLIT);
> PCFieldSplitSetDetectSaddlePoint(pc, PETSC_TRUE);
> KSPSetUp(ksp);
> KSPSolve(ksp, testMesh->rhs, testMesh->solution);
>
> But I will get the following error,
>
> [0]PETSC ERROR: --------------------- Error Message
> --------------------------------------------------------------
> [0]PETSC ERROR: Arguments are incompatible
> [0]PETSC ERROR: Could not find index set
> [0]PETSC ERROR: See https://www.mcs.anl.gov/petsc/documentation/faq.html for
> trouble shooting.
> [0]PETSC ERROR: Petsc Release Version 3.12.5, Mar, 29, 2020
> [0]PETSC ERROR: ./testSolve on a arch-linux2-c-debug named f601294ac804 by
> Unknown Thu Jul 16 13:08:39 2020
> [0]PETSC ERROR: Configure options --with-cc=gcc --with-cxx=g++
> --with-fc=gfortran --download-mpich --download-fblaslapack --with-cuda
> [0]PETSC ERROR: #1 MatNestFindIS() line 365 in
> /usr/local/petsc/petsc-3.12.5/src/mat/impls/nest/matnest.c
> [0]PETSC ERROR: #2 MatNestFindSubMat() line 425 in
> /usr/local/petsc/petsc-3.12.5/src/mat/impls/nest/matnest.c
> [0]PETSC ERROR: #3 MatCreateSubMatrix_Nest() line 456 in
> /usr/local/petsc/petsc-3.12.5/src/mat/impls/nest/matnest.c
> [0]PETSC ERROR: #4 MatCreateSubMatrix() line 7859 in
> /usr/local/petsc/petsc-3.12.5/src/mat/interface/matrix.c
> [0]PETSC ERROR: #5 PCSetUp_FieldSplit() line 676 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/pc/impls/fieldsplit/fieldsplit.c
> [0]PETSC ERROR: #6 PCSetUp() line 894 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/pc/interface/precon.c
> [0]PETSC ERROR: #7 KSPSetUp() line 376 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/ksp/interface/itfunc.c
> [0]PETSC ERROR: --------------------- Error Message
> --------------------------------------------------------------
> [0]PETSC ERROR: Corrupt argument:
> https://www.mcs.anl.gov/petsc/documentation/faq.html#valgrind
> [0]PETSC ERROR: Invalid Pointer to Object: Parameter # 1
> [0]PETSC ERROR: See https://www.mcs.anl.gov/petsc/documentation/faq.html for
> trouble shooting.
> [0]PETSC ERROR: Petsc Release Version 3.12.5, Mar, 29, 2020
> [0]PETSC ERROR: ./testSolve on a arch-linux2-c-debug named f601294ac804 by
> Unknown Thu Jul 16 13:08:39 2020
> [0]PETSC ERROR: Configure options --with-cc=gcc --with-cxx=g++
> --with-fc=gfortran --download-mpich --download-fblaslapack --with-cuda
> [0]PETSC ERROR: #8 MatDestroy() line 1266 in
> /usr/local/petsc/petsc-3.12.5/src/mat/interface/matrix.c
> [0]PETSC ERROR: #9 PCSetUp_FieldSplit() line 697 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/pc/impls/fieldsplit/fieldsplit.c
> [0]PETSC ERROR: #10 PCSetUp() line 894 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/pc/interface/precon.c
> [0]PETSC ERROR: #11 KSPSetUp() line 376 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/ksp/interface/itfunc.c
> [0]PETSC ERROR: #12 KSPSolve() line 703 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/ksp/interface/itfunc.c
>
> I read about the examples on the manual and mostly are based on 2*2
> blocks but still cannot figure out how pcfieldsplit should be set in this 3*
> **3 blocks, and how IS should be set accordingly. I read about
> -fieldsplit_1_pc_type none option suggested on the documentation, but I am
> not sure is it still valid in a 33 blocks.*
>
> *Regards*
> *JT*
> On Jul 16 2020, at 6:57 am, Junchao Zhang <junchao.zhang at gmail.com> wrote:
>
> Adding the MatNestSetVecType() line fixed the problem. But I don't know
> why petsc had this weird design originally.
>
> MatCreateNest(PETSC_COMM_WORLD, 3, NULL, 3, NULL, mblock,
> &testMesh->system);
> + MatNestSetVecType(testMesh->system,VECNEST);
>
> --Junchao Zhang
>
>
> On Wed, Jul 15, 2020 at 2:16 PM Karl Yang <y.juntao at hotmail.com> wrote:
>
> Hi, Barry,
>
> I created a minimum example to reproduce the error. The example code is
> attached.
>
> Mat Object: 1 MPI processes
> type: nest
> Matrix object:
> type=nest, rows=3, cols=3
> MatNest structure:
> (0,0) : type=seqaij, rows=5, cols=5
> (0,1) : NULL
> (0,2) : type=seqaij, rows=5, cols=5
> (1,0) : NULL
> (1,1) : type=seqaij, rows=5, cols=5
> (1,2) : type=seqaij, rows=5, cols=5
> (2,0) : type=seqaij, rows=5, cols=5
> (2,1) : type=seqaij, rows=5, cols=5
> (2,2) : NULL
> Vec Object: 1 MPI processes
> type: nest
> VecNest, rows=3, structure:
> (0) : type=seq, rows=5
> Vec Object: 1 MPI processes
> type: seq
> 1.
> 1.
> 1.
> 1.
> 1.
> (1) : type=seq, rows=5
> Vec Object: 1 MPI processes
> type: seq
> 1.
> 1.
> 1.
> 1.
> 1.
> (2) : type=seq, rows=5
> Vec Object: 1 MPI processes
> type: seq
> 1.
> 1.
> 1.
> 1.
> 1.
> [0]PETSC ERROR: --------------------- Error Message
> --------------------------------------------------------------
> [0]PETSC ERROR: Invalid argument
> [0]PETSC ERROR: Nest vector argument 2 not setup.
> [0]PETSC ERROR: See https://www.mcs.anl.gov/petsc/documentation/faq.html for
> trouble shooting.
> [0]PETSC ERROR: Petsc Release Version 3.12.5, Mar, 29, 2020
> [0]PETSC ERROR: ./testSolve on a arch-linux2-c-debug named f601294ac804 by
> Unknown Thu Jul 16 03:11:02 2020
> [0]PETSC ERROR: Configure options --with-cc=gcc --with-cxx=g++
> --with-fc=gfortran --download-mpich --download-fblaslapack --with-cuda
> [0]PETSC ERROR: #1 VecCopy_Nest() line 68 in
> /usr/local/petsc/petsc-3.12.5/src/vec/vec/impls/nest/vecnest.c
> [0]PETSC ERROR: #2 VecCopy() line 1577 in
> /usr/local/petsc/petsc-3.12.5/src/vec/vec/interface/vector.c
> [0]PETSC ERROR: #3 KSPInitialResidual() line 61 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/ksp/interface/itres.c
> [0]PETSC ERROR: #4 KSPSolve_GMRES() line 236 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/ksp/impls/gmres/gmres.c
> [0]PETSC ERROR: #5 KSPSolve() line 760 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/ksp/interface/itfunc.c
> On Jul 16 2020, at 2:39 am, Barry Smith <bsmith at petsc.dev> wrote:
>
>
> Could be a bug in PETSc, please send a sample program that produces the
> problem.
>
> Barry
>
>
> On Jul 15, 2020, at 1:28 PM, Karl Yang <y.juntao at hotmail.com
> <https://link.getmailspring.com/link/060AB2C3-F3D7-408C-99CF-C4D1B27DD59F@getmailspring.com/0?redirect=mailto%3Ay.juntao%40hotmail.com&recipient=cGV0c2MtdXNlcnNAbWNzLmFubC5nb3Y%3D>>
> wrote:
>
> Hi, Barry,
>
> Thanks for your reply. I output the matrix and vec with matview and
> vecview. And I think I do have the values set as it has been shown.
>
> Mat Object: 1 MPI processes
> type: nest
> Matrix object:
> type=nest, rows=3, cols=3
> MatNest structure:
> (0,0) : type=seqaij, rows=25, cols=25
> (0,1) : NULL
> (0,2) : type=seqaij, rows=25, cols=25
> (1,0) : NULL
> (1,1) : type=seqaij, rows=25, cols=25
> (1,2) : type=seqaij, rows=25, cols=25
> (2,0) : type=seqaij, rows=25, cols=25
> (2,1) : type=seqaij, rows=25, cols=25
> (2,2) : NULL
> Vec Object: 1 MPI processes
> type: nest
> VecNest, rows=3, structure:
> (0) : type=seq, rows=25
> Vec Object: 1 MPI processes
> type: seq
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 75.8279
> -51.0776
> -75.8279
> 0.
> 0.
> -90.8404
> 58.7011
> 90.8404
> 0.
> 0.
> -75.8279
> 51.0776
> 75.8279
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> (1) : name="Vec_0x84000000_0", type=seq, rows=25
> Vec Object: Vec_0x84000000_0 1 MPI processes
> type: seq
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 75.8279
> -51.0776
> -75.8279
> 0.
> 0.
> -90.8404
> 58.7011
> 90.8404
> 0.
> 0.
> -75.8279
> 51.0776
> 75.8279
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> (2) : type=seq, rows=25
> Vec Object: 1 MPI processes
> type: seq
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> 0.
> [0]PETSC ERROR: --------------------- Error Message
> --------------------------------------------------------------
> [0]PETSC ERROR: Invalid argument
> [0]PETSC ERROR: Nest vector argument 4 not setup.
> [0]PETSC ERROR: See https://www.mcs.anl.gov/petsc/documentation/faq.html
> <https://link.getmailspring.com/link/060AB2C3-F3D7-408C-99CF-C4D1B27DD59F@getmailspring.com/1?redirect=https%3A%2F%2Fwww.mcs.anl.gov%2Fpetsc%2Fdocumentation%2Ffaq.html&recipient=cGV0c2MtdXNlcnNAbWNzLmFubC5nb3Y%3D> for
> trouble shooting.
> [0]PETSC ERROR: Petsc Release Version 3.12.5, Mar, 29, 2020
> [0]PETSC ERROR: ./testSolve on a arch-linux2-c-debug named f601294ac804 by
> Unknown Thu Jul 16 02:15:26 2020
> [0]PETSC ERROR: Configure options --with-cc=gcc --with-cxx=g++
> --with-fc=gfortran --download-mpich --download-fblaslapack --with-cuda
> [0]PETSC ERROR: #1 VecPointwiseMult_Nest() line 245 in
> /usr/local/petsc/petsc-3.12.5/src/vec/vec/impls/nest/vecnest.c
> [0]PETSC ERROR: #2 VecPointwiseMult() line 1107 in
> /usr/local/petsc/petsc-3.12.5/src/vec/vec/interface/vector.c
> [0]PETSC ERROR: #3 PCApply_Jacobi() line 272 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/pc/impls/jacobi/jacobi.c
> [0]PETSC ERROR: #4 PCApply() line 444 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/pc/interface/precon.c
> [0]PETSC ERROR: #5 KSP_PCApply() line 281 in
> /usr/local/petsc/petsc-3.12.5/include/petsc/private/kspimpl.h
> [0]PETSC ERROR: #6 KSPInitialResidual() line 65 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/ksp/interface/itres.c
> [0]PETSC ERROR: #7 KSPSolve_GMRES() line 236 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/ksp/impls/gmres/gmres.c
> [0]PETSC ERROR: #8 KSPSolve() line 760 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/ksp/interface/itfunc.c
>
> On Jul 16 2020, at 2:13 am, Barry Smith <bsmith at petsc.dev
> <https://link.getmailspring.com/link/060AB2C3-F3D7-408C-99CF-C4D1B27DD59F@getmailspring.com/2?redirect=mailto%3Absmith%40petsc.dev&recipient=cGV0c2MtdXNlcnNAbWNzLmFubC5nb3Y%3D>>
> wrote:
>
>
> From the error message the second vector you are using to form the nest
> vector has not been completely created/set up. Make sure you called either
> VecCreateSeq(), VecCreateMPI() or did VecCreate(), VecSetType(), VecSetUp()
> and if it is the right hand side make sure you put numerical values in it.
>
> Barry
>
>
> On Jul 15, 2020, at 1:05 PM, Karl Yang <y.juntao at hotmail.com
> <https://link.getmailspring.com/link/060AB2C3-F3D7-408C-99CF-C4D1B27DD59F@getmailspring.com/3?redirect=https%3A%2F%2Flink.getmailspring.com%2Flink%2F540F752A-DB59-4878-9C98-B8F4B4D9FD0D%40getmailspring.com%2F0%3Fredirect%3Dmailto%253Ay.juntao%2540hotmail.com%26recipient%3DYnNtaXRoQHBldHNjLmRldg%253D%253D&recipient=cGV0c2MtdXNlcnNAbWNzLmFubC5nb3Y%3D>>
> wrote:
>
> Hello,
>
> I'm trying to solve a 2*2 block matrix system.
> I managed to form a 2*2 MatNest and a 21 VecNest. However when I try to
> make use of ksp solve, I encounter the following error. There is only one
> or two examples on MatNest and VecNest. I could not figure out what could
> be the trouble.
>
>
> [0]PETSC ERROR: --------------------- Error Message
> --------------------------------------------------------------
> [0]PETSC ERROR: Invalid argument
> [0]PETSC ERROR: Nest vector argument 2 not setup.
> [0]PETSC ERROR: See https://www.mcs.anl.gov/petsc/documentation/faq.html
> <https://link.getmailspring.com/link/060AB2C3-F3D7-408C-99CF-C4D1B27DD59F@getmailspring.com/4?redirect=https%3A%2F%2Flink.getmailspring.com%2Flink%2F540F752A-DB59-4878-9C98-B8F4B4D9FD0D%40getmailspring.com%2F1%3Fredirect%3Dhttps%253A%252F%252Fwww.mcs.anl.gov%252Fpetsc%252Fdocumentation%252Ffaq.html%26recipient%3DYnNtaXRoQHBldHNjLmRldg%253D%253D&recipient=cGV0c2MtdXNlcnNAbWNzLmFubC5nb3Y%3D> for
> trouble shooting.
> [0]PETSC ERROR: Petsc Release Version 3.12.5, Mar, 29, 2020
> [0]PETSC ERROR: ./testSolve on a arch-linux2-c-debug named f601294ac804 by
> Unknown Thu Jul 16 01:56:11 2020
> [0]PETSC ERROR: Configure options --with-cc=gcc --with-cxx=g++
> --with-fc=gfortran --download-mpich --download-fblaslapack --with-cuda
> [0]PETSC ERROR: #1 VecCopy_Nest() line 68 in
> /usr/local/petsc/petsc-3.12.5/src/vec/vec/impls/nest/vecnest.c
> [0]PETSC ERROR: #2 VecCopy() line 1577 in
> /usr/local/petsc/petsc-3.12.5/src/vec/vec/interface/vector.c
> [0]PETSC ERROR: #3 KSPInitialResidual() line 61 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/ksp/interface/itres.c
> [0]PETSC ERROR: #4 KSPSolve_GMRES() line 236 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/ksp/impls/gmres/gmres.c
> [0]PETSC ERROR: #5 KSPSolve() line 760 in
> /usr/local/petsc/petsc-3.12.5/src/ksp/ksp/interface/itfunc.c
>
>
> Regards
> JT
>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
> https://www.cse.buffalo.edu/~knepley/
> <https://link.getmailspring.com/link/1D2D2990-B215-4510-B196-F29BD06D4684@getmailspring.com/1?redirect=http%3A%2F%2Fwww.cse.buffalo.edu%2F~knepley%2F&recipient=a25lcGxleUBnbWFpbC5jb20%3D>
>
>
--
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20200716/a7087d69/attachment-0001.html>
More information about the petsc-users
mailing list