PETSc CG solver uses more iterations than other CG solver
Barry Smith
bsmith at mcs.anl.gov
Sat Mar 10 11:54:58 CST 2007
On Sat, 10 Mar 2007, knutert at stud.ntnu.no wrote:
> Thank you for your reply.
>
> One boundary cell is defined to have constant pressure, since that makes the
> equation system have a unique solution.
This is really not the best way to do it; it can produce very ill-conditioned
matrices.
>I tried your command, and it lowered
> the number of iterations for most of the time steps, but for some it reached
> the maximum number of iterations (10000) without converging.
>
> I also tried making all the boundaries von Neumann and using your command.
> That made the number of iterations more constant, instead of varying between
> 700 and 2000, it stayed on around 1200. But it actually increased the average
> number of iterations somewhat. Still far from the performance of the other
> solver.
> I've also checked the convergence criteria, and it is the same for both
> solvers.
There is something most definitely wrong. Are you sure your matrix is
COMPLETELY symmetric?
Can you send your "model" code to petsc-maint at mcs.anl.gov so we can check it
out?
Since you are on a structured grid eventually you'll want to use simply
geometric multigrid; it is really the "right" way to solve the problem
and will be much better then CG + ICC. With your code we check out how
difficult it is to do this.
Barry
>
>
> Siterer Lisandro Dalcin <dalcinl at gmail.com>:
>
> > On 3/9/07, Knut Erik Teigen <knutert at stud.ntnu.no> wrote:
> > > To solve the Navier-Stokes equations, I use an explicit Runge-Kutta
> > > method with Chorin's projection method,
> > > so a Poisson equation with von Neumann boundary conditions for the
> > > pressure has to be solved at every time-step.
> >
> > All boundary conditions are Neumann type? In that case, please try to
> > run your program with the following command line option:
> >
> > -ksp_constant_null_space
> >
> > and let me know if this corrected your problem.
> >
> >
> > The equation system is
> > > positive definite, so I use the CG solver with the ICC preconditioner.
> > > The problem is that the PETSc solver seems to need a lot more iterations
> > > to reach the solution than another CG solver I'm using. On a small test
> > > problem(a rising bubble) with a 60x40 grid, the PETSc solver needs over
> > > 1000 iterations on average, while the other solver needs less than 100.
> > > I am using KSPSetInitialGuessNonzero, without this the number of
> > > iterations is even higher.
> > > I have also tried applying PETSc to a similar problem, solving the
> > > Poisson equation with von Neumann boundaries and a forcing function of
> > > f=sin(pi * x)+sin(pi *y). For this problem, the number of iterations is
> > > almost exactly the same for PETSc and the other solver.
> > >
> > > Does anyone know what the problem might be? Any help is greatly
> > > appreciated. I've included the -ksp_view of one of the time steps
> > > and the -log_summary below.
> > >
> > > Regards,
> > > Knut Erik Teigen
> > > MSc student
> > > Norwegian University of Science and Technology
> > >
> > > Output from -ksp_view:
> > >
> > > KSP Object:
> > > type: cg
> > > maximum iterations=10000
> > > tolerances: relative=1e-06, absolute=1e-50, divergence=10000
> > > left preconditioning
> > > PC Object:
> > > type: icc
> > > ICC: 0 levels of fill
> > > ICC: factor fill ratio allocated 1
> > > ICC: factor fill ratio needed 0.601695
> > > Factored matrix follows
> > > Matrix Object:
> > > type=seqsbaij, rows=2400, cols=2400
> > > total: nonzeros=7100, allocated nonzeros=7100
> > > block size is 1
> > > linear system matrix = precond matrix:
> > > Matrix Object:
> > > type=seqaij, rows=2400, cols=2400
> > > total: nonzeros=11800, allocated nonzeros=12000
> > > not using I-node routines
> > > Poisson converged after 1403 iterations
> > >
> > > Output from -log_summary
> > >
> > > ---------------------------------------------- PETSc Performance
> > > Summary: ----------------------------------------------
> > >
> > > ./run on a gcc-ifc-d named iept0415 with 1 processor, by knutert Fri Mar
> > > 9 17:06:05 2007
> > > Using Petsc Release Version 2.3.2, Patch 8, Tue Jan 2 14:33:59 PST 2007
> > > HG revision: ebeddcedcc065e32fc252af32cf1d01ed4fc7a80
> > >
> > > Max Max/Min Avg Total
> > > Time (sec): 5.425e+02 1.00000 5.425e+02
> > > Objects: 7.000e+02 1.00000 7.000e+02
> > > Flops: 6.744e+10 1.00000 6.744e+10 6.744e+10
> > > Flops/sec: 1.243e+08 1.00000 1.243e+08 1.243e+08
> > > Memory: 4.881e+05 1.00000 4.881e+05
> > > MPI Messages: 0.000e+00 0.00000 0.000e+00 0.000e+00
> > > MPI Message Lengths: 0.000e+00 0.00000 0.000e+00 0.000e+00
> > > MPI Reductions: 1.390e+03 1.00000
> > >
> > > 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 flops
> > > and VecAXPY() for complex vectors of length
> > > N --> 8N flops
> > >
> > > Summary of Stages: ----- Time ------ ----- Flops ----- --- Messages
> > > --- -- Message Lengths -- -- Reductions --
> > > Avg %Total Avg %Total counts %
> > > Total Avg %Total counts %Total
> > > 0: Main Stage: 5.4246e+02 100.0% 6.7437e+10 100.0% 0.000e+00
> > > 0.0% 0.000e+00 0.0% 1.390e+03 100.0%
> > >
> > > ------------------------------------------------------------------------------------------------------------------------
> > > 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 Flops/sec: Max - maximum over all processors
> > > Ratio - ratio of maximum to minimum over all
> > > processors
> > > Mess: number of messages sent
> > > Avg. len: average message length
> > > 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 flops 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 flops over all processors)/(max time
> > > over all processors)
> > > ------------------------------------------------------------------------------------------------------------------------
> > >
> > >
> > > ##########################################################
> > > # #
> > > # WARNING!!! #
> > > # #
> > > # This code was compiled with a debugging option, #
> > > # To get timing results run config/configure.py #
> > > # using --with-debugging=no, the performance will #
> > > # be generally two or three times faster. #
> > > # #
> > > ##########################################################
> > >
> > >
> > >
> > >
> > > ##########################################################
> > > # #
> > > # WARNING!!! #
> > > # #
> > > # This code was run without the PreLoadBegin() #
> > > # macros. To get timing results we always recommend #
> > > # preloading. otherwise timing numbers may be #
> > > # meaningless. #
> > > ##########################################################
> > >
> > >
> > > Event Count Time (sec) Flops/sec
> > > --- Global --- --- Stage --- Total
> > > Max Ratio Max Ratio Max Ratio Mess Avg len
> > > Reduct %T %F %M %L %R %T %F %M %L %R Mflop/s
> > > ------------------------------------------------------------------------------------------------------------------------
> > >
> > > --- Event Stage 0: Main Stage
> > >
> > > VecDot 1668318 1.0 1.9186e+01 1.0 4.17e+08 1.0 0.0e+00 0.0e+00
> > > 0.0e+00 4 12 0 0 0 4 12 0 0 0 417
> > > VecNorm 835191 1.0 1.0935e+01 1.0 3.67e+08 1.0 0.0e+00 0.0e+00
> > > 0.0e+00 2 6 0 0 0 2 6 0 0 0 367
> > > VecCopy 688 1.0 1.6126e-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 1667630 1.0 2.4141e+01 1.0 3.32e+08 1.0 0.0e+00 0.0e+00
> > > 0.0e+00 4 12 0 0 0 4 12 0 0 0 332
> > > VecAYPX 833815 1.0 1.9062e+01 1.0 2.10e+08 1.0 0.0e+00 0.0e+00
> > > 0.0e+00 4 6 0 0 0 4 6 0 0 0 210
> > > VecAssemblyBegin 688 1.0 8.5354e-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 688 1.0 7.8177e-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
> > > MatMult 834503 1.0 1.5044e+02 1.0 1.18e+08 1.0 0.0e+00 0.0e+00
> > > 0.0e+00 28 26 0 0 0 28 26 0 0 0 118
> > > MatSolve 835191 1.0 1.8130e+02 1.0 1.42e+08 1.0 0.0e+00 0.0e+00
> > > 0.0e+00 33 38 0 0 0 33 38 0 0 0 142
> > > MatCholFctrNum 1 1.0 1.1630e-03 1.0 2.06e+06 1.0 0.0e+00 0.0e+00
> > > 0.0e+00 0 0 0 0 0 0 0 0 0 0 2
> > > MatICCFactorSym 1 1.0 2.9588e-04 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> > > 2.0e+00 0 0 0 0 0 0 0 0 0 0 0
> > > MatAssemblyBegin 688 1.0 2.6343e-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 688 1.0 1.0964e-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 1 1.0 2.6798e-04 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> > > 2.0e+00 0 0 0 0 0 0 0 0 0 0 0
> > > KSPSetup 1 1.0 2.7585e-04 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
> > > 6.0e+00 0 0 0 0 0 0 0 0 0 0 0
> > > KSPSolve 688 1.0 4.2809e+02 1.0 1.58e+08 1.0 0.0e+00 0.0e+00
> > > 1.4e+03 79100 0 0100 79100 0 0100 158
> > > PCSetUp 1 1.0 1.7900e-03 1.0 1.34e+06 1.0 0.0e+00 0.0e+00
> > > 4.0e+00 0 0 0 0 0 0 0 0 0 0 1
> > > PCApply 835191 1.0 1.8864e+02 1.0 1.36e+08 1.0 0.0e+00 0.0e+00
> > > 0.0e+00 35 38 0 0 0 35 38 0 0 0 136
> > > ------------------------------------------------------------------------------------------------------------------------
> > >
> > > Memory usage is given in bytes:
> > >
> > > Object Type Creations Destructions Memory Descendants'
> > > Mem.
> > >
> > > --- Event Stage 0: Main Stage
> > >
> > > Index Set 2 2 19640 0
> > > Vec 694 693 299376 0
> > > Matrix 2 2 56400 0
> > > Krylov Solver 1 1 36 0
> > > Preconditioner 1 1 108 0
> > > ========================================================================================================================
> > > Average time to get PetscTime(): 2.86102e-07
> > > OptionTable: -ksp_type cg
> > > OptionTable: -log_summary -ksp_view
> > > OptionTable: -pc_type icc
> > > Compiled without FORTRAN kernels
> > > Compiled with full precision matrices (default)
> > > sizeof(short) 2 sizeof(int) 4 sizeof(long) 4 sizeof(void*) 4
> > > sizeof(PetscScalar) 8
> > > Configure run at: Thu Mar 8 11:54:22 2007
> > > Configure options: --with-cc=gcc --with-fc=ifort
> > > --download-f-blas-lapack=1 --download-mpich=1 --with-debugging=1
> > > --with-shared=0
> > > -----------------------------------------
> > > Libraries compiled on Thu Mar 8 12:08:22 CET 2007 on iept0415
> > > Machine characteristics: Linux iept0415 2.6.16.21-0.8-default #1 Mon Jul
> > > 3 18:25:39 UTC 2006 i686 i686 i386 GNU/Linux
> > > Using PETSc directory: /opt/petsc-2.3.2-p8
> > > Using PETSc arch: gcc-ifc-debug
> > > -----------------------------------------
> > > Using C compiler: gcc -fPIC -Wall -Wwrite-strings -Wno-strict-aliasing
> > > -g3
> > > Using Fortran compiler: ifort -fPIC -g
> > > -----------------------------------------
> > > Using include paths: -I/opt/petsc-2.3.2-p8
> > > -I/opt/petsc-2.3.2-p8/bmake/gcc-ifc-debug -I/opt/petsc-2.3.2-p8/include
> > > -I/opt/petsc-2.3.2-p8/externalpackages/mpich2-1.0.4p1/gcc-ifc-debug/include
> > > -I/usr/X11R6/include
> > > ------------------------------------------
> > > Using C linker: gcc -fPIC -Wall -Wwrite-strings -Wno-strict-aliasing -g3
> > > Using Fortran linker: ifort -fPIC -g
> > > Using libraries: -Wl,-rpath,/opt/petsc-2.3.2-p8/lib/gcc-ifc-debug
> > > -L/opt/petsc-2.3.2-p8/lib/gcc-ifc-debug -lpetscts -lpetscsnes -lpetscksp
> > > -lpetscdm -lpetscmat -lpetscvec -lpetsc
> > > -Wl,-rpath,/opt/petsc-2.3.2-p8/externalpackages/mpich2-1.0.4p1/gcc-ifc-debug/lib
> > > -L/opt/petsc-2.3.2-p8/externalpackages/mpich2-1.0.4p1/gcc-ifc-debug/lib
> > > -lmpich -lnsl -lrt -L/usr/X11R6/lib -lX11
> > > -Wl,-rpath,/opt/petsc-2.3.2-p8/externalpackages/fblaslapack/gcc-ifc-debug
> > > -L/opt/petsc-2.3.2-p8/externalpackages/fblaslapack/gcc-ifc-debug -lflapack
> > > -Wl,-rpath,/opt/petsc-2.3.2-p8/externalpackages/fblaslapack/gcc-ifc-debug
> > > -L/opt/petsc-2.3.2-p8/externalpackages/fblaslapack/gcc-ifc-debug -lfblas
> > > -lm -Wl,-rpath,/usr/lib/gcc/i586-suse-linux/4.1.0
> > > -L/usr/lib/gcc/i586-suse-linux/4.1.0
> > > -Wl,-rpath,/usr/lib/gcc/i586-suse-linux/4.1.0/../../../../i586-suse-linux/lib
> > > -L/usr/lib/gcc/i586-suse-linux/4.1.0/../../../../i586-suse-linux/lib
> > > -Wl,-rpath,/usr/lib/gcc/i586-suse-linux/4.1.0/../../..
> > > -L/usr/lib/gcc/i586-suse-linux/4.1.0/../../.. -ldl -lgcc_s
> > > -Wl,-rpath,/usr/lib/gcc/i586-suse-linux/4.1.0
> > > -Wl,-rpath,/usr/lib/gcc/i586-suse-linux/4.1.0/../../../../i586-suse-linux/lib
> > > -Wl,-rpath,/usr/lib/gcc/!
> > i5!
> > > 86-suse-linux/4.1.0/../../.. -Wl,-rpath,/opt/intel/fc/9.1.036/lib
> > > -L/opt/intel/fc/9.1.036/lib
> > > -Wl,-rpath,/usr/lib/gcc/i586-suse-linux/4.1.0/
> > > -L/usr/lib/gcc/i586-suse-linux/4.1.0/
> > > -Wl,-rpath,/usr/lib/gcc/i586-suse-linux/4.1.0/../../../
> > > -L/usr/lib/gcc/i586-suse-linux/4.1.0/../../../ -lifport -lifcore -limf
> > > -lm -lipgo -lirc -lirc_s -Wl,-rpath,/usr/lib/gcc/i586-suse-linux/4.1.0
> > > -Wl,-rpath,/usr/lib/gcc/i586-suse-linux/4.1.0/../../../../i586-suse-linux/lib
> > > -Wl,-rpath,/usr/lib/gcc/i586-suse-linux/4.1.0/../../.. -lm
> > > -Wl,-rpath,/usr/lib/gcc/i586-suse-linux/4.1.0
> > > -L/usr/lib/gcc/i586-suse-linux/4.1.0
> > > -Wl,-rpath,/usr/lib/gcc/i586-suse-linux/4.1.0/../../../../i586-suse-linux/lib
> > > -L/usr/lib/gcc/i586-suse-linux/4.1.0/../../../../i586-suse-linux/lib
> > > -Wl,-rpath,/usr/lib/gcc/i586-suse-linux/4.1.0/../../..
> > > -L/usr/lib/gcc/i586-suse-linux/4.1.0/../../.. -ldl -lgcc_s -ldl
> > >
> > >
> > >
> > >
> >
> >
> > --
> > Lisandro Dalcín
> > ---------------
> > Centro Internacional de Métodos Computacionales en Ingeniería (CIMEC)
> > Instituto de Desarrollo Tecnológico para la Industria Química (INTEC)
> > Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
> > PTLC - Güemes 3450, (3000) Santa Fe, Argentina
> > Tel/Fax: +54-(0)342-451.1594
>
>
>
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