Multitrace formulations and Dirichlet-Neumann algorithms

Victorita Dolean, Martin J. Gander

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)

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 languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XXII
EditorsThomas Dickopf, Martin J. Gander, Laurence Halpern, Rolf Krause, Luca F. Pavarino
Place of PublicationCham
PublisherSpringer-Verlag
Pages147-155
Number of pages9
Volume104
ISBN (Print)9783319188263
DOIs
Publication statusPublished - 30 Mar 2016
Event22nd International Conference on Domain Decomposition Methods, DD 2013 - Lugano, Switzerland
Duration: 16 Sep 201320 Sep 2013

Publication series

NameLecture Notes in Computational Science and Engineering
Volume104
ISSN (Print)14397358

Conference

Conference22nd International Conference on Domain Decomposition Methods, DD 2013
CountrySwitzerland
CityLugano
Period16/09/1320/09/13

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