Optimized Schwarz Methods for Maxwell's Equations

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Over the last two decades, classical Schwarz methods have been extended to systems of hyperbolic partial differential equations, and it was observed that the classical Schwarz method can be convergent even without overlap in certain cases. This is in strong contrast to the behavior of classical Schwarz methods applied to elliptic problems, for which overlap is essential for convergence. Over th...

Schwarz preconditioning for high order edge element discretizations of the time-harmonic Maxwell's equations

We focus on high order edge element approximations of waveguide problems. For the associated linear systems, we analyze the impact of two Schwarz preconditioners, the Optimized Additive Schwarz (OAS) and the Optimized Restricted Additive Schwarz (ORAS), on the convergence of the iterative solver.

Optimized Schwarz method for solving time-harmonic Maxwell's equations discretized by a discontinuous Galerkin method

Overlapping Schwarz methods for Maxwell's equations in three dimensions

Two-level overlapping Schwarz methods are considered for nite element problems of 3D Maxwell's equations. N ed elec elements built on tetrahedra and hexahedra are considered. Once the relative overlap is xed, the condition number of the additive Schwarz method is bounded, independently of the diameter of the triangulation and the number of subregions. A similar result is obtained for a multipli...

DG discretization of optimized Schwarz methods for Maxwell's equations

In the last decades, Discontinuous Galerkin (DG) methods have seen rapid growth and are widely used in various application domains (see [13] for an historical introduction). This is due to their main advantage of combining the best of finite element and finite volume methods. For the time-harmonic Maxwell equations, once the problem is discretized with a DG method, finding robust solvers is a d...