Hi Hong,
I did more test today and finally found that the solution accuracy
depends on the initial (first) matrix quality. I modified the ex52f.F to
do the test. There are 6 matrices and right-hand-side vectors. All these
matrices and rhs are from my reactive transport simulation. Results will
be quite different depending on which one you use to do factorization.
Results will also be different if you run with different options. My
code is similar to the First or the Second test below. When the matrix
is well conditioned, it works fine. But if the initial matrix is well
conditioned, it likely to crash when the matrix become ill-conditioned.
Since most of my case are well conditioned so I didn't detect the
problem before. This case is a special one.
How can I avoid this problem? Shall I redo factorization? Can PETSc
automatically detect this prolbem or is there any option available to do
this?
All the data and test code (modified ex52f) can be found via the dropbox
link below.
_
__https://www.dropbox.com/s/4al1a60creogd8m/petsc-superlu-test.tar.gz?dl=0_
Summary of my test is shown below.
First, use the Matrix 1 to setup KSP solver and factorization, then
solve 168 to 172
mpiexec.hydra -n 1 ./ex52f -f0
/home/dsu/work/petsc-superlu-test/matrix_and_rhs_bin/a_flow_check_1.bin
-rhs
/home/dsu/work/petsc-superlu-test/matrix_and_rhs_bin/b_flow_check_1.bin
-loop_matrices flow_check -loop_folder
/home/dsu/work/petsc-superlu-test/matrix_and_rhs_bin -pc_type lu
-pc_factor_mat_solver_package superlu_dist
Norm of error 3.8815E-11 iterations 1
-->Test for matrix 168
Norm of error 4.2307E-01 iterations 32
-->Test for matrix 169
Norm of error 3.0528E-01 iterations 32
-->Test for matrix 170
Norm of error 3.1177E-01 iterations 32
-->Test for matrix 171
Norm of error 3.2793E-01 iterations 32
-->Test for matrix 172
Norm of error 3.1251E-01 iterations 31
Second, use the Matrix 1 to setup KSP solver and factorization using the
implemented SuperLU relative codes. I thought this will generate the
same results as the First test, but it actually not.
mpiexec.hydra -n 1 ./ex52f -f0
/home/dsu/work/petsc-superlu-test/matrix_and_rhs_bin/a_flow_check_1.bin
-rhs
/home/dsu/work/petsc-superlu-test/matrix_and_rhs_bin/b_flow_check_1.bin
-loop_matrices flow_check -loop_folder
/home/dsu/work/petsc-superlu-test/matrix_and_rhs_bin -superlu_default
Norm of error 2.2632E-12 iterations 1
-->Test for matrix 168
Norm of error 1.0817E+04 iterations 1
-->Test for matrix 169
Norm of error 1.0786E+04 iterations 1
-->Test for matrix 170
Norm of error 1.0792E+04 iterations 1
-->Test for matrix 171
Norm of error 1.0792E+04 iterations 1
-->Test for matrix 172
Norm of error 1.0792E+04 iterations 1
Third, use the Matrix 168 to setup KSP solver and factorization, then
solve 168 to 172
mpiexec.hydra -n 1 ./ex52f -f0
/home/dsu/work/petsc-superlu-test/matrix_and_rhs_bin/a_flow_check_168.bin -rhs
/home/dsu/work/petsc-superlu-test/matrix_and_rhs_bin/b_flow_check_168.bin -loop_matrices
flow_check -loop_folder
/home/dsu/work/petsc-superlu-test/matrix_and_rhs_bin -pc_type lu
-pc_factor_mat_solver_package superlu_dist
Norm of error 9.5528E-10 iterations 1
-->Test for matrix 168
Norm of error 9.4945E-10 iterations 1
-->Test for matrix 169
Norm of error 6.4279E-10 iterations 1
-->Test for matrix 170
Norm of error 7.4633E-10 iterations 1
-->Test for matrix 171
Norm of error 7.4863E-10 iterations 1
-->Test for matrix 172
Norm of error 8.9701E-10 iterations 1
Fourth, use the Matrix 168 to setup KSP solver and factorization using
the implemented SuperLU relative codes. I thought this will generate the
same results as the Third test, but it actually not.
mpiexec.hydra -n 1 ./ex52f -f0
/home/dsu/work/petsc-superlu-test/matrix_and_rhs_bin/a_flow_check_168.bin -rhs
/home/dsu/work/petsc-superlu-test/matrix_and_rhs_bin/b_flow_check_168.bin -loop_matrices
flow_check -loop_folder
/home/dsu/work/petsc-superlu-test/matrix_and_rhs_bin -superlu_default
Norm of error 3.7017E-11 iterations 1
-->Test for matrix 168
Norm of error 3.6420E-11 iterations 1
-->Test for matrix 169
Norm of error 3.7184E-11 iterations 1
-->Test for matrix 170
Norm of error 3.6847E-11 iterations 1
-->Test for matrix 171
Norm of error 3.7883E-11 iterations 1
-->Test for matrix 172
Norm of error 3.8805E-11 iterations 1
Thanks very much,
Danyang
On 15-12-03 01:59 PM, Hong wrote:
Danyang :
Further testing a_flow_check_168.bin,
./ex10 -f0
/Users/Hong/Downloads/matrix_and_rhs_bin/a_flow_check_168.bin -rhs
/Users/Hong/Downloads/matrix_and_rhs_bin/x_flow_check_168.bin -pc_type
lu -pc_factor_mat_solver_package superlu -ksp_monitor_true_residual
-mat_superlu_conditionnumber
Recip. condition number = 1.610480e-12
0 KSP preconditioned resid norm 6.873340313547e+09 true resid norm
7.295020990196e+03 ||r(i)||/||b|| 1.000000000000e+00
1 KSP preconditioned resid norm 2.051833296449e-02 true resid norm
2.976859070118e-02 ||r(i)||/||b|| 4.080672384793e-06
Number of iterations = 1
Residual norm 0.0297686
condition number of this matrix = 1/1.610480e-12 = 1.e+12,
i.e., this matrix is ill-conditioned.
Hong
Hi Hong,
The binary format of matrix, rhs and solution can be downloaded
via the link below.
https://www.dropbox.com/s/cl3gfi0s0kjlktf/matrix_and_rhs_bin.tar.gz?dl=0
Thanks,
Danyang
On 15-12-03 10:50 AM, Hong wrote:
Danyang:
To my surprising, solutions from SuperLU at timestep 29 seems
not correct for the first 4 Newton iterations, but the
solutions from iteration solver and MUMPS are correct.
Please find all the matrices, rhs and solutions at timestep
29 via the link below. The data is a bit large so that I just
share it through Dropbox. A piece of matlab code to read
these data and then computer the norm has also been attached.
_https://www.dropbox.com/s/rr8ueysgflmxs7h/results-check.tar.gz?dl=0_
Can you send us matrix in petsc binary format?
e.g., call MatView(M, PETSC_VIEWER_BINARY_(PETSC_COMM_WORLD))
or '-ksp_view_mat binary'
Hong
Below is a summary of the norm from the three solvers at
timestep 29, newton iteration 1 to 5.
Timestep 29
Norm of residual seq 1.661321e-09, superlu 1.657103e+04,
mumps 3.731225e-11
Norm of residual seq 1.753079e-09, superlu 6.675467e+02,
mumps 1.509919e-13
Norm of residual seq 4.914971e-10, superlu 1.236362e-01,
mumps 2.139303e-17
Norm of residual seq 3.532769e-10, superlu 1.304670e-04,
mumps 5.387000e-20
Norm of residual seq 3.885629e-10, superlu 2.754876e-07,
mumps 4.108675e-21
Would anybody please check if SuperLU can solve these
matrices? Another possibility is that something is wrong in
my own code. But so far, I cannot find any problem in my code
since the same code works fine if I using iterative solver or
direct solver MUMPS. But for other cases I have tested, all
these solvers work fine.
Please let me know if I did not write down the problem clearly.
Thanks,
Danyang
