Geodesic
A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 3, pp. 487-506

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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 : 10.1051/m2an/2009010
Classification : 74F10, 65B99, 65M12
Keywords: Schwarz method, fluid-structure interaction, coupled problems, nonlinear elasticity, nonlinear acoustics, elasto-acoustic 
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     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 },
     pages = {487--506},
     publisher = {EDP-Sciences},
     volume = {43},
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     year = {2009},
     doi = {10.1051/m2an/2009010},
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     zbl = {1165.74017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2009010/}
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Ernst, Roland; Flemisch, Bernd; Wohlmuth, Barbara. A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 3, pp. 487-506. doi: 10.1051/m2an/2009010

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