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Schwarz methods for second order Maxwell equations in 3D with coefficient jumps

Dolean, Victorita and Gander, Martin J. and Veneros, Erwin (2016) Schwarz methods for second order Maxwell equations in 3D with coefficient jumps. In: Domain Decomposition Methods in Science and Engineering XXII. Lecture Notes in Computational Science and Engineering, 104 . Springer-Verlag, Cham, pp. 471-479. ISBN 9783319188263

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    We study non-overlapping Schwarz Methods for solving second order time-harmonic 3D Maxwell equations in heterogeneous media. Choosing the interfaces between the subdomains to be aligned with the discontinuities in the coefficients, we show for a model problem that while the classical Schwarz method is not convergent, optimized transmission conditions dependent on the discontinuities of the coefficients lead to convergent methods. We prove asymptotically that the resulting methods converge in certain cases independently of the mesh parameter, and convergence can even become better as the coefficient jumps increase.