25-10-2012, 11:47 AM
Nonlinear Schwarz-Fas Methods for Unstructured Finite Element Elliptic Problems
ABSTRACT
This paper provides extensions of an element agglomeration AMG method to nonlinear elliptic problems discretized by
the finite element method on general unstructured meshes. The method constructs coarse discretization spaces and
corresponding coarse nonlinear operators as well as their Jacobians. We introduce both standard (fairly quasi-uniformly
coarsened) and non-standard (coarsened away) coarse meshes and respective finite element spaces.We use both kind of spaces
in FAS type coarse subspace correction (or Schwarz) algorithms. Their performance is illustrated on a number of model
problems. The coarsened away spaces seem to perform better than the standard spaces for problems with nonlinearities in the
principal part of the elliptic operator.