Hi
I have been using the trust region method as implemented in dtrnlspbc to solve a system of non-linear equations but now I am stuck. The solver stops after iteration 1 with stopping criteria 2 which means as I understand it that the trust region is too small. The residual is close to the initial residual (0.65 compared to 0.70) and this happens independent of the initial size of the trust region, rs, the stopping criteria eps and the initial guess of the solution vector which I believe is fairly good.
The problem I am trying to solve is related to electronic structures and has approximately 150 unknowns, n, and n+3 equations. It can be described as a set of 10 simple conservation laws each for something behaving like flows within and between 15 (can vary) levels plus three global conservation laws. The solution is expected to be nearly, but not quite, degenerate between the different levels. Flow 1 at level A is expected to be similar to flow 1 at level B, but different from flow 2 at level A and so on. The flows are restricted to be between 0.0 and 1.0 (normalized).
I am using the same method to solve a similar but smaller local problem in the code without any problem and I have double and triple checked the external subroutine calculating the value fcn. Could it be that my problem is just too ill conditioned to be solvable (hard to tell without the code, I know, but it is very difficult to extract just a small piece of code showing the problem) or is my starting guess too bad? Or is this what I should expect from the solver?
Any and all help is appreciated!
Per