We present an open finite element framework, called GetDDM, for testing optimized Schwarz domain decomposition techniques for time-harmonic wave problems. After a review of Schwarz domain decomposition methods and associated transmission conditions, we discuss the implementation, based on the open source software GetDP and Gmsh. The solver, along with ready-to-use examples for Helmholtz and Maxwell's equations, is freely available online for further testing.
a b s t r a c tWe present an efficient method to solve high-frequency scattering problems by heterogeneous penetrable objects in two dimensions. This is achieved by extending the so-called Local Multiple Traces Formulation, introduced recently by Hiptmair and Jerez-Hanckes, to purely spectral discretizations employing weighted Chebyshev polynomials. Together with regularization strategies to handle boundary integral operators singularities, matrix entries are quickly computed via the Fast Fourier Transform. The resulting Fredholm first-kind formulation is free from spurious resonances, and though ill-conditioned, it possesses built-in Calderón-type preconditioners. Numerical results obtained for different settings validate our claims and greatly motivate future research in this direction.
International audienceWe present a flexible finite element solver for testing optimized Schwarz domain decomposition techniques for the time-harmonic Maxwell equations. After a review of non-overlapping Schwarz domain decomposition methods and associated transmission conditions, we discuss the implementation, based on the open source software GetDP and Gmsh. The solver, along with ready-to-use examples, is available online for further testing
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