Overlapping Schwarz methods in H(curl) on polyhedral domains

Fast Solvers and Schwarz Preconditioners for Spectral Nédélec Elements for a Model Problem in H(curl)

1 1. Introduction. In this paper, we present fast solvers and overlapping additive Schwarz methods for spectral Nédélec element discretizations for a model problem in H(curl). Results of numerical experiments in two dimensions and arguments for a theoretical condition number bound in two and three dimensions are presented. We first show the derivation of the model problem in the implicit time d...

Two-level Overlapping Schwarz Method for H(curl) in 2d for Irregular Subdomains

A bound is obtained for the condition number of a two-level overlapping Schwarz algorithm for problems posed in H(curl) in 2D, where the subdomains are only assumed to be uniform in the sense of Peter Jones. The coarse space is based on energy minimization and its dimension equals the number of subdomain edges. Local direct solvers over overlapping subdomains are also used. The bound is indepen...

Fachrichtung 6 . 1 – Mathematik Preprint Nr . 323 Characterization of trace spaces of H ( curl , Ω ) on curvilinear Lipschitz polyhedral domains Ω

Domain Decomposition Preconditioners for Spectral Nédélec Elements in Two and Three Dimensions

In this paper, we present several domain decomposition preconditioners for high-order Spectral Nédélec element discretizations for a Maxwell model problem in H(curl), in particular overlapping Schwarz preconditioners and Balancing Neumann-Neumann preconditioners. For an efficient and fast implementation of these preconditioners, fast matrix-vector products and direct solvers for problems posed ...

A Two-level Overlapping Schwarz Method for H(curl) in Two Dimensions with Irregular Subdomains

A bound is obtained for the condition number of a two-level overlapping Schwarz algorithm for problems posed in H(curl) in two dimensions, where the subdomains are only assumed to be uniform in the sense of Peter Jones. The coarse space is based on energy minimization and its dimension equals the number of interior subdomain edges. Local direct solvers are used on the overlapping subdomains. Ou...