Commun. Comput. Phys., 11 (2012), pp. 472-488.


Non-Matching Grids for a Flexible Discretization in Computational Acoustics

Bernd Flemisch 1, Manfred Kaltenbacher 2*, Simon Triebenbacher 2, Barbara Wohlmuth 3

1 Institute of Hydraulic Engineering, University of Stuttgart, Germany.
2 Applied Mechatronics, Alps-Adriatic University Klagenfurt, Austria.
3 Department of Numerical Mathematics, Technical University of Munich, Germany.

Received 14 December 2009; Accepted (in revised version) 28 August 2010
Available online 24 October 2011
doi:10.4208/cicp.141209.280810s

Abstract

Flexible discretization techniques for the approximative solution of coupled wave propagation problems are investigated. In particular, the advantages of using non-matching grids are presented, when one subregion has to be resolved by a substantially finer grid than the other subregion. We present the non-matching grid technique for the case of a mechanical-acoustic coupled as well as for acoustic-acoustic coupled systems. For the first case, the problem formulation remains essentially the same as for the matching situation, while for the acoustic-acoustic coupling, the formulation is enhanced with Lagrange multipliers within the framework of Mortar Finite Element Methods. The applications will clearly demonstrate the superiority of the Mortar Finite Element Method over the standard Finite Element Method both concerning the flexibility for the mesh generation as well as the computational time.

AMS subject classifications: 65L60, 74S05

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Key words: Nonmatching grids, Mortar FEM, computational acoustics, piezoelectric actuators.

*Corresponding author.
Email: Bernd.Flemisch@iws.uni-stuttgart.de (B. Flemisch), manfred.kaltenbacher@aau.at (M. Kaltenbacher), simon.triebenbacher@aau.at (S. Triebenbacher), barbara.wohlmuth@ma.tum.de (B. Wohlmuth)
 

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