I would like to use full approximation scheme(FAS) for solving nonlinear PDE. I am looking into practical implementation of FAS in parallel(MPI) settings. I noticed the most common/effective smoother choice is GaussSeidel-Newton iteration. Are there any other possibilities? Are there any parallel variants of GaussSeidel-Newton available in the literature? Can anybody recommend some literature/review paper which would discuss properties of the nonlinear smoothers in general?
I would suggest looking into the papers of Mavriplis, Diskin and Nishikawa. Mavriplis and one of his post-docs (Reza-Ahrabi) worked on implicit block ILU preconditioners and other smoothing strategies for Finite Element CFD Codes. Mavriplis himself does a lot of work on Finite Volume FAS (including working a great deal on general agglomeration strategies) for CFD codes, and his website has many papers on multigrid smoothing, including his VKI lectures from 95. Diskin studied under Brandt (the godfather of Multilevel techniques) and still works a great deal on different techniques and smoothers (including mixed precision smoothers). Nishikawa worked with Diskin on a FASMG solver using a newton krylov solver as a smoother (James Thomas worked on this as well), this showed highly optimal behavior. These are the authors to look at to get information on multigrid techniques for scientific computing, IMO.