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A domain decomposition method for the parallelization of a three-dimensional Maxwell solver based on a constrained formulation. (English) Zbl 1230.78035

Summary: The numerical solution of very large three-dimensional electromagnetic field problems are challenging for various applications in industry. In this paper, we propose a nonoverlapping domain decomposition approach for solving the three-dimensional Maxwell equations on MIMD computers, based on a mixed variational formulation. It is especially well adapted for the solution of the Vlasov-Maxwell equations, widely used to simulate complex devices like particle injectors or accelerators. This approach has the important property that it leads to reuse without modification most of an existing sequential code. The continuity at the interfaces is imposed by duality using Lagrange multipliers. Hence, the resulting parallel algorithm requires only to add an external preconditioned Uzawa solver. We present the results of some numerical experiments on a parallel distributed memory machine.

MSC:

78M30 Variational methods applied to problems in optics and electromagnetic theory
65Y05 Parallel numerical computation
65Y10 Numerical algorithms for specific classes of architectures
65F08 Preconditioners for iterative methods

Software:

METIS
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