Victorita Dolean

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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)
In the recent years, there has been an increasing interest in discontinuous Galerkin time domain (DGTD) methods for the solution of the unsteady Maxwell 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)
Robust Coarse Spaces for Systems of PDEs via Generalized Eigenproblems in the Overlaps Nicole Spillane Frédérik Nataf Laboratoire Jacques-Louis Loins, CNRS UMR 7598 Université Pierre et Marie Curie, 75005 Paris, France Victorita Dolean Laboratoire J.-A. Dieudonné, CNRS UMR 6621 Université de Nice-Sophia Antipolis, 06108 Nice Cedex 02, France Patrice Hauret(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)
Coarse grid correction is a key ingredient in order to have scalable domain decomposition methods. In this work we construct the coarse grid space using the low frequency modes of the subdomain DtN maps, and apply the obtained two-level preconditioners to the extended or the original linear system arising from an overlapping domain decomposition. Our method(More)
Interface conditions (IC) between subdomains have an important impact on the convergence rate of domain decomposition algorithms. We rst recall the Schwarz method which is based on the use of Dirichlet conditions on the boundaries of the subdomains and overlapping subdomains. We explain how it is possible to replace them by more e cient ICs with normal and(More)
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, very fine meshes need to be used in(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)
FETI is a very popular method which has proved to be extremely efficient on many large scale industrial problems. One drawback is that it performs best when the decomposition of the global problem is closely related to the parameters in equations. This is somewhat confirmed by the fact that the theoretical analysis goes through only if some assumptions on(More)