[petsc-users] Convergence problem in solving a symmetric positive definite matrix in a CFD code
Xiao, Jianjun (IKET)
jianjun.xiao at kit.edu
Wed Dec 4 08:59:39 CST 2013
Hello,
I am using Petsc to solve the linear equation in a CFD code. The matrix is symmetric positive definite.
Please find my input and output below.
1. When I used KSPCR solver, ||r(i)||/||b|| is inf. What is the reason? Does it mean ||b|| is zero? When I used the KSPLGMRES solver, it seems ||r(i)||/||b|| is OK. However, it seems the calculated results are not right.
2. I am not sure if I set the solver and matrix properly. Did I miss something?
Thank you.
****************************************
INPUT:
CALL KSPCreate(PETSC_COMM_WORLD,solver,ierr)
CALL DMSetMatType(da_ksp,MATMPISBAIJ,ierr)
CALL DMCreateMatrix(da_ksp,mat,ierr)
CALL MatMPISBAIJSetPreallocation(mat,1,4,PETSC_NULL_INTEGER,1,PETSC_NULL_INTEGER,ierr)
CALL MatZeroEntries(mat,ierr)
CALL MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY,ierr)
CALL MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY,ierr)
CALL KSPSetOperators(solver,mat,mat,SAME_NONZERO_PATTERN,ierr)
! CALL KSPSetType(solver,KSPCR,ierr)
CALL KSPSetType(solver,KSPLGMRES,ierr)
epsi = 1.0-e5
CALL KSPSetTolerances(solver,epsi,PETSC_DEFAULT_DOUBLE_PRECISION,&
& PETSC_DEFAULT_DOUBLE_PRECISION,itmax,ierr)
CALL KSPGetPC(solver,gfprec,ierr)
CALL PCSetType(prec,PCBJACOBI,ierr)
CALL KSPMonitorSet(solver,KSPMonitorTrueResidualNorm,&
PETSC_NULL_OBJECT,PETSC_NULL_FUNCTION,ierr )
CALL KSPSetInitialGuessNonzero(solver,PETSC_TRUE,ierr)
CALL KSPSolve(solver,bvec,xsol,ierr)
CALL KSPGetIterationNumber(solver,iter,ierr)
CALL KSPGetResidualNorm(solver,dmax,ierr)
CALL KSPView(solver,PETSC_VIEWER_STDOUT_WORLD,ierr)
**************************************
OUTPUT CALL KSPSetType(solver,KSPCR,ierr):
0 KSP preconditioned resid norm 2.226482634319e+05 true resid norm 1.204978940624e+07 ||r(i)||/||b|| inf
1 KSP preconditioned resid norm 1.684243557244e+05 true resid norm 6.742321430949e+06 ||r(i)||/||b|| inf
2 KSP preconditioned resid norm 1.039386033131e+05 true resid norm 5.094347016880e+06 ||r(i)||/||b|| inf
3 KSP preconditioned resid norm 3.767761162917e+04 true resid norm 2.085014289432e+06 ||r(i)||/||b|| inf
4 KSP preconditioned resid norm 2.220316358489e+04 true resid norm 1.039841616110e+06 ||r(i)||/||b|| inf
5 KSP preconditioned resid norm 1.009108756815e+04 true resid norm 6.764592620620e+05 ||r(i)||/||b|| inf
6 KSP preconditioned resid norm 7.266143334386e+03 true resid norm 4.713756053613e+05 ||r(i)||/||b|| inf
7 KSP preconditioned resid norm 4.925270026573e+03 true resid norm 3.276759177651e+05 ||r(i)||/||b|| inf
8 KSP preconditioned resid norm 2.595039666791e+03 true resid norm 1.774916597474e+05 ||r(i)||/||b|| inf
9 KSP preconditioned resid norm 1.970388137453e+03 true resid norm 1.449811653036e+05 ||r(i)||/||b|| inf
10 KSP preconditioned resid norm 1.455914234388e+03 true resid norm 7.916294162841e+04 ||r(i)||/||b|| inf
11 KSP preconditioned resid norm 8.335194818556e+02 true resid norm 4.530953608250e+04 ||r(i)||/||b|| inf
12 KSP preconditioned resid norm 3.022320555777e+02 true resid norm 1.728551635678e+04 ||r(i)||/||b|| inf
13 KSP preconditioned resid norm 7.190336024797e+01 true resid norm 4.186842086105e+03 ||r(i)||/||b|| inf
14 KSP preconditioned resid norm 1.718291655675e+01 true resid norm 1.089751055004e+03 ||r(i)||/||b|| inf
15 KSP preconditioned resid norm 1.150683059424e+01 true resid norm 8.672405273471e+02 ||r(i)||/||b|| inf
16 KSP preconditioned resid norm 8.663479440949e+00 true resid norm 5.776737380768e+02 ||r(i)||/||b|| inf
17 KSP preconditioned resid norm 5.282161990683e+00 true resid norm 2.977735906695e+02 ||r(i)||/||b|| inf
18 KSP preconditioned resid norm 3.802629315725e+00 true resid norm 2.789114564993e+02 ||r(i)||/||b|| inf
19 KSP preconditioned resid norm 1.722575171383e+00 true resid norm 1.051323829526e+02 ||r(i)||/||b|| inf
KSP Object: 1 MPI processes
type: cr
maximum iterations=1000
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using nonzero initial guess
using PRECONDITIONED norm type for convergence test
PC Object: 1 MPI processes
type: bjacobi
block Jacobi: number of blocks = 1
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: icc
0 levels of fill
tolerance for zero pivot 2.22045e-14
using Manteuffel shift [POSITIVE_DEFINITE]
matrix ordering: natural
factor fill ratio given 1, needed 1
Factored matrix follows:
Mat Object: 1 MPI processes
type: seqsbaij
rows=27, cols=27
package used to perform factorization: petsc
total: nonzeros=81, allocated nonzeros=81
total number of mallocs used during MatSetValues calls =0
block size is 1
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: seqsbaij
rows=27, cols=27
total: nonzeros=81, allocated nonzeros=108
total number of mallocs used during MatSetValues calls =0
block size is 1
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: mpisbaij
rows=27, cols=27
total: nonzeros=81, allocated nonzeros=135
total number of mallocs used during MatSetValues calls =0
block size is 1
OUTPUT: CALL KSPSetType(solver,KSPLGMRES,ierr)
0 KSP preconditioned resid norm 2.362537325084e+04 true resid norm 1.138584383312e+06 ||r(i)||/||b|| 1.000000000000e+00
1 KSP preconditioned resid norm 8.501213683423e+03 true resid norm 3.655528853686e+05 ||r(i)||/||b|| 3.210591070162e-01
2 KSP preconditioned resid norm 5.487567253725e+03 true resid norm 3.005741194777e+05 ||r(i)||/||b|| 2.639893220769e-01
3 KSP preconditioned resid norm 2.470452880657e+03 true resid norm 1.545469272201e+05 ||r(i)||/||b|| 1.357360328187e-01
4 KSP preconditioned resid norm 1.750803325456e+03 true resid norm 1.182312309352e+05 ||r(i)||/||b|| 1.038405520646e-01
5 KSP preconditioned resid norm 1.123492053552e+03 true resid norm 6.754319630701e+04 ||r(i)||/||b|| 5.932208213726e-02
6 KSP preconditioned resid norm 5.150241959277e+02 true resid norm 3.689413898730e+04 ||r(i)||/||b|| 3.240351749775e-02
7 KSP preconditioned resid norm 4.182894544871e+02 true resid norm 3.052196222024e+04 ||r(i)||/||b|| 2.680693909701e-02
8 KSP preconditioned resid norm 2.520093155629e+02 true resid norm 1.880976788356e+04 ||r(i)||/||b|| 1.652031079932e-02
9 KSP preconditioned resid norm 1.186491314806e+02 true resid norm 6.797080217853e+03 ||r(i)||/||b|| 5.969764136483e-03
10 KSP preconditioned resid norm 5.851092821372e+01 true resid norm 2.973659280245e+03 ||r(i)||/||b|| 2.611716201127e-03
11 KSP preconditioned resid norm 1.669909189055e+01 true resid norm 5.658829814125e+02 ||r(i)||/||b|| 4.970057465277e-04
12 KSP preconditioned resid norm 3.090594692756e+00 true resid norm 2.161527454147e+02 ||r(i)||/||b|| 1.898434130864e-04
13 KSP preconditioned resid norm 2.164618839184e+00 true resid norm 1.620745991834e+02 ||r(i)||/||b|| 1.423474637093e-04
14 KSP preconditioned resid norm 1.291593952428e+00 true resid norm 9.095542547366e+01 ||r(i)||/||b|| 7.988465923722e-05
15 KSP preconditioned resid norm 6.100583411632e-01 true resid norm 4.021646656091e+01 ||r(i)||/||b|| 3.532146334551e-05
16 KSP preconditioned resid norm 2.723496807925e-01 true resid norm 1.676660466866e+01 ||r(i)||/||b|| 1.472583403954e-05
17 KSP preconditioned resid norm 1.377718471538e-01 true resid norm 8.551854245272e+00 ||r(i)||/||b|| 7.510953400221e-06
KSP Object: 1 MPI processes
type: lgmres
GMRES: restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
GMRES: happy breakdown tolerance 1e-30
LGMRES: aug. dimension=2
LGMRES: number of matvecs=170
maximum iterations=1000
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using nonzero initial guess
using PRECONDITIONED norm type for convergence test
PC Object: 1 MPI processes
type: bjacobi
block Jacobi: number of blocks = 1
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: icc
0 levels of fill
tolerance for zero pivot 2.22045e-14
using Manteuffel shift [POSITIVE_DEFINITE]
matrix ordering: natural
factor fill ratio given 1, needed 1
Factored matrix follows:
Mat Object: 1 MPI processes
type: seqsbaij
rows=27, cols=27
package used to perform factorization: petsc
total: nonzeros=81, allocated nonzeros=81
total number of mallocs used during MatSetValues calls =0
block size is 1
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: seqsbaij
rows=27, cols=27
total: nonzeros=81, allocated nonzeros=108
total number of mallocs used during MatSetValues calls =0
block size is 1
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: mpisbaij
rows=27, cols=27
total: nonzeros=81, allocated nonzeros=135
total number of mallocs used during MatSetValues calls =0
More information about the petsc-users
mailing list