[petsc-users] Errors encountered with KSPsolver with MATNEST and VECNEST
Yang Juntao
Y.Juntao at hotmail.com
Thu Jul 16 05:53:57 CDT 2020
Hi, Matt,
In case, I want to put blocks of matrices(assembled independently) together as the system matrix just as in the example. What would be your recommended approach?
I first looked into MatCreateBlockMat, but it only supports sequential and then I was directed to MATNEST. Do I have to assemble directly on “system matrix”.
“
Matrices of this type are nominally-sparse matrices in which each "entry" is a Mat<https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/Mat.html#Mat> object. Each Mat<https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/Mat.html#Mat> must have the same size and be sequential. The local and global sizes must be compatible with this decomposition. For matrices containing parallel submatrices and variable block sizes, see MATNEST<https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MATNEST.html#MATNEST>.
“
Regards
Juntao
From: Matthew Knepley <knepley at gmail.com>
Sent: Thursday, July 16, 2020 5:56 PM
To: Karl Yang <y.juntao at hotmail.com>
Cc: Junchao Zhang <junchao.zhang at gmail.com>; petsc-users at mcs.anl.gov
Subject: Re: [petsc-users] Errors encountered with KSPsolver with MATNEST and VECNEST
On Thu, Jul 16, 2020 at 5:43 AM Karl Yang <y.juntao at hotmail.com<mailto: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<mailto: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:
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 22 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<mailto: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<mailto: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<mailto: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/20200716/85764fba/attachment-0001.html>
More information about the petsc-users
mailing list