### Abstract

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.

Original language | English |
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Title of host publication | Domain Decomposition Methods in Science and Engineering XXII |

Editors | Thomas Dickopf, Martin J. Gander, Laurence Halpern, Rolf Krause, Luca F. Pavarino |

Place of Publication | Cham |

Publisher | Springer-Verlag |

Pages | 147-155 |

Number of pages | 9 |

Volume | 104 |

ISBN (Print) | 9783319188263 |

DOIs | |

Publication status | Published - 30 Mar 2016 |

Event | 22nd International Conference on Domain Decomposition Methods, DD 2013 - Lugano, Switzerland Duration: 16 Sep 2013 → 20 Sep 2013 |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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Volume | 104 |

ISSN (Print) | 14397358 |

### Conference

Conference | 22nd International Conference on Domain Decomposition Methods, DD 2013 |
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Country | Switzerland |

City | Lugano |

Period | 16/09/13 → 20/09/13 |

### Keywords

- simulation
- computational physics
- mathematical software

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## Cite this

Dolean, V., & Gander, M. J. (2016). Multitrace formulations and Dirichlet-Neumann algorithms. In T. Dickopf, M. J. Gander, L. Halpern, R. Krause, & L. F. Pavarino (Eds.),

*Domain Decomposition Methods in Science and Engineering XXII*(Vol. 104, pp. 147-155). (Lecture Notes in Computational Science and Engineering; Vol. 104). Springer-Verlag. https://doi.org/10.1007/978-3-319-18827-0_13