A GenEO Domain Decomposition method for Saddle Point problems

Abstract

We introduce an adaptive domain decomposition (DD) method for solving saddle point problems defined as a block two by two matrix. The algorithm does not require any knowledge of the constrained space. We assume that all sub matrices are sparse and that the diagonal blocks are the sum of positive semi definite matrices. The latter assumption enables the design of adaptive coarse space for DD methods, see [5].

Can DtN and GenEO coarse spaces be sufficiently robust for heterogeneous Helmholtz problems?

“…The Generalised Eigenproblems in the Overlap (GenEO) coarse space was derived in [52] to provide a rigorously robust approach for symmetric positive definite problems even in the presence of heterogeneities. In recent years, this approach have been extended and used within various settings and applications, for example [7,19,38,48]; see also the discussion on developments for other spectral coarse spaces in [51].…”

Can DtN and GenEO Coarse Spaces Be Sufficiently Robust for Heterogeneous Helmholtz Problems?

“…The Generalised Eigenproblems in the Overlap (GenEO) coarse space was derived in [35] to provide a rigorously robust approach for symmetric positive definite problems even in the presence of heterogeneities. In recent years, this approach has been extended and used within various settings and applications-for example, [39,45,48,49]; see also the discussion on developments for other spectral coarse spaces in [50].…”