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.

    ORCID iDs

    Dolean, Victorita ORCID logoORCID: and Gander, Martin J.; Dickopf, Thomas, Gander, Martin J., Halpern, Laurence, Krause, Rolf and Pavarino, Luca F.