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Hi Hong,<br>
<br>
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. <br>
<br>
<br>
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?<br>
<br>
All the data and test code (modified ex52f) can be found via the
dropbox link below. <br>
<u><br>
</u><u><a class="moz-txt-link-freetext" href="https://www.dropbox.com/s/4al1a60creogd8m/petsc-superlu-test.tar.gz?dl=0">https://www.dropbox.com/s/4al1a60creogd8m/petsc-superlu-test.tar.gz?dl=0</a></u><br>
<br>
<br>
Summary of my test is shown below. <br>
<br>
First, use the Matrix 1 to setup KSP solver and factorization, then
solve 168 to 172<br>
<br>
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<br>
<br>
Norm of error 3.8815E-11 iterations 1<br>
-->Test for matrix 168<br>
Norm of error 4.2307E-01 iterations 32<br>
-->Test for matrix 169<br>
Norm of error 3.0528E-01 iterations 32<br>
-->Test for matrix 170<br>
Norm of error 3.1177E-01 iterations 32<br>
-->Test for matrix 171<br>
Norm of error 3.2793E-01 iterations 32<br>
-->Test for matrix 172<br>
Norm of error 3.1251E-01 iterations 31<br>
<br>
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.<br>
<br>
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<br>
<br>
Norm of error 2.2632E-12 iterations 1<br>
-->Test for matrix 168<br>
Norm of error 1.0817E+04 iterations 1<br>
-->Test for matrix 169<br>
Norm of error 1.0786E+04 iterations 1<br>
-->Test for matrix 170<br>
Norm of error 1.0792E+04 iterations 1<br>
-->Test for matrix 171<br>
Norm of error 1.0792E+04 iterations 1<br>
-->Test for matrix 172<br>
Norm of error 1.0792E+04 iterations 1<br>
<br>
<br>
Third, use the Matrix 168 to setup KSP solver and factorization,
then solve 168 to 172<br>
<br>
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<br>
<br>
Norm of error 9.5528E-10 iterations 1<br>
-->Test for matrix 168<br>
Norm of error 9.4945E-10 iterations 1<br>
-->Test for matrix 169<br>
Norm of error 6.4279E-10 iterations 1<br>
-->Test for matrix 170<br>
Norm of error 7.4633E-10 iterations 1<br>
-->Test for matrix 171<br>
Norm of error 7.4863E-10 iterations 1<br>
-->Test for matrix 172<br>
Norm of error 8.9701E-10 iterations 1<br>
<br>
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.<br>
<br>
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<br>
<br>
Norm of error 3.7017E-11 iterations 1<br>
-->Test for matrix 168<br>
Norm of error 3.6420E-11 iterations 1<br>
-->Test for matrix 169<br>
Norm of error 3.7184E-11 iterations 1<br>
-->Test for matrix 170<br>
Norm of error 3.6847E-11 iterations 1<br>
-->Test for matrix 171<br>
Norm of error 3.7883E-11 iterations 1<br>
-->Test for matrix 172<br>
Norm of error 3.8805E-11 iterations 1<br>
<br>
Thanks very much,<br>
<br>
Danyang<br>
<br>
<div class="moz-cite-prefix">On 15-12-03 01:59 PM, Hong wrote:<br>
</div>
<blockquote
cite="mid:CAGCphBvdEmCRdC5u1bETyMyZ5gb1GHy30jEG2F=F-KXFhd67pw@mail.gmail.com"
type="cite">
<div dir="ltr">
<div class="gmail_extra">
<div class="gmail_quote">Danyang :</div>
<div class="gmail_quote">Further testing a_flow_check_168.bin,</div>
<div class="gmail_quote">
<div class="gmail_quote">./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</div>
<div class="gmail_quote"> Recip. condition number =
1.610480e-12</div>
<div class="gmail_quote"> 0 KSP preconditioned resid norm
6.873340313547e+09 true resid norm 7.295020990196e+03
||r(i)||/||b|| 1.000000000000e+00</div>
<div class="gmail_quote"> 1 KSP preconditioned resid norm
2.051833296449e-02 true resid norm 2.976859070118e-02
||r(i)||/||b|| 4.080672384793e-06</div>
<div class="gmail_quote">Number of iterations = 1</div>
<div class="gmail_quote">Residual norm 0.0297686</div>
<div class="gmail_quote"><br>
</div>
<div class="gmail_quote">condition number of this matrix =
1/1.610480e-12 = 1.e+12,</div>
<div class="gmail_quote">i.e., this matrix is
ill-conditioned. </div>
<div class="gmail_quote"><br>
</div>
<div class="gmail_quote">Hong</div>
<div class="gmail_quote"><br>
</div>
<div class="gmail_quote"><br>
</div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
<div text="#000000" bgcolor="#FFFFFF"> Hi Hong,<br>
<br>
The binary format of matrix, rhs and solution can be
downloaded via the link below.<br>
<br>
<a moz-do-not-send="true"
href="https://www.dropbox.com/s/cl3gfi0s0kjlktf/matrix_and_rhs_bin.tar.gz?dl=0"
target="_blank">https://www.dropbox.com/s/cl3gfi0s0kjlktf/matrix_and_rhs_bin.tar.gz?dl=0</a><br>
<br>
Thanks,<br>
<br>
Danyang
<div>
<div class="h5"><br>
<br>
On 15-12-03 10:50 AM, Hong wrote:<br>
<blockquote type="cite">
<div dir="ltr">
<div class="gmail_extra">
<div class="gmail_quote">Danyang:<br>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
<div text="#000000" bgcolor="#FFFFFF"><br>
<br>
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. <br>
<br>
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. <br>
<u><a moz-do-not-send="true"
href="https://www.dropbox.com/s/rr8ueysgflmxs7h/results-check.tar.gz?dl=0"
target="_blank">https://www.dropbox.com/s/rr8ueysgflmxs7h/results-check.tar.gz?dl=0</a></u></div>
</blockquote>
<div><br>
</div>
<div>Can you send us matrix in petsc binary
format?</div>
<div><br>
</div>
<div>e.g., call MatView(M,
PETSC_VIEWER_BINARY_(PETSC_COMM_WORLD))</div>
<div>or '-ksp_view_mat binary'</div>
<div><br>
</div>
<div>Hong</div>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
<div text="#000000" bgcolor="#FFFFFF"><br>
<br>
Below is a summary of the norm from the
three solvers at timestep 29, newton
iteration 1 to 5.<br>
<br>
Timestep 29<br>
Norm of residual seq 1.661321e-09,
superlu 1.657103e+04, mumps 3.731225e-11
<br>
Norm of residual seq 1.753079e-09,
superlu 6.675467e+02, mumps 1.509919e-13
<br>
Norm of residual seq 4.914971e-10,
superlu 1.236362e-01, mumps 2.139303e-17
<br>
Norm of residual seq 3.532769e-10,
superlu 1.304670e-04, mumps 5.387000e-20
<br>
Norm of residual seq 3.885629e-10,
superlu 2.754876e-07, mumps 4.108675e-21
<br>
<br>
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.<br>
<br>
Please let me know if I did not write
down the problem clearly.<br>
<br>
Thanks,<br>
<br>
Danyang<br>
<br>
<br>
<br>
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