[petsc-users] Use block Jacobi preconditioner with SNES
Smith, Barry F.
bsmith at mcs.anl.gov
Tue Aug 28 12:38:18 CDT 2018
Example? Without the callback I don't think you can access the subblocks at the appropriate time to set their prefixes
Barry
> On Aug 28, 2018, at 12:32 PM, Matthew Knepley <knepley at gmail.com> wrote:
>
> On Tue, Aug 28, 2018 at 10:04 AM Adam Denchfield <adenchfi at hawk.iit.edu> wrote:
> " PETSc developers - do you think we should put the callback functionality into PETSc? It allows doing things that are otherwise not doable but is rather ugly (perhaps too specialized)?"
>
> Though I only worked on it over the summer, the functionality you describe (using different solvers on different blocks) sounds useful to me. Quantum mechanics applications sometimes produce block matrices where the blocks have significantly different structure.
>
> I don't think we need callbacks, you just need to give different prefixes to different blocks. I have done this before.
>
> Matt
>
> On Tue, Aug 28, 2018, 5:37 AM Matthew Knepley <knepley at gmail.com> wrote:
> On Tue, Aug 28, 2018 at 5:34 AM Ali Reza Khaz'ali <arkhazali at cc.iut.ac.ir> wrote:
>
> > Actually you do not need my new branch to achieve what you desired. All you need in your main program is something like
> >
> > ierr = SNESCreate(PETSC_COMM_WORLD,&snes);CHKERRQ(ierr);
> > ierr = SNESGetKSP(snes,&ksp);CHKERRQ(ierr);
> > ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
> > ierr = PCSetType(pc,PCBJACOBI);CHKERRQ(ierr);
> > ierr = PCBJacobiSetTotalBlocks(pc,3,lens);CHKERRQ(ierr); /* here you set your block sizes to whatever you need */
> >
> > Then simply do not call PCBJacobiGetSubKSP() but use the options database to set the inner solver with -sub_pc_type lu -sub_ksp_type preonly
> >
> > I have updated the branch to move the PCBJacobiSetTotalBlocks() to the main program but left the callback in there for setting the inner solver types (though as I just said you don't need to use the callback since you can control the solver from the options database). The callback is needed, if, for example, you wished to use a different solver on different blocks (which is not your case).
> >
> > Barry
> >
> > PETSc developers - do you think we should put the callback functionality into PETSc? It allows doing things that are otherwise not doable but is rather ugly (perhaps too specialized)?
> >
> >
> >
>
> It works! Thanks a lot. Here is log of a 30x30x10 system (18000 blocks,
> with GMRes solver). I like to have variable sized block preconditioners
> and solvers in PETSc. Their application is more than it may first
> appear. If it is possible, I would like to contribute to PETSc code, to
> build a variable sized block Jacobi and block ILU(k) at the first step
> (If I can, of course). Where can I start?
>
> Okay, the best place to start I think is to make an example which shows what you want
> to demonstrate. Then we can offer feedback, and if anything should move to the library,
> we can do that in a subsequent contribution.
>
> The best way, I think, to make an example is to fork the PETSc repository on Bitbucket
> (or Github), add you example code to the relevant directory, such as
>
> $PETSC_DIR/src/snes/examples/tutorials
>
> It will build with
>
> make ex1001
>
> or whatever number you choose, and then you make a Pull Request (there is documentation
> here: https://bitbucket.org/petsc/petsc/wiki/pull-request-instructions-git). Note there is a
> Developer's Manual which has things like code structure guidelines.
>
> Thanks,
>
> Matt
>
> type: newtonls
> maximum iterations=2000, maximum function evaluations=2000
> tolerances: relative=0.0001, absolute=1e-05, solution=1e-05
> total number of linear solver iterations=3
> total number of function evaluations=2
> norm schedule ALWAYS
> SNESLineSearch Object: 1 MPI processes
> type: bt
> interpolation: cubic
> alpha=1.000000e-04
> maxstep=1.000000e+08, minlambda=1.000000e-12
> tolerances: relative=1.000000e-08, absolute=1.000000e-15,
> lambda=1.000000e-08
> maximum iterations=40
> KSP Object: 1 MPI processes
> type: gmres
> restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
> happy breakdown tolerance 1e-30
> maximum iterations=5000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-06, divergence=10000.
> left preconditioning
> using PRECONDITIONED norm type for convergence test
> PC Object: 1 MPI processes
> type: bjacobi
> number of blocks = 18000
> Local solve is same for all blocks, in the following KSP and PC
> objects:
> KSP Object: (sub_) 1 MPI processes
> type: preonly
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> left preconditioning
> using NONE norm type for convergence test
> PC Object: (sub_) 1 MPI processes
> type: lu
> out-of-place factorization
> tolerance for zero pivot 2.22045e-14
> matrix ordering: nd
> factor fill ratio given 0., needed 0.
> Factored matrix follows:
> Mat Object: 1 MPI processes
> type: mkl_pardiso
> rows=6, cols=6
> package used to perform factorization: mkl_pardiso
> total: nonzeros=26, allocated nonzeros=26
> total number of mallocs used during MatSetValues calls =0
> MKL_PARDISO run parameters:
> MKL_PARDISO phase: 33
> MKL_PARDISO iparm[1]: 1
> MKL_PARDISO iparm[2]: 2
> MKL_PARDISO iparm[3]: 1
> MKL_PARDISO iparm[4]: 0
> MKL_PARDISO iparm[5]: 0
> MKL_PARDISO iparm[6]: 0
> MKL_PARDISO iparm[7]: 0
> MKL_PARDISO iparm[8]: 0
> MKL_PARDISO iparm[9]: 0
> MKL_PARDISO iparm[10]: 13
> MKL_PARDISO iparm[11]: 1
> MKL_PARDISO iparm[12]: 0
> MKL_PARDISO iparm[13]: 1
> MKL_PARDISO iparm[14]: 0
> MKL_PARDISO iparm[15]: 144
> MKL_PARDISO iparm[16]: 144
> MKL_PARDISO iparm[17]: 0
> MKL_PARDISO iparm[18]: 37
> MKL_PARDISO iparm[19]: 0
> MKL_PARDISO iparm[20]: 0
> MKL_PARDISO iparm[21]: 0
> MKL_PARDISO iparm[22]: 0
> MKL_PARDISO iparm[23]: 0
> MKL_PARDISO iparm[24]: 0
> MKL_PARDISO iparm[25]: 0
> MKL_PARDISO iparm[26]: 0
> MKL_PARDISO iparm[27]: 0
> MKL_PARDISO iparm[28]: 0
> MKL_PARDISO iparm[29]: 0
> MKL_PARDISO iparm[30]: 0
> MKL_PARDISO iparm[31]: 0
> MKL_PARDISO iparm[32]: 0
> MKL_PARDISO iparm[33]: 0
> MKL_PARDISO iparm[34]: -1
> MKL_PARDISO iparm[35]: 1
> MKL_PARDISO iparm[36]: 0
> MKL_PARDISO iparm[37]: 0
> MKL_PARDISO iparm[38]: 0
> MKL_PARDISO iparm[39]: 0
> MKL_PARDISO iparm[40]: 0
> MKL_PARDISO iparm[41]: 0
> MKL_PARDISO iparm[42]: 0
> MKL_PARDISO iparm[43]: 0
> MKL_PARDISO iparm[44]: 0
> MKL_PARDISO iparm[45]: 0
> MKL_PARDISO iparm[46]: 0
> MKL_PARDISO iparm[47]: 0
> MKL_PARDISO iparm[48]: 0
> MKL_PARDISO iparm[49]: 0
> MKL_PARDISO iparm[50]: 0
> MKL_PARDISO iparm[51]: 0
> MKL_PARDISO iparm[52]: 0
> MKL_PARDISO iparm[53]: 0
> MKL_PARDISO iparm[54]: 0
> MKL_PARDISO iparm[55]: 0
> MKL_PARDISO iparm[56]: 0
> MKL_PARDISO iparm[57]: -1
> MKL_PARDISO iparm[58]: 0
> MKL_PARDISO iparm[59]: 0
> MKL_PARDISO iparm[60]: 0
> MKL_PARDISO iparm[61]: 144
> MKL_PARDISO iparm[62]: 145
> MKL_PARDISO iparm[63]: 21
> MKL_PARDISO iparm[64]: 0
> MKL_PARDISO maxfct: 1
> MKL_PARDISO mnum: 1
> MKL_PARDISO mtype: 11
> MKL_PARDISO n: 6
> MKL_PARDISO nrhs: 1
> MKL_PARDISO msglvl: 0
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=6, cols=6
> total: nonzeros=26, allocated nonzeros=26
> total number of mallocs used during MatSetValues calls =0
> using I-node routines: found 4 nodes, limit used is 5
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=108000, cols=108000
> total: nonzeros=2868000, allocated nonzeros=8640000
> total number of mallocs used during MatSetValues calls =0
> not using I-node routines
> ************************************************************************************************************************
> *** WIDEN YOUR WINDOW TO 120 CHARACTERS. Use 'enscript -r
> -fCourier9' to print this document ***
> ************************************************************************************************************************
>
> ---------------------------------------------- PETSc Performance
> Summary: ----------------------------------------------
>
> E:\Documents\Visual Studio 2015\Projects\compsim\x64\Release\compsim.exe
> on a named ALIREZA-PC with 1 processor, by AliReza Tue Aug 28 13:57:09 2018
> Using Petsc Development GIT revision: v3.9.3-1238-gce82fdcfd6 GIT Date:
> 2018-08-27 15:47:19 -0500
>
> Max Max/Min Avg Total
> Time (sec): 1.353e+02 1.000 1.353e+02
> Objects: 1.980e+05 1.000 1.980e+05
> Flop: 2.867e+07 1.000 2.867e+07 2.867e+07
> Flop/sec: 2.119e+05 1.000 2.119e+05 2.119e+05
> MPI Messages: 0.000e+00 0.000 0.000e+00 0.000e+00
> MPI Message Lengths: 0.000e+00 0.000 0.000e+00 0.000e+00
> MPI Reductions: 0.000e+00 0.000
>
> Flop counting convention: 1 flop = 1 real number operation of type
> (multiply/divide/add/subtract)
> e.g., VecAXPY() for real vectors of length
> N --> 2N flop
> and VecAXPY() for complex vectors of length
> N --> 8N flop
>
> Summary of Stages: ----- Time ------ ----- Flop ------ --- Messages
> --- -- Message Lengths -- -- Reductions --
> Avg %Total Avg %Total Count
> %Total Avg %Total Count %Total
> 0: Main Stage: 1.3529e+02 100.0% 2.8668e+07 100.0% 0.000e+00
> 0.0% 0.000e+00 0.0% 0.000e+00 0.0%
>
> ------------------------------------------------------------------------------------------------------------------------
> See the 'Profiling' chapter of the users' manual for details on
> interpreting output.
> Phase summary info:
> Count: number of times phase was executed
> Time and Flop: Max - maximum over all processors
> Ratio - ratio of maximum to minimum over all processors
> Mess: number of messages sent
> AvgLen: average message length (bytes)
> Reduct: number of global reductions
> Global: entire computation
> Stage: stages of a computation. Set stages with PetscLogStagePush()
> and PetscLogStagePop().
> %T - percent time in this phase %F - percent flop in this
> phase
> %M - percent messages in this phase %L - percent message
> lengths in this phase
> %R - percent reductions in this phase
> Total Mflop/s: 10e-6 * (sum of flop over all processors)/(max time
> over all processors)
> ------------------------------------------------------------------------------------------------------------------------
> Event Count Time (sec)
> Flop --- Global --- --- Stage ---- Total
> Max Ratio Max Ratio Max Ratio Mess AvgLen
> Reduct %T %F %M %L %R %T %F %M %L %R Mflop/s
> ------------------------------------------------------------------------------------------------------------------------
>
> --- Event Stage 0: Main Stage
>
> BuildTwoSidedF 2 1.0 1.2701e-04 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
> SNESSolve 1 1.0 1.1583e+02 1.0 2.87e+07 1.0 0.0e+00 0.0e+00
> 0.0e+00 86100 0 0 0 86100 0 0 0 0
> SNESFunctionEval 2 1.0 5.4101e+00 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 4 0 0 0 0 4 0 0 0 0 0
> SNESJacobianEval 1 1.0 9.3770e+01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 69 0 0 0 0 69 0 0 0 0 0
> SNESLineSearch 1 1.0 3.1033e+00 1.0 6.82e+06 1.0 0.0e+00 0.0e+00
> 0.0e+00 2 24 0 0 0 2 24 0 0 0 2
> VecDot 1 1.0 1.8688e-04 1.0 2.16e+05 1.0 0.0e+00 0.0e+00
> 0.0e+00 0 1 0 0 0 0 1 0 0 0 1156
> VecMDot 3 1.0 9.9299e-04 1.0 1.30e+06 1.0 0.0e+00 0.0e+00
> 0.0e+00 0 5 0 0 0 0 5 0 0 0 1305
> VecNorm 7 1.0 6.0845e-03 1.0 1.51e+06 1.0 0.0e+00 0.0e+00
> 0.0e+00 0 5 0 0 0 0 5 0 0 0 248
> VecScale 4 1.0 1.4437e+00 1.0 4.32e+05 1.0 0.0e+00 0.0e+00
> 0.0e+00 1 2 0 0 0 1 2 0 0 0 0
> VecCopy 3 1.0 1.6059e+00 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 1 0 0 0 0 1 0 0 0 0 0
> VecSet 90002 1.0 1.3843e-02 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
> VecAXPY 1 1.0 3.1733e-01 1.0 2.16e+05 1.0 0.0e+00 0.0e+00
> 0.0e+00 0 1 0 0 0 0 1 0 0 0 1
> VecWAXPY 1 1.0 2.2665e-04 1.0 1.08e+05 1.0 0.0e+00 0.0e+00
> 0.0e+00 0 0 0 0 0 0 0 0 0 0 477
> VecMAXPY 4 1.0 8.6085e-04 1.0 1.94e+06 1.0 0.0e+00 0.0e+00
> 0.0e+00 0 7 0 0 0 0 7 0 0 0 2258
> VecAssemblyBegin 2 1.0 1.6379e-04 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
> VecAssemblyEnd 2 1.0 1.4112e-05 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
> VecReduceArith 2 1.0 3.1304e-04 1.0 4.32e+05 1.0 0.0e+00 0.0e+00
> 0.0e+00 0 2 0 0 0 0 2 0 0 0 1380
> VecReduceComm 1 1.0 2.1382e-06 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
> VecNormalize 4 1.0 1.4441e+00 1.0 1.30e+06 1.0 0.0e+00 0.0e+00
> 0.0e+00 1 5 0 0 0 1 5 0 0 0 1
> MatMult 4 1.0 2.0402e-02 1.0 2.25e+07 1.0 0.0e+00 0.0e+00
> 0.0e+00 0 79 0 0 0 0 79 0 0 0 1103
> MatSolve 72000 1.0 5.3514e+00 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 4 0 0 0 0 4 0 0 0 0 0
> MatLUFactorSym 18000 1.0 1.9405e+00 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 1 0 0 0 0 1 0 0 0 0 0
> MatLUFactorNum 18000 1.0 1.8373e-01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
> MatAssemblyBegin 18002 1.0 1.0409e-03 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
> MatAssemblyEnd 18002 1.0 3.3879e-02 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
> MatGetRowIJ 18000 1.0 3.1819e-02 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
> MatCreateSubMats 1 1.0 3.7015e-01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
> MatGetOrdering 18000 1.0 3.0787e-01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
> MatZeroEntries 1 1.0 2.7952e-02 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
> MatView 3 1.0 2.9153e-01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
> KSPSetUp 18001 1.0 7.5898e-03 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
> KSPSolve 1 1.0 1.6244e+01 1.0 2.16e+07 1.0 0.0e+00 0.0e+00
> 0.0e+00 12 75 0 0 0 12 75 0 0 0 1
> KSPGMRESOrthog 3 1.0 8.4669e-02 1.0 2.59e+06 1.0 0.0e+00 0.0e+00
> 0.0e+00 0 9 0 0 0 0 9 0 0 0 31
> PCSetUp 18001 1.0 3.3536e+00 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 2 0 0 0 0 2 0 0 0 0 0
> PCSetUpOnBlocks 1 1.0 2.5973e+00 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 2 0 0 0 0 2 0 0 0 0 0
> PCApply 4 1.0 6.2752e+00 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 5 0 0 0 0 5 0 0 0 0 0
> PCApplyOnBlocks 72000 1.0 5.9278e+00 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> 0.0e+00 4 0 0 0 0 4 0 0 0 0 0
> ------------------------------------------------------------------------------------------------------------------------
>
> Memory usage is given in bytes:
>
> Object Type Creations Destructions Memory Descendants' Mem.
> Reports information only for process 0.
>
> --- Event Stage 0: Main Stage
>
> SNES 1 0 0 0.
> DMSNES 1 0 0 0.
> SNESLineSearch 1 0 0 0.
> Vector 36020 0 0 0.
> Matrix 36001 0 0 0.
> Distributed Mesh 2 0 0 0.
> Index Set 90000 36000 29088000 0.
> Star Forest Graph 4 0 0 0.
> Discrete System 2 0 0 0.
> Krylov Solver 18001 0 0 0.
> DMKSP interface 1 0 0 0.
> Preconditioner 18001 0 0 0.
> Viewer 1 0 0 0.
> ========================================================================================================================
> Average time to get PetscTime(): 1.28294e-07
> #PETSc Option Table entries:
> -ksp_atol 1e-6
> -ksp_rtol 1e-5
> -snes_rtol 1e-4
> -sub_ksp_type preonly
> -sub_pc_factor_mat_solver_type mkl_pardiso
> -sub_pc_type lu
> #End of PETSc Option Table entries
> Compiled without FORTRAN kernels
> Compiled with full precision matrices (default)
> sizeof(short) 2 sizeof(int) 4 sizeof(long) 4 sizeof(void*) 8
> sizeof(PetscScalar) 8 sizeof(PetscInt) 4
> Configure options: --prefix=/home/alireza/PetscGit
> --with-mkl_pardiso-dir=/cygdrive/E/Program_Files_x86/IntelSWTools/compilers_and_libraries/windows/mkl
> --with-hypre-incl
> ude=/cygdrive/E/hypre-2.11.2/Builds/Bins/include
> --with-hypre-lib=/cygdrive/E/hypre-2.11.2/Builds/Bins/lib/HYPRE.lib
> --with-ml-include=/cygdrive/E/Trilinos-master/Bins/in
> clude --with-ml-lib=/cygdrive/E/Trilinos-master/Bins/lib/ml.lib
> ظ€ôwith-openmp --with-cc="win32fe icl" --with-fc="win32fe ifort"
> --with-mpi-include=/cygdrive/E/Program_Fi
> les_x86/IntelSWTools/compilers_and_libraries/windows/mpi/intel64/include
> --with-mpi-lib=/cygdrive/E/Program_Files_x86/IntelSWTools/compilers_and_libraries/windows/mpi/int
> el64/lib/impi.lib
> --with-mpi-mpiexec=/cygdrive/E/Program_Files_x86/IntelSWTools/compilers_and_libraries/windows/mpi/intel64/bin/mpiexec.exe
> --with-debugging=0 --with-blas
> -lib=/cygdrive/E/Program_Files_x86/IntelSWTools/compilers_and_libraries/windows/mkl/lib/intel64_win/mkl_rt.lib
> --with-lapack-lib=/cygdrive/E/Program_Files_x86/IntelSWTool
> s/compilers_and_libraries/windows/mkl/lib/intel64_win/mkl_rt.lib
> -CFLAGS="-O2 -MT -wd4996 -Qopenmp" -CXXFLAGS="-O2 -MT -wd4996 -Qopenmp"
> -FFLAGS="-MT -O2 -Qopenmp"
> -----------------------------------------
> Libraries compiled on 2018-08-27 22:42:15 on AliReza-PC
> Machine characteristics: CYGWIN_NT-6.1-2.10.0-0.325-5-3-x86_64-64bit
> Using PETSc directory: /home/alireza/PetscGit
> Using PETSc arch:
> -----------------------------------------
>
> Using C compiler: /home/alireza/PETSc/lib/petsc/bin/win32fe/win32fe icl
> -O2 -MT -wd4996 -Qopenmp
> Using Fortran compiler:
> /home/alireza/PETSc/lib/petsc/bin/win32fe/win32fe ifort -MT -O2 -Qopenmp
> -fpp
> -----------------------------------------
>
> Using include paths: -I/home/alireza/PetscGit/include
> -I/cygdrive/E/Program_Files_x86/IntelSWTools/compilers_and_libraries/windows/mkl/include
> -I/cygdrive/E/hypre-2.11.2/
> Builds/Bins/include -I/cygdrive/E/Trilinos-master/Bins/include
> -I/cygdrive/E/Program_Files_x86/IntelSWTools/compilers_and_libraries/windows/mpi/intel64/include
> -----------------------------------------
>
> Using C linker: /home/alireza/PETSc/lib/petsc/bin/win32fe/win32fe icl
> Using Fortran linker: /home/alireza/PETSc/lib/petsc/bin/win32fe/win32fe
> ifort
> Using libraries: -L/home/alireza/PetscGit/lib
> -L/home/alireza/PetscGit/lib -lpetsc
> /cygdrive/E/hypre-2.11.2/Builds/Bins/lib/HYPRE.lib
> /cygdrive/E/Trilinos-master/Bins/lib
> /ml.lib
> /cygdrive/E/Program_Files_x86/IntelSWTools/compilers_and_libraries/windows/mkl/lib/intel64_win/mkl_rt.lib
> /cygdrive/E/Program_Files_x86/IntelSWTools/compilers_and
> _libraries/windows/mkl/lib/intel64_win/mkl_rt.lib
> /cygdrive/E/Program_Files_x86/IntelSWTools/compilers_and_libraries/windows/mpi/intel64/lib/impi.lib
> Gdi32.lib User32.lib
> Advapi32.lib Kernel32.lib Ws2_32.lib
> -----------------------------------------
>
>
>
> --
> 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/
>
>
> --
> 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/
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