On adaptive definition of the plane wave basis for wave boundary elements in acoustic scattering: The 2D case

CMES - Computer Modeling in Engineering and Sciences

Volumn 55, Issue 2, 2010, Pages 147-169

  Trevelyan, J ^a   Coates, G ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Adaptivity; Boundary elements; Boundary integral equation; Plane wave basis; Wave scattering

Indexed keywords

ACOUSTIC SCATTERING; ADAPTIVITY; BOUNDARY ELEMENTS; CONVERGENCE PROPERTIES; ERROR INDICATORS; GLOBAL PROPERTIES; H-REFINEMENT; PARTITION OF UNITY; PLANE WAVE; PLANE WAVE BASIS; SHORT WAVELENGTHS; WAVE BOUNDARY; WAVE SCATTERING;

BOUNDARY ELEMENT METHOD; BOUNDARY INTEGRAL EQUATIONS; COMMUNICATION CHANNELS (INFORMATION THEORY); ELECTROMAGNETIC WAVE SCATTERING;

ELASTIC WAVES;

EID: 77951210270     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (38)

1. Abboud, T.; Nédélec, J.; Zhou, B. (1995): Improvement of the integral equation method for high frequency problems. In 3rd Intl. Conf. on Mathematical Aspects of Wave Propagation Phenomena, pp. 178-187. SIAM, Philadelphia.
2. Anand, A.; Boubendir, Y.; Ecevit, F.; Reitich, F. (2006): Analysis of multiple scattering iterations for high-frequency scattering problems. ii: The threedimensional scalar case. Preprint 147/2006, Max Planck Institute.
3. Bebendorf, M. (2000): Approximation of boundary element matrices. Numer. Math., vol.86, pp. 565-589.
4. Bériot, H.; Perrey-Debain, E.; Ben Tahar, M.; Vayssade, C. (2010): Plane wave basis in Galerkin BEM for bidimensional wave scattering. Engineering Analysis with Boundary Elements, vol.34, pp. 130-143.
5. Brancati, A.; Aliabadi, M.; Benedetti, I. (2009): Hierarchical Adaptive Cross Approximation GMRES technique for solution of acoustic problems using the boundary element method. CMES: Computer Modeling in Engineering and Sciences, vol.43, pp. 149-172.
6. Brebbia, C.; Ciskowski, R. (1991): Boundary Element Methods in Acoustics. CMP and Elsevier Applied Science, Southampton.
7. Bruno, O.; Geuzaine, C.; Munro, J.; Reitich, F. (2004): Prescribed error tolerances within fixed computational times for scattering problems of arbitrarily high frequency: the convex case. Phil. Trans. Royal Soc. London A, vol.362, no.1816, pp. 629-645.
8. Burton, A.; Miller, G. (1971): The application of integral equation methods to the numerical solution of some exterior boundary-value problems. Phil. Trans. Royal Soc. London A, vol.323, pp. 201-210.
9. Cessenat, O.; Després, B. (1998): Application of the ultra-weak variational formulation of elliptic PDE's to the two-dimensional Helmholtz problem. SIAM J. Numer. Anal., vol.35, pp. 255-299.
10. Chandrasekhar, B.; Rao, S. (2008): A faster method of moments solution to double layer formulation of acoustic scattering. CMES: Computer Modeling in Engineering and Sciences, vol.33, pp. 199-214.
11. Chew, W.; Jin, J.; Michielssen, E.; Song, J. (1997): Fast solution methods in electromagnetics. IEEE Trans Antennas Propag, vol.45, pp. 533-543.
12. Darve, E. (2000): The fast multipole method: numerical implementation. Journal of Computational Physics, vol.1608, pp. 195-240.
13. de la Bourdonnaye, A. (1994): A microlocal discretization method and its utilization for a scattering problem. Comptes Rendus de l'Académie des Sciences., Paris, Série I, vol.38, pp. 385-388.
14. Dominguez, V.; Graham, I.; Smyshlyaev, V. (2007): A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering. Numer. Math., vol.106, pp. 471-510.
15. Farhat, C.; Harari, I.; Franca, L. (2001): The discontinuous enrichment method. Computer Methods in Applied Mechanics and Engineering, vol.190, pp. 6455-6479.
16. Honnor, M.; Trevelyan, J.; Huybrechs, D. (2009): Numerical evaluation of 2D partition of unity boundary integrals for Helmholtz problems. Journal of Computational and Applied Mathematics, vol. to appear.
17. Huybrechs, D.; Vandewalle, S. (2006): On the evaluation of highly oscillatory integrals by analytic continuation. SIAM J. Numer. Anal., vol.44, pp. 1026-1048.
18. Kim, T.; Dominguez, V.; Graham, I.; Smyshlyaev, V. (2009): Recent progress on hybrid numerical-asymptotic moethods for high-frequency scattering problems. In Proc. 7th UK Conf. on boundary integral methods, pp. 15-23. Univ. of Nottingham.
19. Ladevèze, P.; Sourcis, B.; Riou, H.; Faverjon, B. (2008): An adaptative computational ́wavé approach. In Proc. WCCM8/ECCOMAS, Venice, Italy.
20. Laghrouche, O.; Bettess, P.; Astley, R. (2002): Modelling of short wave diffraction problems using approximating systems of plane waves. International Journal for Numerical Methods in Engineering, vol.54, pp. 1501-1533.
21. Laghrouche, O.; Bettess, P.; Perrey-Debain, E.; Trevelyan, J. (2003): Plane wave basis finite elements for wave scattering in three dimensions. Communications in Numerical Methods in Engineering, vol.19, no.9, pp. 715-723.
22. Langdon, S.; Chandler-Wilde, S. (2006): A wavenumber independent boundary element method for as acoustic scattering problem. SIAM J. Numerical Analysis, vol.43, pp. 2450-2477.
23. Massimi, P.; Tezaur, R.; Farhat, C. (2008): A discontinuous enrichment method for three-dimensional multiscale harmonic wave propagation problems in multi-fluid and fluid-solid media. International Journal for Numerical Methods in Engineering, vol.76, pp. 400-425.
24. Melenk, J.; Babuška, I. (1996): The partition of unity finite element method. basic theory and applications. Computer Methods in Applied Mechanics and Engineering, vol.139, pp. 289-314.
25. Mohsen, A.; Hesham, M. (2006): An efficient method for solving the nonuniqueness problem in acoustic scattering. Communications in Numerical Methods in Engineering, vol.22, pp. 1067-1076.
26. Morse, P.; Feshbach, H. (1981): Methods of Theoretical Physics. Feshbach Publishing.
27. Ortiz, P.; Sanchez, E. (2000): An improved partition of unity finite element model for diffraction problems. International Journal for Numerical Methods in Engineering, vol.50, pp. 2727-2740.
28. Perrey-Debain, E.; Laghrouche, O.; Bettess, P.; Trevelyan, J. (2004): Plane wave basis finite elements and boundary elements for three dimensional wave scattering. Phil. Trans. Royal Society London A, vol.362, no.1816, pp. 561-577. (Pubitemid 38361636)
29. Perrey-Debain, E.; Trevelyan, J.; Bettess, P. (2002): New special wave boundary elements for short wave problems. Communications in Numerical Methods in Engineering, vol.18, no.4, pp. 259-268.
30. Perrey-Debain, E.; Trevelyan, J.; Bettess, P. (2003): Plane wave approximation in the direct collocation boundary element method for radiation and wave scattering: numerical aspects and applications. Journal of Sound and Vibration, vol.261, no.5, pp. 839-858.
31. Perrey-Debain, E.; Trevelyan, J.; Bettess, P. (2003): Wave boundary elements for acoustic computations. Journal of Computational Acoustics, vol.11, no.2, pp. 305-321. (Pubitemid 37170688)
32. Riou, H.; Ladevèze, P.; Sourcis, B. (2008): The multiscale VTCR approach applied to acoustics problems. Journal of Computational Acoustics, vol.16(4), pp. 487-505.
33. Schenck, H. (1968): Improved integral formulation for acoustic radiation problems. Journal of the Acoustical Society of America, vol.44, pp. 41-58.
34. Soares, D. (2009): Numerical modelling of electromagnetic wave propagation by Meshless Local Petrov-Galerkin formulations. CMES: Computer Modeling in Engineering and Sciences, vol.50, pp. 97-114.
35. Strouboulis, T.; Babuška, I.; Hidajat, R. (2006): The generalized finite element method for Helmholtz equation: Theory, computation and open problems. Computer Methods in Applied Mechanics and Engineering, vol.195, pp. 4711-4731.
36. Trevelyan, J. (2007): Numerical steepest descent evaluation of 2D partition of unity boundary integrals for Helmholtz problems. Oberwolfach Report, vol.5/2007, pp. 74-76.
37. Trevelyan, J.; Bettess, P.; Perrey-Debain, E. (2004): Experiments in adaptive selection of plane wave basis directions for wave boundary elements. In Developments in Mechanics of Structures and Materials.
38. Trevelyan, J.; Honnor, M. (2009): A numerical coordinate transformation for efficient evaluation of oscillatory integrals over wave boundary elements. J. Integral Equations and Appl., vol.21, pp. 447-468.