A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 3, p. 487-506

A new Schwarz method for nonlinear systems is presented, constituting the multiplicative variant of a straightforward additive scheme. Local convergence can be guaranteed under suitable assumptions. The scheme is applied to nonlinear acoustic-structure interaction problems. Numerical examples validate the theoretical results. Further improvements are discussed by means of introducing overlapping subdomains and employing an inexact strategy for the local solvers.

DOI : https://doi.org/10.1051/m2an/2009010
Classification:  74F10,  65B99,  65M12
Keywords: Schwarz method, fluid-structure interaction, coupled problems, nonlinear elasticity, nonlinear acoustics, elasto-acoustic
@article{M2AN_2009__43_3_487_0,
     author = {Ernst, Roland and Flemisch, Bernd and Wohlmuth, Barbara},
     title = {A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {3},
     year = {2009},
     pages = {487-506},
     doi = {10.1051/m2an/2009010},
     zbl = {1165.74017},
     mrnumber = {2536246},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2009__43_3_487_0}
}
Ernst, Roland; Flemisch, Bernd; Wohlmuth, Barbara. A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 3, pp. 487-506. doi : 10.1051/m2an/2009010. http://www.numdam.org/item/M2AN_2009__43_3_487_0/

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