[petsc-users] When does DIVERGED_LINE_SEARCH Happen?

[Dafang Wang]

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
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