No Access

MULTI-FIELD THREE-NODE TRIANGULAR FINITE ELEMENT MODEL FOR HELMHOLTZ PROBLEM

K. Y. SZE

Department of Mechanical Engineering, The University of Hong Kong, Pokfulam, Hong Kong, P. R. China

Search for more papers by this author

Q. H. ZHANG

Department of Mechanical Engineering, The University of Hong Kong, Pokfulam, Hong Kong, P. R. China

Department of Scientific Computing & Computer Applications, Sun Yat-Sen University, Guangzhou, P. R. China

Search for more papers by this author

, and

G. H. LIU

Department of Mechanical Engineering, The University of Hong Kong, Pokfulam, Hong Kong, P. R. China

Search for more papers by this author

https://doi.org/10.1142/S0218396X11004353Cited by:2 (Source: Crossref)

Abstract

In this paper, four three-node triangular finite element models which can readily be incorporated into the standard finite element program framework are devised via a multi-field variational functional for the bounded plane Helmholtz problem. In the models, boundary and domain fields are independently assumed. The former is constructed by nodal interpolation and the latter comprises nonsingular solutions of the Helmholtz equation. The equality of the two fields are enforced along the element boundary. Among the four devised models, the most accurate one is 1/3 to 1/2 less erroneous than the conventional single-field model in most examples.

Keywords:

References

A. P. Zielinski and I. Herrera, Int. J. Numer. Meth. Engng. 24, 871 (1987). Crossref, Web of Science, Google Scholar
Y. K. Cheung, W. G. Jin and O. C. Zienkiewicz, Int. J. Numer. Meth. Engng. 32, 63 (1991), DOI: 10.1002/nme.1620320105. Crossref, Web of Science, Google Scholar
I. Herrera, Numer. Meth. Partial Differential Eqns. 16, 561 (2000). Crossref, Web of Science, Google Scholar
J. Sladek, V. Sladek and R. V. Keer, Adv. Engng. Software 33, 469 (2002). Crossref, Web of Science, Google Scholar
J. R. Chang and R. F. Liu, J. Sound Vibration 275, 991 (2004). Crossref, Web of Science, Google Scholar
M. Stojek, Int. J. Numer. Meth. Engng. 41, 831 (1998). Crossref, Web of Science, Google Scholar
M. Stojek, M. Markiewicz and O. Mahrenholtz, Comput. Struct. 75, 335 (2000), DOI: 10.1016/S0045-7949(99)00097-8. Crossref, Web of Science, Google Scholar
J. A. T. Freitas and C. Cismasiu, Int. J. Solids Struct. 40, 671 (2003). Crossref, Web of Science, Google Scholar
K. Y. Sze and Y. K. Cheung, Comm. Numer. Meth. Engng. 24, 2047 (2008), DOI: 10.1002/cnm.1094. Crossref, Web of Science, Google Scholar
K. Y. Sze, G. H. Liu and H. Fan, Comput. Meth. Appl. Mech. Engrg. 199, 598 (2010), DOI: 10.1016/j.cma.2009.10.012. Crossref, Web of Science, Google Scholar
K. Y. Sze and G. H. Liu, Comput. Mech. 46, 455 (2010), DOI: 10.1007/s00466-010-0494-0. Crossref, Web of Science, Google Scholar
J. M. Melenk and I. Babuška, Int. J. Numer. Meth. Engng. 40, 727 (1997). Web of Science, Google Scholar
P. Mayer and J. Mandel, The finite ray element method for the Helmholtz equation of scattering: First numerical experiments, Report 111, Center of Computational Mathematics, University of Colorado at Denver (1997) . Google Scholar
O. Laghrouche and P. Bettess, J. Comput. Acoustics 8, 189 (2000), DOI: 10.1016/S0218-396X(00)00012-1. Link, Web of Science, Google Scholar
P. Ortiz and E. Sanchez, Int. J. Numer. Meth. Engng. 50, 2727 (2001), DOI: 10.1002/nme.161. Crossref, Web of Science, Google Scholar
C. Farhat, I. Harari and U. Hetmaniuk, Comput. Meth. Appl. Mech. Engng. 192, 1389 (2003). Crossref, Web of Science, Google Scholar
C. Farhat, I. Harari and U. Hetmaniuk, Comput. Meth. Appl. Mech. Engng. 192, 3195 (2003). Crossref, Web of Science, Google Scholar
C. Farhat, R. Tezaur and Wiedemann-Goiran, Int. J. Numer. Meth. Engng. 61, 1938 (2004), DOI: 10.1002/nme.1139. Crossref, Web of Science, Google Scholar
R. Tezaur and C. Farhat, Int. J. Numer. Meth. Engng. 66, 796 (2006), DOI: 10.1002/nme.1575. Crossref, Web of Science, Google Scholar
J. A. Freitas, J. P. Almeida and E. M. B. Pereira, Comput. Mech. 23, 488 (1999). Crossref, Web of Science, Google Scholar
R. L. Spilker, S. M. Maskeri and E. Kania, Int. J. Numer. Meth. Engng. 17, 1469 (1981), DOI: 10.1002/nme.1620171004. Crossref, Web of Science, Google Scholar
K. Y. Sze, C. L. Chow and W. J. Chen, Commun. Numer. Meth. Engng. 8, 385 (1992). Crossref, Web of Science, Google Scholar
W. Chen and M. Tanaka, Comput. Math. Appl. 43, 379 (2002). Crossref, Web of Science, Google Scholar
W. Chen, Z. J. Fu and B. T. Jin, Engng. Anal. Boundary Elements 34, 196 (2010), DOI: 10.1016/j.enganabound.2009.09.007. Crossref, Web of Science, Google Scholar
T. H. H. Pian, Finite Elements Anal. Des. 21, 5 (1995), DOI: 10.1016/0168-874X(95)00024-2. Crossref, Web of Science, Google Scholar
K. Y. Sze, W. K. Chan and T. H. H. Pian, Int. J. Numer. Meth. Engng. 55, 853 (2000), DOI: 10.1002/nme.535. Crossref, Web of Science, Google Scholar
G. H. Liu, Formulation of multifield finite element models for Helmholtz problems, Ph.D. Thesis, Department of Mechanical Engineering, The University of Hong Kong (2010) . Google Scholar
C. Kimberling, Congressus Numer. 129, 1 (1998). Google Scholar
R. D. Cook , D. S. Malkus and M. E. Plesha , Concepts and Applications of Finite Element Analysis , 3rd edn. ( Wiley , 1989 ) . Google Scholar