Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities in the PDE coefficients, especially for systems of PDEs. Here, we introduce in a varia-tional setting a… (More)
Over the last two decades, classical Schwarz methods have been extended to systems of hyperbolic partial differential equations, using characteristic transmission conditions, and it has been 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… (More)
Coarse grid correction is a key ingredient in order to have scalable domain decomposition methods. For smooth problems, the theory and practice of such two-level methods is well established, but this is not the case for problems with complicated variation and high contrasts in the coefficients. Stable coarse spaces for high contrast problems are also… (More)
In the recent years, there has been an increasing interest in discontinuous Galerkin time domain (DGTD) methods for the solution of the unsteady Max-well equations modeling electromagnetic wave propagation. One of the main features of DGTD methods is their ability to deal with unstructured meshes which are particularly well suited to the discretization of… (More)
— In this document, we present a parallel implementation in FreeFem++ of scal-able two-level domain decomposition methods. Numerical studies with highly heterogeneous problems are then performed on large clusters in order to assert the performance of our code.
In a previous paper, two of the authors have proposed and analyzed an entire hierarchy of optimized Schwarz methods for Maxwell's equations in both the time-harmonic and the time-domain case. The optimization process has been performed in a particular situation where the electric conductivity was neglected. Here, we take into account this physical parameter… (More)
In this paper the Smith factorization is used systematically to derive a new domain decomposition method for the Stokes problem. In two dimensions the key idea is the transformation of the Stokes problem into a scalar bi-harmonic problem. We show, how a proposed domain decomposition method for the bi-harmonic problem leads to a domain decomposition method… (More)
a r t i c l e i n f o a b s t r a c t The time-harmonic Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental for the simulation of many modern devices we have become used to in everyday life. The numerical solution of these equations is hampered by two fundamental problems: first, in the high frequency regime,… (More)