Peter Bastian: Multilevel Spectral Domain Decomposition Methods

Overlapping domain decomposition methods with spectral coarse spaces are introduced in the framework of subspace correction methods.

On that basis, convergence results independent of the mesh size and coefficient variation are obtained for discontinuous Galerkin discretizations of the elliptic model problem with full tensor as well as for extensions to more than two levels. Numerical results for highly heterogeneous problems with up to 16384 subdomains are shown.