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Multiple-Stencil Dispersion Analysis of the Lagrange Multipliers in a Discontinuous Galerkin Method for the Helmholtz Equation

Department of Solid Mechanics, Materials and Systems, Tel Aviv University, 69978 Ramat Aviv, Israel

Department of Aerospace Engineering Sciences and Center for Aerospace Structures, University of Colorado, Boulder, CO 80309-0429, USA

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Ulrich Hetmaniuk

Department of Aerospace Engineering Sciences and Center for Aerospace Structures, University of Colorado, Boulder, CO 80309-0429, USA

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https://doi.org/10.1142/S0218396X03001894Cited by:11 (Source: Crossref)

Abstract

We analyze the dispersion properties of elements obtained by a discontinuous Galerkin method with Lagrange multipliers. The dispersion analysis of these elements presents a challenge in that the Lagrange multiplier degrees of freedom are directional, and hence an unbounded mesh is made up of more than one repeating pattern. Two approaches to overcome this difficulty are presented. The similarity in the two sets of results offers mutual validation of the two approaches.

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References

N. N. Abboud and P. M. Pinsky, Int. J. Numer. Meth. Eng. 35(6), 1183 (1992), DOI: 10.1002/nme.1620350604. Web of Science, Google Scholar
I. Babuškaet al., Comput. Meth. Appl. Mech. Eng. 128(3-4), 325 (1995), DOI: 10.1016/0045-7825(95)00890-X. Web of Science, Google Scholar
I. Babuška and J. M. Melenk, Int. J. Numer. Meth. Eng. 40(4), 727 (1997). Web of Science, Google Scholar
I. Babuška and S. A. Sauter, SIAM J. Numer. Anal. 34(6), 2392 (1997), DOI: 10.1137/S0036142994269186. Web of Science, Google Scholar
F. Ben Belgacem and Y. Maday, RAIRO Modél. Math. Anal. Num.ér. 31(2), 289 (1997). Google Scholar
P. Bouillard, Int. J. Numer. Meth. Eng. 45(7), 783 (1999). Web of Science, Google Scholar
O. Cessenat and B. Despres, SIAM J. Numer. Anal. 35(1), 255 (1998), DOI: 10.1137/S0036142995285873. Web of Science, Google Scholar
M. A. Christon and T. E. Voth, Int. J. Numer. Meth. Eng. 47(7), 1285 (2000). Web of Science, Google Scholar
A. Deraemaeker, I. Babuška and P. Bouillard, Int. J. Numer. Meth. Eng. 46(4), 471 (1999). Web of Science, Google Scholar
S. Dey, J. J. Shirron and L. S. Couchman, Comput. Structures 79(6), 617 (2001), DOI: 10.1016/S0045-7949(00)00167-X. Web of Science, Google Scholar
C. Farhat, J. Comput. Sys. Eng. 2(2/3), 149 (1991), DOI: 10.1016/0956-0521(91)90015-W. Google Scholar
C. Farhat, I. Harari and L. P. Franca, Comput. Meth. Appl. Mech. Eng. 190(48), 6455 (2001), DOI: 10.1016/S0045-7825(01)00232-8. Web of Science, Google Scholar
C. Farhat, I. Harari and U. Hetmaniuk, Comput. Meth. Appl. Mech. Eng. 192(11–12), 1389 (2003), DOI: 10.1016/S0045-7825(02)00646-1. Web of Science, Google Scholar
C. Farhat, A. Macedo and M. Lesoinne, Numer. Math. 85(2), 283 (2000), DOI: 10.1007/PL00005389. Web of Science, Google Scholar
L. P. Francaet al., Int. J. Numer. Meth. Eng. 40(21), 4003 (1997). Web of Science, Google Scholar
K. Gerdes and F. Ihlenburg, Comput. Meth. Appl. Mech. Eng. 170(1-2), 155 (1999), DOI: 10.1016/S0045-7825(98)00239-4. Web of Science, Google Scholar
C. I. Goldstein, Appl. Numer. Math. 2(3–5), 409 (1986), DOI: 10.1016/0168-9274(86)90043-7. Web of Science, Google Scholar
K. Grosh and P. M. Pinsky, Comput. Meth. Appl. Mech. Eng. 113(1–2), 67 (1994), DOI: 10.1016/0045-7825(94)90212-7. Web of Science, Google Scholar
I. Harari, Comput. Meth. Appl. Mech. Eng. 140(1–2), 39 (1997), DOI: 10.1016/S0045-7825(96)01034-1. Web of Science, Google Scholar
I. Harari, Comput. Meth. Appl. Mech. Eng. 190(20–21), 2533 (2001), DOI: 10.1016/S0045-7825(00)00251-6. Web of Science, Google Scholar
I. Harari and T. J. R. Hughes, Comput. Meth. Appl. Mech. Eng. 87(1), 59 (1991), DOI: 10.1016/0045-7825(91)90146-W. Web of Science, Google Scholar
I. Harari and T. J. R. Hughes, Comput. Meth. Appl. Mech. Eng. 98(3), 411 (1992), DOI: 10.1016/0045-7825(92)90006-6. Web of Science, Google Scholar
F. Ihlenburg and I. Babuška, Int. J. Numer. Meth. Eng. 38(22), 3745 (1995), DOI: 10.1002/nme.1620382203. Web of Science, Google Scholar
O. Laghrouche and P. Bettess, J. Comput. Acoust. 8(1), 189 (2000). Link, Web of Science, Google Scholar
P. Monk and D.-Q. Wang, Comput. Meth. Appl. Mech. Eng. 175(1–2), 121 (1999), DOI: 10.1016/S0045-7825(98)00326-0. Web of Science, Google Scholar
R. Mullen and T. Belytschko, Int. J. Numer. Meth. Eng. 18(1), 11 (1982), DOI: 10.1002/nme.1620180103. Web of Science, Google Scholar
A. A. Oberai and P. M. Pinsky, J. Comput. Acoust. 8(1), 211 (2000). Link, Web of Science, Google Scholar
M. E. Rose, Numer. Math. 24(3), 185 (1975), DOI: 10.1007/BF01436591. Web of Science, Google Scholar
L. L. Thompson and P. M. Pinsky, Int. J. Numer. Meth. Eng. 38(3), 371 (1995), DOI: 10.1002/nme.1620380303. Web of Science, Google Scholar