Tom,
> I would like your opinion and advice on solving indefinite problems with > dealii. Does dealii has any solver classes (iterative) to deal with these > problems ? Yes, plenty in fact. There are BiCGStab, GMRES, Minres, to list just a couple. > Does the adaptive multigrid techniques be a good strategy; as > presently I use Two level Optimized Schwarz methods, which seems to be > working > fine for my indefinite Maxwell's equations. Have anyone solved any indefinite > problems iteratively with dealii before ? Yes, many of the tutorial programs solve indefinite problems. Take a look, for example, at the advection problems, or the saddle point problems, or the coupled multiphysics problems, all of which have indefinite matrices. > Also, I'm hoping to try implement the aforesaid ORAS schemes with dealii data > structures. But this needs some time as I'm a Mechanical Engineer, and also > the mathematics of these methods involving restriction and partition of unity > from geometric partitioning or domain decomposition seems quite different > from > the MPI parallelizing strategy (which I guess is algebraic) of dealii. Please > correct me if have some information stated wrongly. Some previous work where > an iterative solver (similar to the one I have stated) was cooked with the > solver classes of dealii also would be a perfect starting point. > see the method here: https://arxiv.org/abs/1705.08138 > <https://nam01.safelinks.protection.outlook.com/?url=https%3A%2F%2Farxiv.org%2Fabs%2F1705.08138&data=02%7C01%7CWolfgang.Bangerth%40colostate.edu%7C42883fea63d14f1fba0708d7731b3cee%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C637104433135935173&sdata=nhQdMUArCdSVEYLP%2FEZfusmJB8KZsSTovnjc8fWKSus%3D&reserved=0> We've generally tried to always think of our linear systems as *global*, where each processor only happens to store a certain number of rows. This has proven to be an easier perspective to work with than the domain decomposition approach. In your context, I would try to think about how you would solve the problem on a single processor first. (In the context of the DD approach, looking at how the system is solved for each subdomain may give a hint.) One can then try and generalize this approach to a parallel setting. Best W. -- ------------------------------------------------------------------------ Wolfgang Bangerth email: [email protected] www: http://www.math.colostate.edu/~bangerth/ -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/78714b07-0ce2-5f4d-b875-c48f33ba8392%40colostate.edu.
