From: Nachiket Gokhale <gokhalen@bu...>  20051221 18:52:25

On Wed, 20051221 at 12:38 0600, Roy Stogner wrote: > On Wed, 21 Dec 2005, li pan wrote: > > > I used Newton iteration to solve a nonlinear elastic > > problem. This method is embedded in a Newmark implicit > > time integration. At the first several timestep the > > Newton iteration convergenced very well (10 steps). > > Did you see quadratic convergence? I agree with everything that Roy said. If it is not too much trouble, could you post the constitutive relations that you are using?. That is, (strain energy function (W), the second PiolaKirchhoff tensor (S), and the material tangent modulus (C_{IJKL}). I ask this just to make sure that you are assembling the right consistent tangent matrix. Nachiket. > The first thing you ought to check > if Newton's method is behaving oddly is whether you get quadratic > convergence as you approach the root  if not, then (assuming your > linear solves are accurate enough) your Jacobian (i.e. your system > matrix, not the geometric Jacobians) is probably inconsistent with > your residual function. If that happens, your iteration can still > converge, but the region of convergence may be smaller. > > Other possible problems: > > You may be starting from a bad initial guess. This has happened to me > before, when I left junk in a solution vector. Depending on whether > you're solving for the next timestep's solution or for the > delta_solution, a relatively safe initial guess might be the previous > timestep's solution or zero. > > The nonlinearities in your problem may be so bad that the region of > covnergence is too small for you to hit with your initial guess. In > that case you'll want to use a slower but safer method (successive > approximation, perhaps, or continuation) to get close to the root > followed by Newton to eliminate the last of your error. > > > The error could be numerical calculation of inversing matrix, > > because I used simple Gauss elimination. I will apply the method of > > Petsc. > > We've had some problems before with LASPACK not converging, but Gauss > elimination isn't one of them  I often switch to complete LU > factorization as a preconditioner when I'm trying to make sure that > the linear solver isn't causing me problems. Gauss is bad because > it's slow, not because it's inaccurate. >  > Roy Stogner > > >  > This SF.net email is sponsored by: Splunk Inc. Do you grep through log files > for problems? Stop! Download the new AJAX search engine that makes > searching your log files as easy as surfing the web. DOWNLOAD SPLUNK! > http://ads.osdn.com/?ad_id=7637&alloc_id=16865&op=click > _______________________________________________ > Libmeshusers mailing list > Libmeshusers@... > https://lists.sourceforge.net/lists/listinfo/libmeshusers  