Prolate and oblate spheroidal acoustic infinite elements

Computer Methods in Applied Mechanics and Engineering

Volumn 158, Issue 1-2, 1998, Pages 117-141

  Burnett, David S ^a   Holford, Richard L ^a  

^a LUCENT TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARCHITECTURAL ACOUSTICS; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL MODELS;

ACOUSTIC INFINITE ELEMENTS;

ACOUSTIC WAVES;

EID: 0032074453     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(97)00251-X     Document Type: Article

References (14)

1. [1] D.S. Burnett, A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion, J. Acoust. Soc. Am. 96 (1994) 2798-2816.
2. [2] R.L. Holford, A multipole expansion for the acoustic field exterior to a prolate or oblate spheroid, J. Acoust. Soc. Am., submitted.
3. [3] F.V. Atkinson, On Sommerfeld's 'Radiation Condition', Phil. Mag. 40 (1949) 645-651.
4. [4] C.H. Wilcox, A generalization of theorems of Rellich and Atkinson, Proc. Am. Math. Soc. 7 (1956) 271-276.
5. [5] C.H. Wilcox, An expansion theorem for electromagnetic fields, Comm. Pure Appl. Math. 9 (1956) 115-134.
6. [6] D. Colton and R. Kress, Integral Equation Methods in Scattering Theory, Sec. 3.2 (Wiley, New York, 1983).
7. [7] According to Ref. [4], the differentiability properties of this expansion were first proved by R.B. Barrar and A.F. Kay in unpublished work.
8. [8] B.A. Szabo and I. Babuska, Finite Element Analysis (Wiley, New York, 1991).
9. [9] D.S. Burnett, Finite Element Analysis: From Concepts to Applications (Addison-Wesley, Reading, MA, 1987).
10. [10] Ibid., p. 578.
11. [11] L.F. Demkowicz and I. Babuska, Texas Institute for Computational and Applied Mathematics, private communication.
12. [12] J.S. Shirron, Naval Research Laboratory, private communication.
13. [13] F. Ihlenburg and I. Babuska, Finite element solution of the Helmholtz equation with high wave number. Part I: The h-version of the FEM, Comput. Math. Applic. 30(9) (1995) 9-37.
14. [14] L.F. Demkowicz and K. Gerdes, Convergence of the infinite element methods for the Helmholtz equation, Texas Institute for Computational and Applied Mathematics Report 95-07, The University of Texas at Austin, June 1995.