# PETSc CG solver uses more iterations than other CG solver

Knut Erik Teigen knutert at stud.ntnu.no
Fri Mar 9 10:12:00 CST 2007

```Hello,

I am using PETSc to calculate two-phase flow with the level set method,
on a structured grid using finite differences.
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. 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
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    #
#   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
--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/i586-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

```