# [petsc-users] A number of questions about DMDA with SNES and Quasi-Newton methods

zakaryah . zakaryah at gmail.com
Tue Aug 29 23:21:21 CDT 2017

```​OK, this is very helpful (and not totally clear from the "Why is Newton's
method not converging" FAQ at this address:
https://scicomp.stackexchange.com/questions/30/why-is-newtons-method-not-converging.
Here's the output, using the intermediate grid and the options -snes_type
newtonls -snes_monitor -ksp_monitor -ksp_monitor_true_residual
-ksp_converged_reason -snes_converged_reason -pc_type lu
-snes_linesearch_monitor:​

0 SNES Function norm 1.370293318432e+04

0 KSP Residual norm 7.457516441709e+02

0 KSP preconditioned resid norm 7.457516441709e+02 true resid norm
1.370293318432e+04 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 1.244742959480e-10

1 KSP preconditioned resid norm 1.244742959480e-10 true resid norm
9.866304569403e-09 ||r(i)||/||b|| 7.200140609815e-13

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: gnorm after quadratic fit 6.541326653047e+05

Line search: Cubic step no good, shrinking lambda, current gnorm
8.963755251044e+04 lambda=5.0000000000000003e-02

Line search: Cubic step no good, shrinking lambda, current gnorm
1.788913078169e+04 lambda=2.5000000000000001e-02

Line search: Cubically determined step, current gnorm
1.340565818376e+04 lambda=1.2500000000000001e-02

1 SNES Function norm 1.340565818376e+04

0 KSP Residual norm 3.837938728414e+02

0 KSP preconditioned resid norm 3.837938728414e+02 true resid norm
1.340565818376e+04 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 3.935624425879e-11

1 KSP preconditioned resid norm 3.935624425879e-11 true resid norm
4.012917478400e-09 ||r(i)||/||b|| 2.993450544086e-13

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: gnorm after quadratic fit 7.752009107979e+05

Line search: Cubic step no good, shrinking lambda, current gnorm
9.942192482364e+04 lambda=5.0000000000000003e-02

Line search: Cubic step no good, shrinking lambda, current gnorm
1.724069009956e+04 lambda=2.5000000000000001e-02

Line search: Cubically determined step, current gnorm
1.272263847462e+04 lambda=1.2500000000000001e-02

2 SNES Function norm 1.272263847462e+04

0 KSP Residual norm 8.610741245938e+01

0 KSP preconditioned resid norm 8.610741245938e+01 true resid norm
1.272263847462e+04 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 3.953708398506e-12

1 KSP preconditioned resid norm 3.953708398506e-12 true resid norm
1.259105691297e-09 ||r(i)||/||b|| 9.896576828850e-14

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: gnorm after quadratic fit 1.126216236986e+04

lambda=1.0000000000000001e-01

3 SNES Function norm 1.126216236986e+04

0 KSP Residual norm 6.100581225849e+01

0 KSP preconditioned resid norm 6.100581225849e+01 true resid norm
1.126216236986e+04 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 3.714526144776e-12

1 KSP preconditioned resid norm 3.714526144776e-12 true resid norm
1.150524854441e-09 ||r(i)||/||b|| 1.021584325156e-13

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: gnorm after quadratic fit 9.992994468502e+03

lambda=1.0000000000000001e-01

4 SNES Function norm 9.992994468502e+03

0 KSP Residual norm 5.452156705070e+01

0 KSP preconditioned resid norm 5.452156705070e+01 true resid norm
9.992994468502e+03 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 2.345517221383e-12

1 KSP preconditioned resid norm 2.345517221383e-12 true resid norm
6.645776037775e-10 ||r(i)||/||b|| 6.650435020976e-14

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: gnorm after quadratic fit 8.954956134809e+03

lambda=1.0000000000000001e-01

5 SNES Function norm 8.954956134809e+03

0 KSP Residual norm 1.869342714623e+02

0 KSP preconditioned resid norm 1.869342714623e+02 true resid norm
8.954956134809e+03 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 6.952075013553e-12

1 KSP preconditioned resid norm 6.952075013553e-12 true resid norm
2.332836306210e-09 ||r(i)||/||b|| 2.605078429298e-13

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: gnorm after quadratic fit 9.366608314830e+04

Line search: Cubic step no good, shrinking lambda, current gnorm
1.702858832608e+04 lambda=5.0000000000000003e-02

Line search: Cubic step no good, shrinking lambda, current gnorm
9.141708166107e+03 lambda=2.5000000000000001e-02

Line search: Cubically determined step, current gnorm
8.847002105227e+03 lambda=1.2500000000000001e-02

6 SNES Function norm 8.847002105227e+03

0 KSP Residual norm 4.136774315749e+01

0 KSP preconditioned resid norm 4.136774315749e+01 true resid norm
8.847002105227e+03 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 2.340140336645e-12

1 KSP preconditioned resid norm 2.340140336645e-12 true resid norm
6.952836046439e-10 ||r(i)||/||b|| 7.858974106416e-14

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: gnorm after quadratic fit 7.928904942575e+03

lambda=1.0000000000000001e-01

7 SNES Function norm 7.928904942575e+03

0 KSP Residual norm 9.421715655897e+01

0 KSP preconditioned resid norm 9.421715655897e+01 true resid norm
7.928904942575e+03 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 5.662350656880e-12

1 KSP preconditioned resid norm 5.662350656880e-12 true resid norm
1.323447274435e-09 ||r(i)||/||b|| 1.669142566370e-13

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: gnorm after quadratic fit 4.679455846837e+04

Line search: Cubic step no good, shrinking lambda, current gnorm
1.024301325332e+04 lambda=5.0000000000000003e-02

Line search: Cubically determined step, current gnorm
7.882357228991e+03 lambda=2.5000000000000001e-02

8 SNES Function norm 7.882357228991e+03

0 KSP Residual norm 3.101373992455e+01

0 KSP preconditioned resid norm 3.101373992455e+01 true resid norm
7.882357228991e+03 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 1.176793992597e-12

1 KSP preconditioned resid norm 1.176793992597e-12 true resid norm
4.948698048884e-10 ||r(i)||/||b|| 6.278195602050e-14

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: Using full step: fnorm 7.882357228991e+03 gnorm
5.263287196819e+03

9 SNES Function norm 5.263287196819e+03

0 KSP Residual norm 8.541947236232e+00

0 KSP preconditioned resid norm 8.541947236232e+00 true resid norm
5.263287196819e+03 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 1.741221887649e-12

1 KSP preconditioned resid norm 1.741221887649e-12 true resid norm
9.735248249306e-10 ||r(i)||/||b|| 1.849651726242e-13

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: gnorm after quadratic fit 4.836381737060e+03

lambda=1.0000000000000001e-01

10 SNES Function norm 4.836381737060e+03

0 KSP Residual norm 1.926518638579e+01

0 KSP preconditioned resid norm 1.926518638579e+01 true resid norm
4.836381737060e+03 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 1.278653333162e-11

1 KSP preconditioned resid norm 1.278653333162e-11 true resid norm
1.211659620475e-08 ||r(i)||/||b|| 2.505301868938e-12

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: gnorm after quadratic fit 4.550187794983e+03

lambda=1.0000000000000001e-01

11 SNES Function norm 4.550187794983e+03

0 KSP Residual norm 5.492305435155e+00

0 KSP preconditioned resid norm 5.492305435155e+00 true resid norm
4.550187794983e+03 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 3.941029797735e-13

1 KSP preconditioned resid norm 3.941029797735e-13 true resid norm
2.123615113926e-10 ||r(i)||/||b|| 4.667093336823e-14

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: gnorm after quadratic fit 3.210238905481e+03

lambda=4.4544417493894700e-01

12 SNES Function norm 3.210238905481e+03

0 KSP Residual norm 7.578202966222e+00

0 KSP preconditioned resid norm 7.578202966222e+00 true resid norm
3.210238905481e+03 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 3.800509410151e-12

1 KSP preconditioned resid norm 3.800509410151e-12 true resid norm
3.408323024026e-09 ||r(i)||/||b|| 1.061703855812e-12

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: gnorm after quadratic fit 2.924559961092e+03

lambda=1.0000000000000001e-01

13 SNES Function norm 2.924559961092e+03

0 KSP Residual norm 5.076980628354e+00

0 KSP preconditioned resid norm 5.076980628354e+00 true resid norm
2.924559961092e+03 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 1.468522311180e-13

1 KSP preconditioned resid norm 1.468522311180e-13 true resid norm
9.059064389128e-11 ||r(i)||/||b|| 3.097582032733e-14

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: gnorm after quadratic fit 2.389633730237e+03

lambda=2.1257217805235396e-01

14 SNES Function norm 2.389633730237e+03

0 KSP Residual norm 5.166598232781e+00

0 KSP preconditioned resid norm 5.166598232781e+00 true resid norm
2.389633730237e+03 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 2.249406847764e-13

1 KSP preconditioned resid norm 2.249406847764e-13 true resid norm
4.780078098549e-11 ||r(i)||/||b|| 2.000339231098e-14

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: gnorm after quadratic fit 2.093485770827e+03

lambda=1.5993239844479040e-01

15 SNES Function norm 2.093485770827e+03

0 KSP Residual norm 8.445727235216e+00

0 KSP preconditioned resid norm 8.445727235216e+00 true resid norm
2.093485770827e+03 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 1.917214128329e-13

1 KSP preconditioned resid norm 1.917214128329e-13 true resid norm
1.577089911021e-10 ||r(i)||/||b|| 7.533320421842e-14

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: gnorm after quadratic fit 1.967949189728e+03

lambda=1.0000000000000001e-01

16 SNES Function norm 1.967949189728e+03

0 KSP Residual norm 2.548962277036e+01

0 KSP preconditioned resid norm 2.548962277036e+01 true resid norm
1.967949189728e+03 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 4.393171339150e-12

1 KSP preconditioned resid norm 4.393171339150e-12 true resid norm
6.268541493766e-10 ||r(i)||/||b|| 3.185316738097e-13

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: gnorm after quadratic fit 3.445905389608e+03

Line search: Cubic step no good, shrinking lambda, current gnorm
2.129006719528e+03 lambda=5.0000000000000003e-02

Line search: Cubic step no good, shrinking lambda, current gnorm
1.969320033677e+03 lambda=1.8287150237426619e-02

Line search: Cubically determined step, current gnorm
1.963119931876e+03 lambda=8.7403113229804347e-03

17 SNES Function norm 1.963119931876e+03

0 KSP Residual norm 1.189834379636e+02

0 KSP preconditioned resid norm 1.189834379636e+02 true resid norm
1.963119931876e+03 ||r(i)||/||b|| 1.000000000000e+00

1 KSP Residual norm 3.213937715681e-11

1 KSP preconditioned resid norm 3.213937715681e-11 true resid norm
8.137767291258e-08 ||r(i)||/||b|| 4.145323553147e-11

Linear solve converged due to CONVERGED_RTOL iterations 1

Line search: gnorm after quadratic fit 1.329932469429e+05

Line search: Cubic step no good, shrinking lambda, current gnorm
2.079971894561e+04 lambda=5.0000000000000003e-02

Line search: Cubic step no good, shrinking lambda, current gnorm
4.672632539568e+03 lambda=2.5000000000000001e-02

Line search: Cubic step no good, shrinking lambda, current gnorm
2.337320012333e+03 lambda=1.2500000000000001e-02

Line search: Cubic step no good, shrinking lambda, current gnorm
1.989655494060e+03 lambda=3.7908486903933652e-03

Line search: Cubic step no good, shrinking lambda, current gnorm
1.964061592872e+03 lambda=4.3979444116724767e-04

Line search: Cubic step no good, shrinking lambda, current gnorm
1.963285343925e+03 lambda=9.8760011176842895e-05

Line search: Cubic step no good, shrinking lambda, current gnorm
1.963156689078e+03 lambda=2.3385231527184855e-05

Line search: Cubic step no good, shrinking lambda, current gnorm
1.963128672876e+03 lambda=5.6482781216089357e-06

Line search: Cubic step no good, shrinking lambda, current gnorm
1.963122042807e+03 lambda=1.3692247365910180e-06

Line search: Cubic step no good, shrinking lambda, current gnorm
1.963120443658e+03 lambda=3.3226543340386796e-07

Line search: Cubic step no good, shrinking lambda, current gnorm
1.963120056069e+03 lambda=8.0648305027594934e-08

Line search: Cubic step no good, shrinking lambda, current gnorm
1.963119962021e+03 lambda=1.9576315045380916e-08

Line search: Cubic step no good, shrinking lambda, current gnorm
1.963119939193e+03 lambda=4.7519586695347587e-09

Line search: Cubic step no good, shrinking lambda, current gnorm
1.963119933652e+03 lambda=1.1534950726729967e-09

Line search: Cubic step no good, shrinking lambda, current gnorm
1.963119932307e+03 lambda=2.8000026447574534e-10

Line search: Cubic step no good, shrinking lambda, current gnorm
1.963119931981e+03 lambda=6.7967445495582766e-11

Line search: Cubic step no good, shrinking lambda, current gnorm
1.963119931902e+03 lambda=1.6498100190994443e-11

Line search: Cubic step no good, shrinking lambda, current gnorm
1.963119931882e+03 lambda=4.0046243381676681e-12

Line search: Cubic step no good, shrinking lambda, current gnorm
1.963119931878e+03 lambda=9.7209812173761137e-13

Line search: unable to find good step length! After 19 tries

Line search: fnorm=1.9631199318761367e+03,
gnorm=1.9631199318776339e+03, ynorm=1.1898343796305618e+02,
minlambda=9.9999999999999998e-13, lambda=9.7209812173761137e-13, initial
slope=-3.8538398668951751e+06

Nonlinear solve did not converge due to DIVERGED_LINE_SEARCH iterations 17
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