[petsc-users] When does DIVERGED_LINE_SEARCH Happen?

[Dafang Wang]

Hi Barry,

Thanks for your tips. I have read the webpage you mentioned many times 
before, but still I have been stuck on the line-search problem for weeks.

I cannot guarantee my Jacobian is correct but I believe an incorrect 
Jacobian is very unlikely. My Jacobian-calculation code has been under 
test for a year with both analytical and realistic models, and the 
results have been good until recently when I ran a very realistic 
physical model.

Also, I looked up the implementation of SNESSolve_NEWTONLS() in "ls.c". 
According to the algorithm, when the function "SNESLineSearchApply()" 
does not succeed, one may encounter two possible outcomes: 
CONVERGED_SNORM_RELATIVE (if the search step is too small) or otherwise, 
DIVERGED_LINE_SEARCH. Does this mean that both these two outcomes 
indicate that the line search fails?

I ask this question because my simulation encountered many 
CONVERGED_SNORM_RELATIVE. I treated them as if my nonlinear system 
converged, accepted the nonlinear solution, and then proceeded to the 
next time step of my simulation. Apparently, such practice has worked 
well in most cases, (even when I encountered suspicious 
DIVERGED_LINE_SEARCH behaviors). However, I wonder if there are any 
potential pitfalls in my practice such as missing a nonlinear solve 
divergence and taking a partial solution as the correct solution.

Thank you very much for your time and help.

Best,
Dafang

On 03/15/2014 11:15 AM, Barry Smith wrote:
>     Failed line search are almost always due to an incorrect Jacobian. Please let us know if the suggestions at http://www.mcs.anl.gov/petsc/documentation/faq.html#newton don’t help.
>
>     Barry
>
> On Mar 14, 2014, at 8:57 PM, Dafang Wang <dafang.wang at jhu.edu> wrote:
>
>> Hi,
>>
>> Does anyone know what the error code DIVERGED_LINE_SEARCH means in the SNES nonlinear solve? Or what scenario would lead to this error code?
>>
>> Running a solid mechanics simulation, I found that the occurrence of DIVERGED_LINE_SEARCH was very unpredictable and sensitive to the input values to my nonlinear system, although my system should not be that unstable. As shown by the two examples below, my system diverged in one case and converged in the other, although the input values in these two cases differed by only 1e-4,
>>
>> Moreover, the Newton steps in the two cases were very similar up to NL step 1. Since then, however, Case 1 encountered a line-search divergence whereas Case 2 converged successfully. This is my main confusion. (Note that each residual vector contains 3e04 DOF, so when their L2 norms differ within 1e-4, the two systems should be very close.)
>>
>> My simulation input consists of two scalar values (p1 and p2), each of which acts as a constant pressure boundary condition.
>>
>> Case 1, diverge:
>> p1= -10.190869   p2= -2.367555
>>    NL step  0, |residual|_2 = 1.621402e-02
>>        Line search: Using full step: fnorm 1.621401550027e-02 gnorm 7.022558235262e-05
>>    NL step  1, |residual|_2 = 7.022558e-05
>>        Line search: Using full step: fnorm 7.022558235262e-05 gnorm 1.636418730611e-06
>>    NL step  2, |residual|_2 = 1.636419e-06
>> Nonlinear solve did not converge due to DIVERGED_LINE_SEARCH iterations 2
>> Case 2: converge:
>> p1= -10.190747 p2= -2.367558
>>    NL step  0, |residual|_2 = 1.621380e-02
>>        Line search: Using full step: fnorm 1.621379778276e-02 gnorm 6.976373804153e-05
>>    NL step  1, |residual|_2 = 6.976374e-05
>>        Line search: Using full step: fnorm 6.976373804153e-05 gnorm 4.000992847275e-07
>>    NL step  2, |residual|_2 = 4.000993e-07
>>        Line search: Using full step: fnorm 4.000992847275e-07 gnorm 1.621646014441e-08
>>    NL step  3, |residual|_2 = 1.621646e-08
>> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 3
>>
>> Aside from the input values, the initial solution in both cases may differ very slightly. (Each case is one time step in a time-sequence simulation. The two cases behaved nearly identically up to the last time step before the step shown above, so their initial solutions may differ by a cumulative error but such error should be very small.)  Is it possible that little difference in initial guess leads to different local minimum regions where the line search in Case 1 failed?
>>
>> Any comments will be greatly appreciated.
>>
>> Thanks,
>> Dafang
>> -- 
>> Dafang Wang, Ph.D
>> Postdoctoral Fellow
>> Institute of Computational Medicine
>> Department of Biomedical Engineering
>> Johns Hopkins University
>> Hackerman Hall Room 218
>> Baltimore, MD, 21218

-- 
Dafang Wang, Ph.D
Postdoctoral Fellow
Institute of Computational Medicine
Department of Biomedical Engineering
Johns Hopkins University
Hackerman Hall Room 218
Baltimore, MD, 21218