Hostname: page-component-cc8bf7c57-fxdwj Total loading time: 0 Render date: 2024-12-11T14:25:50.640Z Has data issue: false hasContentIssue false

Non-Matching Grids for a Flexible Discretization in Computational Acoustics

Published online by Cambridge University Press:  20 August 2015

Bernd Flemisch*
Affiliation:
Institute of Hydraulic Engineering, University of Stuttgart, Germany
Manfred Kaltenbacher*
Affiliation:
Applied Mechatronics, Alps-Adriatic University Klagenfurt, Austria
Simon Triebenbacher*
Affiliation:
Applied Mechatronics, Alps-Adriatic University Klagenfurt, Austria
Barbara Wohlmuth*
Affiliation:
Department of Numerical Mathematics, Technical University of Munich, Germany
Get access

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.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Adams, R.. Sobolev Spaces. Pure and Applied Mathematics, Academic Press, 1975.Google Scholar
[2]Bamberger, A., Glowinski, R., and Tran, Q. H.. A domain decomposition method for the acoustic wave equation with discontinuous coefficients and grid change. SIAM J. Numer. Anal., 34(2):603639, 1997.CrossRefGoogle Scholar
[3]Belgacem, F. B.. The mortar finite element method with lagrange multipliers. Numer. Math., 84(2):173197, 1999.Google Scholar
[4]Belgacem, F. B.. A stabilized domain decomposition method with nonmatching grids for stokes problem in three dimensions. SIAM J. Numer. Anal., 42(2):667685, 2004.Google Scholar
[5]Berenger, J.-P.. A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys., 114(2):185200, 1994.CrossRefGoogle Scholar
[6]Bernardi, C., Maday, Y., and Patera, A. T.. A new nonconforming approach to domain decomposition: The mortar element method. In Nonlinear partial differential equations and their applications. College de France Seminar, Vol. XI (Paris, 1989-1991), volume 299 of Pitman Res. Notes Math. Ser., pages 13-51. Longman Sci. Tech., Harlow, 1994.Google Scholar
[7]Braess, D. and Kaltenbacher, M.. Efficient 3d-finite-element-formulation for thin mechanical and piezoelectric structures. Int. J. Numer. Meth. Engr., 73(2):147161, 2008.CrossRefGoogle Scholar
[8]Flemisch, B.. Non-matching Triangulations of Curvilinear Interfaces Applied to Electro-Mechanics and Elasto-Acoustics. PhD thesis, University of Stuttgart, Institute for Applied Analysis and Numerical Simulation, 2006.Google Scholar
[9]Flemisch, B., Kaltenbacher, M., and Wohlmuth, B.. Elasto-acoustic and acoustic-acoustic coupling on nonmatching grids. Int. J. Numer. Meth. Engr., 67(13):1791–1810, 2005.Google Scholar
[10]Gander, M.J. and Japhet, C.. Analgorithm for non-matching grid projections with linear complexity. In Domain Decomposition Methods in Science and Engineering XVIII, volume 70, pages 185192. Springer, 2009.CrossRefGoogle Scholar
[11]Ganis, B. and Yotov, I.. Implementation of a mortar mixed finite element method using a Multiscale Flux Basis. Comput. Meth. Appl. Mech. Engr., 198:39893998, 2009.Google Scholar
[12]Hughes, T. J.. The Finite Element Method. Dover, Mineola, N.Y., 1. edition, 2000.Google Scholar
[13]Kaltenbacher, M.. Numerical Simulation of Mechatronic Sensors and Actuators. Springer, Berlin, 2. edition, 2007.Google Scholar
[14]Schenk, O. and Gärtner, K.. Solving unsymmetric sparse systems of linear equations with pardiso. Future Gener. Comput. Syst., 20(3):475487, 2004.Google Scholar
[15]Wein, F., Kaltenbacher, M., Bänsch, E., Leugering, G., and Schury, F.. Topology optimization of a piezoelectric-mechanical actuator with single- and multiple-frequency excitation. Int. J. App. Electromag. Mech., 30:201221, 2009.CrossRefGoogle Scholar
[16]Wohlmuth, B.. A mortar finite element method using dual spaces for the Lagrange multiplier. SIAM J. Numer. Anal., 38(3):9891012, 2000.Google Scholar
[17]Wohlmuth, B. I.. A comparison of dual Lagrange multiplier spaces for mortar finite element discretizations. M2AN Math. Model. Numer. Anal., 36(6):9951012, 2002.Google Scholar