An alternating iterative algorithm for the Cauchy problem associated to the Helmholtz equation

Computer Methods in Applied Mechanics and Engineering

Volumn 192, Issue 5-6, 2003, Pages 709-722

  Marin, L ^a   Elliott, L ^a   Heggs, P J ^b   Ingham, D B ^a   Lesnic, D ^a   Wen, X ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Cauchy problem; Helmholtz equation; Inverse problem; Iterative BEM

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY ELEMENT METHOD; ITERATIVE METHODS; PROBLEM SOLVING;

ITERATIVE ALGORITHMS;

COMPUTATIONAL METHODS;

ALGORITHM;

EID: 0037474371     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(02)00592-3     Document Type: Article

References (29)

1. D.E. Beskos, Boundary element method in dynamic analysis: Part II (1986-1996), ASME Appl. Mech. Rev. 50 (1997) 149-197.
2. J.T. Chen, F.C. Wong, Dual formulation of multiple reciprocity method for the acoustic mode of a cavity with a thin partition, J. Sound Vibration 217 (1998) 75-95.
3. I. Harari, P.E. Barbone, M. Slavutin, R. Shalom, Boundary infinite elements for the Helmholtz equation in exterior domains, Int. J. Numer. Meth. Engrg. 41 (1998) 1105-1131.
4. W.S. Hall, X.Q. Mao, A boundary element investigation of irregular frequencies in electromagnetic scattering, Engrg. Anal. Boundary Elem. 16 (1995) 245-252.
5. D.Q. Kern, A.D. Kraus, Extended Surface Heat Transfer, McGraw-Hill, New York, 1972.
6. M. Manzoor, D.B. Ingham, P.J. Heggs, The one-dimensional analysis of fin assembly heat transfer, ASME J. Heat Transfer 105 (1983) 646-651.
7. A.S. Wood, G.E. Tupholme, M.I.H. Bhatti, P.J. Heggs, Steady-state heat transfer through extended plane surfaces, Int. Comm. Heat Mass Transfer 22 (1995) 99-109.
8. Y. Niwa, S. Kobayashi, M. Kitahara, Determination of eigenvalue by boundary element method, Chapter 7, in: P.K. Banerjee, R. Shaw (Eds.), Development in Boundary Element Methods, Applied Science Publisher, New York, 1982.
9. G. De Mey, A simplified integral equation method for the calculation of the eigenvalues of Helmholtz equation, Int. J. Numer. Meth. Engrg. 11 (1977) 1340-1342.
10. J.R. Hutchinson, An alternative BEM formulation applied to membrane vibrations, in: C.A. Brebbia, G. Maier (Eds.), Boundary Elements VII, Springer Verlag, Berlin, 1985, pp. 613-625.
11. A.J. Nowak, C.A. Brebbia, Solving Helmholtz equation by boundary elements using multiple reciprocity method, in: G.M. Calomagno, C.A. Brebbia (Eds.), Computer Experiment in Fluid Flow, CMP/Springer Verlag, Berlin, 1989, pp. 265-270.
12. N. Kamiya, E. Andoh, Eigenvalue analysis by boundary element method, J. Sound Vibration 160 (1993) 279-287.
13. N. Kamiya, E. Andoh, K. Nogae, Eigenvalue analysis by boundary element method: New developments, Engrg. Anal. Boundary Elem. 16 (1993) 203-207.
14. C.F. Nardini, C.A. Brebbia, A new approach to free vibration analysis using boundary elements, in: C.A. Brebbia, T. Futagami, M. Tanaka (Eds.), Boundary Elements V, Springer Verlag, Berlin, 1983, pp. 719-730.
15. J.P. Agnantiaris, D. Polyzer, D. Beskos, Three-dimensional structural vibration analysis by the dual reciprocity BEM, Comput. Mech. 21 (1998) 372-381.
16. M.A. Golberg, C.S. Chen, H. Bowman, H. Power, Some comments on the use of radial basis functions in the dual reciprocity method, Comput. Mech. 22 (1998) 61-69.
17. G. Chen, J. Zhou, Boundary Element Methods, Academic Press, London, 1992.
18. M.R. Bai, Application of BEM-based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries, J. Acoust. Soc. Am. 92 (1992) 533-549.
19. B.K. Kim, J.G. Ih, On the reconstruction of the vibro-acoustic field over the surface enclosing an interior space using the boundary element method, J. Acoust. Soc. Am. 100 (1996) 3003-3016.
20. Z. Wang, S.R. Wu, Helmholtz equation-least-squares method for reconstructing the acoustic pressure field, J. Acoust. Soc. Am. 102 (1997) 2020-2032.
21. S.R. Wu, J. Yu, Application of BEM-based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries, J. Acoust. Soc. Am. 104 (1998) 2054-2060.
22. T. DeLillo, V. Isakov, N. Valdivia, L. Wang, The detection of the source of acoustical noise in two dimensions, SIAM J. Appl. Math. 61 (2001) 2104-2121.
23. V.A. Kozlov, V.G. Maz'ya, A.F. Fomin, An iterative method for solving the Cauchy problem for elliptic equations, Comput. Maths. Math. Phys. 31 (1991) 45-52.
24. J.L. Lions, E. Magenes, Non-Homogeneous Boundary Value Problems and Their Applications, Springer Verlag, Berlin, 1972.
25. G. Fichera, Sul problema della derivata obliqua e sul problema misto per l'equazione di Laplace, Boll. Un. Mat. Ital. 7 (1952) 367-377.
26. P. Schiavone, Mixed problem in the theory of elastic plates with transverse shear deformation, Q. Jl. Mech. Appl. Math. 50 (1997) 239-249.
27. W.L. Wendland, E. Stephan, G.C. Hsiao, On the integral equation method for the plane mixed boundary value problem for the Laplacian, Math. Meth. Appl. Sci. 1 (1979) 265-321.
28. T. Johansson, private communication.
29. V.A. Morozov, On the solution of functional equations by the method of regularization, Soviet Math. Dokl. 167 (1966) 414-417.