Hello,
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):
* The matrix is very ill-conditioned. Check the condition number
<http://www.mcs.anl.gov/petsc/documentation/faq.html#conditionnumber>.
o Try to improve it by choosing the relative scaling of
components/boundary conditions.
o Try |-ksp_diagonal_scale -ksp_diagonal_scale_fix|.
o Perhaps change the formulation of the problem to produce more
friendly algebraic equations.
* The matrix is nonlinear (e.g. evaluated using finite differencing of
a nonlinear function). Try different differencing parameters,
|./configure --with-precision=__float128 --download-f2cblaslapack|,
check if it converges in "easier" parameter regimes.
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.
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?
If it's useful, below is console output with -pc_type=svd
Time Step 1, time = 1e-10
dt = 1e-10
|residual|_2 of individual variables:
potential: 8.12402e+07
potentialliq: 0.000819748
em: 49.206
emliq: 3.08187e-11
Arp: 2375.94
0 Nonlinear |R| = 8.124020e+07
SVD: condition number 1.457087640207e+12, 0 of 851 singular
values are (nearly) zero
SVD: smallest singular values: 5.637144317564e-09
9.345415388433e-08 4.106132915572e-05 1.017339655185e-04
1.147649477723e-04
SVD: largest singular values : 1.498505466947e+03
1.577560767570e+03 1.719172328193e+03 2.344218235296e+03
8.213813311188e+03
0 KSP unpreconditioned resid norm 3.185019606208e+05 true resid
norm 3.185019606208e+05 ||r(i)||/||b|| 1.000000000000e+00
1 KSP unpreconditioned resid norm 6.382886902896e-07 true resid
norm 6.382761808414e-07 ||r(i)||/||b|| 2.003994511046e-12
Linear solve converged due to CONVERGED_RTOL iterations 1
Line search: Using full step: fnorm 8.124020470169e+07 gnorm
1.097605946684e+01
|residual|_2 of individual variables:
potential: 8.60047
potentialliq: 0.335436
em: 2.26472
emliq: 0.642578
Arp: 6.39151
1 Nonlinear |R| = 1.097606e+01
SVD: condition number 1.457473763066e+12, 0 of 851 singular
values are (nearly) zero
SVD: smallest singular values: 5.637185516434e-09
9.347128557672e-08 1.017339655587e-04 1.146760266781e-04
4.064422034774e-04
SVD: largest singular values : 1.498505466944e+03
1.577544976882e+03 1.718956369043e+03 2.343692402876e+03
8.216049987736e+03
0 KSP unpreconditioned resid norm 2.653715381459e+01 true resid
norm 2.653715381459e+01 ||r(i)||/||b|| 1.000000000000e+00
1 KSP unpreconditioned resid norm 6.031179341420e-05 true resid
norm 6.031183387732e-05 ||r(i)||/||b|| 2.272731819648e-06
Linear solve converged due to CONVERGED_RTOL iterations 1
Line search: gnorm after quadratic fit 2.485190757827e+11
Line search: Cubic step no good, shrinking lambda, current
gnorm 2.632996340352e+10 lambda=5.0000000000000003e-02
Line search: Cubic step no good, shrinking lambda, current
gnorm 4.290675557416e+09 lambda=2.5000000000000001e-02
Line search: Cubic step no good, shrinking lambda, current
gnorm 4.332980055153e+08 lambda=1.2500000000000001e-02
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.677118626669e+07 lambda=6.2500000000000003e-03
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.024469780306e+05 lambda=3.1250000000000002e-03
Line search: Cubic step no good, shrinking lambda, current
gnorm 7.011543252988e+03 lambda=1.5625000000000001e-03
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.750171277470e+03 lambda=7.8125000000000004e-04
Line search: Cubic step no good, shrinking lambda, current
gnorm 3.486970625406e+02 lambda=3.4794637057251714e-04
Line search: Cubic step no good, shrinking lambda, current
gnorm 7.830624839582e+01 lambda=1.5977866967992950e-04
Line search: Cubic step no good, shrinking lambda, current
gnorm 2.147529381328e+01 lambda=6.8049915671999093e-05
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.138950943123e+01 lambda=1.7575203052774536e-05
Line search: Cubically determined step, current gnorm
1.095195976135e+01 lambda=1.7575203052774537e-06
|residual|_2 of individual variables:
potential: 8.59984
potentialliq: 0.395753
em: 2.26492
emliq: 0.642578
Arp: 6.34735
2 Nonlinear |R| = 1.095196e+01
SVD: condition number 1.457459214030e+12, 0 of 851 singular
values are (nearly) zero
SVD: smallest singular values: 5.637295371943e-09
9.347057884198e-08 1.017339655949e-04 1.146738253493e-04
4.064421554132e-04
SVD: largest singular values : 1.498505466946e+03
1.577543742603e+03 1.718948052797e+03 2.343672206864e+03
8.216128082047e+03
0 KSP unpreconditioned resid norm 2.653244141805e+01 true resid
norm 2.653244141805e+01 ||r(i)||/||b|| 1.000000000000e+00
1 KSP unpreconditioned resid norm 4.480869560737e-05 true resid
norm 4.480686665183e-05 ||r(i)||/||b|| 1.688757771886e-06
Linear solve converged due to CONVERGED_RTOL iterations 1
Line search: gnorm after quadratic fit 2.481752147885e+11
Line search: Cubic step no good, shrinking lambda, current
gnorm 2.631959989642e+10 lambda=5.0000000000000003e-02
Line search: Cubic step no good, shrinking lambda, current
gnorm 4.289110800463e+09 lambda=2.5000000000000001e-02
Line search: Cubic step no good, shrinking lambda, current
gnorm 4.332043942482e+08 lambda=1.2500000000000001e-02
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.677933337886e+07 lambda=6.2500000000000003e-03
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.027980597206e+05 lambda=3.1250000000000002e-03
Line search: Cubic step no good, shrinking lambda, current
gnorm 7.054113639063e+03 lambda=1.5625000000000001e-03
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.771258630210e+03 lambda=7.8125000000000004e-04
Line search: Cubic step no good, shrinking lambda, current
gnorm 3.517070127496e+02 lambda=3.4519087020105563e-04
Line search: Cubic step no good, shrinking lambda, current
gnorm 7.844350966118e+01 lambda=1.5664532891249369e-04
Line search: Cubic step no good, shrinking lambda, current
gnorm 2.114833995101e+01 lambda=6.5367917100814859e-05
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.144636844292e+01 lambda=1.6044984646715980e-05
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.095640770627e+01 lambda=1.6044984646715980e-06
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.095196729511e+01 lambda=1.6044984646715980e-07
Line search: Cubically determined step, current gnorm
1.095195451041e+01 lambda=2.3994454223607641e-08
|residual|_2 of individual variables:
potential: 8.59983
potentialliq: 0.396107
em: 2.26492
emliq: 0.642578
Arp: 6.34733
3 Nonlinear |R| = 1.095195e+01
SVD: condition number 1.457474387942e+12, 0 of 851 singular
values are (nearly) zero
SVD: smallest singular values: 5.637237413167e-09
9.347057670885e-08 1.017339654798e-04 1.146737961973e-04
4.064420550524e-04
SVD: largest singular values : 1.498505466946e+03
1.577543716995e+03 1.718947893048e+03 2.343671853830e+03
8.216129148438e+03
0 KSP unpreconditioned resid norm 2.653237816527e+01 true resid
norm 2.653237816527e+01 ||r(i)||/||b|| 1.000000000000e+00
1 KSP unpreconditioned resid norm 8.525213442515e-05 true resid
norm 8.527696332776e-05 ||r(i)||/||b|| 3.214071607022e-06
Linear solve converged due to CONVERGED_RTOL iterations 1
Line search: gnorm after quadratic fit 2.481576195523e+11
Line search: Cubic step no good, shrinking lambda, current
gnorm 2.632005412624e+10 lambda=5.0000000000000003e-02
Line search: Cubic step no good, shrinking lambda, current
gnorm 4.289212002697e+09 lambda=2.5000000000000001e-02
Line search: Cubic step no good, shrinking lambda, current
gnorm 4.332196637845e+08 lambda=1.2500000000000001e-02
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.678040222943e+07 lambda=6.2500000000000003e-03
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.027868984884e+05 lambda=3.1250000000000002e-03
Line search: Cubic step no good, shrinking lambda, current
gnorm 7.010733464460e+03 lambda=1.5625000000000001e-03
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.751519860441e+03 lambda=7.8125000000000004e-04
Line search: Cubic step no good, shrinking lambda, current
gnorm 3.497889916171e+02 lambda=3.4753778542938795e-04
Line search: Cubic step no good, shrinking lambda, current
gnorm 7.932631084466e+01 lambda=1.5879606741873878e-04
Line search: Cubic step no good, shrinking lambda, current
gnorm 2.194608479634e+01 lambda=6.5716583192912669e-05
Line search: Cubic step no good, shrinking lambda, current
gnorm 1.117190149691e+01 lambda=1.1541218569257328e-05
Line search: Cubically determined step, current gnorm
1.093879875464e+01 lambda=1.1541218569257329e-06
|residual|_2 of individual variables:
potential: 8.59942
potentialliq: 0.403326
em: 2.26505
emliq: 0.714844
Arp: 6.3169
4 Nonlinear |R| = 1.093880e+01
