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Hello,<br>
<br>
I have an application built on top of the Moose framework, and I'm
trying to debug a solve that is not converging. My linear solve
converges very nicely. However, my non-linear solve does not, and
the problem appears to be in the line search. Reading the PetSc FAQ,
I see that the most common cause of poor line searches are bad
Jacobians. However, I'm using a finite-differenced Jacobian; if I
run -snes_type=test, I get "norm of matrix ratios" < 1e-15. Thus
in this case the Jacobian should be accurate. I'm wondering then if
my problem might be these (taken from the FAQ page):<br>
<br>
<ul>
<li> The matrix is very ill-conditioned. Check the <a
href="http://www.mcs.anl.gov/petsc/documentation/faq.html#conditionnumber">condition
number</a>.
<ul>
<li> Try to improve it by choosing the relative scaling of
components/boundary conditions.</li>
<li>Try <code>-ksp_diagonal_scale -ksp_diagonal_scale_fix</code>.</li>
<li>Perhaps change the formulation of the problem to produce
more friendly algebraic equations.</li>
</ul>
</li>
<li> The matrix is nonlinear (e.g. evaluated using finite
differencing of a nonlinear function). Try different
differencing parameters, <code>./configure
--with-precision=__float128 --download-f2cblaslapack</code>,
check if it converges in "easier" parameter regimes. </li>
</ul>
I'm almost ashamed to share my condition number because I'm sure it
must be absurdly high. Without applying -ksp_diagonal_scale and
-ksp_diagonal_scale_fix, the condition number is around 1e25. When I
do apply those two parameters, the condition number is reduced to
1e17. Even after scaling all my variable residuals so that they were
all on the order of unity (a suggestion on the Moose list), I still
have a condition number of 1e12. I have no experience with condition
numbers, but knowing that perfect condition number is unity, 1e12
seems unacceptable. What's an acceptable upper limit on the
condition number? Is it problem dependent? Having already tried
scaling the individual variable residuals, I'm not exactly sure what
my next method would be for trying to reduce the condition number.<br>
<br>
I definitely have a nonlinear problem. Could I be having problems
because I'm finite differencing non-linear residuals to form my
Jacobian? I can see about using a different differencing parameter.
I'm also going to consider trying quad precision. However, my
hypothesis is that my condition number is the fundamental problem.
Is that a reasonable hypothesis?<br>
<br>
If it's useful, below is console output with -pc_type=svd<br>
<br>
<blockquote>Time Step 1, time = 1e-10<br>
dt = 1e-10<br>
|residual|_2 of individual variables:<br>
potential: 8.12402e+07<br>
potentialliq: 0.000819748<br>
em: 49.206<br>
emliq: 3.08187e-11<br>
Arp: 2375.94<br>
<br>
0 Nonlinear |R| = 8.124020e+07<br>
SVD: condition number 1.457087640207e+12, 0 of 851 singular
values are (nearly) zero<br>
SVD: smallest singular values: 5.637144317564e-09
9.345415388433e-08 4.106132915572e-05 1.017339655185e-04
1.147649477723e-04<br>
SVD: largest singular values : 1.498505466947e+03
1.577560767570e+03 1.719172328193e+03 2.344218235296e+03
8.213813311188e+03<br>
0 KSP unpreconditioned resid norm 3.185019606208e+05 true
resid norm 3.185019606208e+05 ||r(i)||/||b|| 1.000000000000e+00<br>
1 KSP unpreconditioned resid norm 6.382886902896e-07 true
resid norm 6.382761808414e-07 ||r(i)||/||b|| 2.003994511046e-12<br>
Linear solve converged due to CONVERGED_RTOL iterations 1<br>
Line search: Using full step: fnorm 8.124020470169e+07 gnorm
1.097605946684e+01<br>
|residual|_2 of individual variables:<br>
potential: 8.60047<br>
potentialliq: 0.335436<br>
em: 2.26472<br>
emliq: 0.642578<br>
Arp: 6.39151<br>
<br>
1 Nonlinear |R| = 1.097606e+01<br>
SVD: condition number 1.457473763066e+12, 0 of 851 singular
values are (nearly) zero<br>
SVD: smallest singular values: 5.637185516434e-09
9.347128557672e-08 1.017339655587e-04 1.146760266781e-04
4.064422034774e-04<br>
SVD: largest singular values : 1.498505466944e+03
1.577544976882e+03 1.718956369043e+03 2.343692402876e+03
8.216049987736e+03<br>
0 KSP unpreconditioned resid norm 2.653715381459e+01 true
resid norm 2.653715381459e+01 ||r(i)||/||b|| 1.000000000000e+00<br>
1 KSP unpreconditioned resid norm 6.031179341420e-05 true
resid norm 6.031183387732e-05 ||r(i)||/||b|| 2.272731819648e-06<br>
Linear solve converged due to CONVERGED_RTOL iterations 1<br>
Line search: gnorm after quadratic fit 2.485190757827e+11<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 2.632996340352e+10 lambda=5.0000000000000003e-02<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 4.290675557416e+09 lambda=2.5000000000000001e-02<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 4.332980055153e+08 lambda=1.2500000000000001e-02<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.677118626669e+07 lambda=6.2500000000000003e-03<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.024469780306e+05 lambda=3.1250000000000002e-03<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 7.011543252988e+03 lambda=1.5625000000000001e-03<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.750171277470e+03 lambda=7.8125000000000004e-04<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 3.486970625406e+02 lambda=3.4794637057251714e-04<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 7.830624839582e+01 lambda=1.5977866967992950e-04<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 2.147529381328e+01 lambda=6.8049915671999093e-05<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.138950943123e+01 lambda=1.7575203052774536e-05<br>
Line search: Cubically determined step, current gnorm
1.095195976135e+01 lambda=1.7575203052774537e-06<br>
|residual|_2 of individual variables:<br>
potential: 8.59984<br>
potentialliq: 0.395753<br>
em: 2.26492<br>
emliq: 0.642578<br>
Arp: 6.34735<br>
<br>
2 Nonlinear |R| = 1.095196e+01<br>
SVD: condition number 1.457459214030e+12, 0 of 851 singular
values are (nearly) zero<br>
SVD: smallest singular values: 5.637295371943e-09
9.347057884198e-08 1.017339655949e-04 1.146738253493e-04
4.064421554132e-04<br>
SVD: largest singular values : 1.498505466946e+03
1.577543742603e+03 1.718948052797e+03 2.343672206864e+03
8.216128082047e+03<br>
0 KSP unpreconditioned resid norm 2.653244141805e+01 true
resid norm 2.653244141805e+01 ||r(i)||/||b|| 1.000000000000e+00<br>
1 KSP unpreconditioned resid norm 4.480869560737e-05 true
resid norm 4.480686665183e-05 ||r(i)||/||b|| 1.688757771886e-06<br>
Linear solve converged due to CONVERGED_RTOL iterations 1<br>
Line search: gnorm after quadratic fit 2.481752147885e+11<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 2.631959989642e+10 lambda=5.0000000000000003e-02<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 4.289110800463e+09 lambda=2.5000000000000001e-02<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 4.332043942482e+08 lambda=1.2500000000000001e-02<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.677933337886e+07 lambda=6.2500000000000003e-03<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.027980597206e+05 lambda=3.1250000000000002e-03<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 7.054113639063e+03 lambda=1.5625000000000001e-03<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.771258630210e+03 lambda=7.8125000000000004e-04<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 3.517070127496e+02 lambda=3.4519087020105563e-04<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 7.844350966118e+01 lambda=1.5664532891249369e-04<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 2.114833995101e+01 lambda=6.5367917100814859e-05<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.144636844292e+01 lambda=1.6044984646715980e-05<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.095640770627e+01 lambda=1.6044984646715980e-06<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.095196729511e+01 lambda=1.6044984646715980e-07<br>
Line search: Cubically determined step, current gnorm
1.095195451041e+01 lambda=2.3994454223607641e-08<br>
|residual|_2 of individual variables:<br>
potential: 8.59983<br>
potentialliq: 0.396107<br>
em: 2.26492<br>
emliq: 0.642578<br>
Arp: 6.34733<br>
<br>
3 Nonlinear |R| = 1.095195e+01<br>
SVD: condition number 1.457474387942e+12, 0 of 851 singular
values are (nearly) zero<br>
SVD: smallest singular values: 5.637237413167e-09
9.347057670885e-08 1.017339654798e-04 1.146737961973e-04
4.064420550524e-04<br>
SVD: largest singular values : 1.498505466946e+03
1.577543716995e+03 1.718947893048e+03 2.343671853830e+03
8.216129148438e+03<br>
0 KSP unpreconditioned resid norm 2.653237816527e+01 true
resid norm 2.653237816527e+01 ||r(i)||/||b|| 1.000000000000e+00<br>
1 KSP unpreconditioned resid norm 8.525213442515e-05 true
resid norm 8.527696332776e-05 ||r(i)||/||b|| 3.214071607022e-06<br>
Linear solve converged due to CONVERGED_RTOL iterations 1<br>
Line search: gnorm after quadratic fit 2.481576195523e+11<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 2.632005412624e+10 lambda=5.0000000000000003e-02<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 4.289212002697e+09 lambda=2.5000000000000001e-02<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 4.332196637845e+08 lambda=1.2500000000000001e-02<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.678040222943e+07 lambda=6.2500000000000003e-03<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.027868984884e+05 lambda=3.1250000000000002e-03<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 7.010733464460e+03 lambda=1.5625000000000001e-03<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.751519860441e+03 lambda=7.8125000000000004e-04<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 3.497889916171e+02 lambda=3.4753778542938795e-04<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 7.932631084466e+01 lambda=1.5879606741873878e-04<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 2.194608479634e+01 lambda=6.5716583192912669e-05<br>
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.117190149691e+01 lambda=1.1541218569257328e-05<br>
Line search: Cubically determined step, current gnorm
1.093879875464e+01 lambda=1.1541218569257329e-06<br>
|residual|_2 of individual variables:<br>
potential: 8.59942<br>
potentialliq: 0.403326<br>
em: 2.26505<br>
emliq: 0.714844<br>
Arp: 6.3169<br>
<br>
4 Nonlinear |R| = 1.093880e+01<br>
</blockquote>
<br>
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