Multitrace formulations and Dirichlet-Neumann algorithms

Dolean, Victorita and Gander, Martin J.; Dickopf, Thomas and Gander, Martin J. and Halpern, Laurence and Krause, Rolf and Pavarino, Luca F., eds. (2016) Multitrace formulations and Dirichlet-Neumann algorithms. In: Domain Decomposition Methods in Science and Engineering XXII. Lecture Notes in Computational Science and Engineering, 104 . Springer-Verlag, CHE, pp. 147-155. ISBN 9783319188263

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    Multitrace formulations (MTF) for boundary integral equations (BIE) were developed over the last few years in [1, 2, 4] for the simulation of electromagnetic problems in piecewise constant media, see also [3] for associated boundary integral methods. The MTFs are naturally adapted to the developments of new block preconditioners, as indicated in [5], but very little is known so far about such associated iterative solvers. The goal of our presentation is to give an elementary introduction to MTFs, and also to establish a natural connection with the more classical Dirichlet-Neumann algorithms that are well understood in the domain decomposition literature, see for example [6, 7]. We present for a model problem a convergence analysis for a naturally arising block iterative method associated with the MTF, and also first numerical results to illustrate what performance one can expect from such an iterative solver.