[Libmesh-users] Concerns in Solving a Nonlinear System Repeatedly for Multiple Times

[Dafang W. <daf...@jh...>]

Hi,

My question concerns repeated solving a nonlinear system for multiple times. I am trying 
to fit some input parameters for an inherently unstable nonlinear implicit system. Fewer 
than 5 parameters need fitting, so it is a small parameter-fitting problem. To fulfill 
this goal, I am solving the nonlinear system repeatedly as follows:

NonlinearImplicitSystem system;
Initialize the input parameters to the object "system";
Repeat
     Update the input parameters to "system"; (The update does NOT depend on the system's 
current solution.)
     system.solve();
Until system.solution() meets the defined goal

Here is my problem: because the system is by nature unstable, system.solve() sometimes did 
not converge; then in the next round of solve, I obtained a very odd solution even though 
system.solve() converged well.  My question is whether a failed nonlinear solve will leave 
some bad intermediate values in the NonlinearSystem object and thereby influence its next 
solve? For example, I think that the system.solution will be used as the initial guess in 
the next solve; then will a partial solution be bad enough to crash the system?

In my problem,  the input parameters were updated independently from system.solution. Also 
my update change was small, thus unlikely responsible for the failure of the next solve. 
The remaining uncertainty is the NonlinearSystem's partial solution or its internal state 
variables.

Any comments will be greatly appreciated.

Best,
Dafang



-- 
Dafang Wang, Ph.D.
Postdoctoral Fellow
Institute of Computational Medicine
Hackerman Hall, Room 218
Johns Hopkins University, Baltimore, 21218
http://lagniappe.icm.jhu.edu/~dwang/