×

Three-dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of mid-frequency Helmholtz problems. (English) Zbl 1110.76319

Summary: Recently, a discontinuous Galerkin finite element method with plane wave basis functions and Lagrange multiplier degrees of freedom was proposed for the efficient solution in two dimensions of Helmholtz problems in the mid-frequency regime. In this paper, this method is extended to three dimensions and several new elements are proposed. Computational results obtained for several wave guide and acoustic scattering model problems demonstrate one to two orders of magnitude solution time improvement over the higher-order Galerkin method.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76Q05 Hydro- and aero-acoustics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Farhat, Computer Methods in Applied Mechanics and Engineering 192 pp 1389– (2003)
[2] Farhat, International Journal for Numerical Methods in Engineering 61 pp 1938– (2004)
[3] Babuška, SIAM Journal on Numerical Analysis 36 pp 2392– (1997)
[4] Farhat, Computer Methods in Applied Mechanics and Engineering 190 pp 6455– (2001)
[5] Monk, Computer Methods in Applied Mechanics and Engineering 175 pp 121– (1999)
[6] Melenk, Computer Methods in Applied Mechanics and Engineering 139 pp 289– (1996)
[7] Babuška, International Journal for Numerical Methods in Engineering 40 pp 727– (1997)
[8] Laghrouche, Journal of Computational Acoustics 8 pp 189– (2000) · Zbl 1360.76146
[9] Rose, Numerical Mathematics 24 pp 185– (1975)
[10] Cessenat, SIAM Journal on Numerical Analysis 35 pp 255– (1998)
[11] Farhat, Wave Motion 39 pp 307– (2004)
[12] Babuška, Numerical Mathematics 20 pp 179– (1973)
[13] Brezzi, Rev. Francaise d’Automat. Inform. Rech. Opér. 8-R2 pp 129– (1974)
[14] Huttunen, ECCOMAS (2004)
[15] Laghrouche, International Journal for Numerical Methods in Engineering 54 pp 1501– (2002)
[16] Farhat, Numerische Mathematik 85 pp 283– (2000)
[17] Farhat, Journal of Computational Acoustics 13 pp 499– (2005)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.