Computing acoustic waves in an inhomogeneous medium of the plane by a coupling of spectral and finite elements

SIAM Journal on Numerical Analysis

Volumn 41, Issue 5, 2003, Pages 1729-1750

  Meddahi, Salim ^a   Márquez, Antonio ^a   Selgas, Virginia ^a  

^a UNIVERSITY OF OVIEDO   (Spain)

Author keywords

Exterior boundary value problem; Finite element; Helmholtz equation; Integral equation; Spectral method; Variational formulation

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; BOUNDARY ELEMENT METHOD; CALCULATIONS; FINITE ELEMENT METHOD; GALERKIN METHODS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS;

EXTERIOR BOUNDARY VALUE PROBLEM; HELMHOLTZ EQUATIONS; SPECTRAL METHOD; VARIATIONAL FORMULATION;

ACOUSTIC WAVES;

EID: 4344635247     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142902406624     Document Type: Conference Paper

References (25)

1. R. ADAMS, Sobolev Spaces, Academic Press, New York, 1975.
2. A. BAYLISS, M. GUNZBURGER, AND E. TUKEL, Boundary conditions for the numerical solution of elliptic equations in exterior regions, SIAM J. Appl. Math., 42 (1982), pp. 430-451.
3. J. BÉRENGER, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114 (1994), pp. 185-200.
4. PH. G. CIARLET, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
5. D. COLTON AND R. KRESS, Inverse Acoustic and Electromagnetic Scattering Theory, 2nd ed., Springer-Verlag, Berlin, 1998.
6. D. GIVOLI, Numerical Methods for Problems in Infinite Domains, Elsevier, Amsterdam, 1992.
7. C. GOLDSTEIN, The finite element method with non-uniform mesh sizes applied to the exterior Helmholtz problem, Numer. Math., 38 (1981), pp. 61-82.
8. F. IHLENBURG, Finite Element Analysis of Acoustic Scattering, Springer-Verlag, New York, 1998.
9. C. JOHNSON AND J. C. NÉDÉLEC, On the coupling of boundary integral and finite element methods, Math. Comp., 35 (1980), pp. 557-566.
10. S. JOHNSON AND M. TRACEY, Inverse scattering solutions by a sinc basis, multiple source, moment method I: Theory, Ultrason. Imaging, 5 (1983), pp. 361-375.
11. A. KIRSCH, An Introduction to the Mathematical Theory of Inverse Problems, Springer-Verlag, New York, 1996.
12. R. KRESS, Linear Integral Equations, 2nd ed., Springer-Verlag, New York, 1999.
13. R. Li, On the coupling of BEM and FEM for exterior problems for the Helmholtz equation, Math. Comp., 68 (1999), pp. 945-953.
14. M. MASMOUDI, Numerical solution for exterior problems, Numer. Math., 51 (1987), pp. 87-101.
15. S. MEDDAHI, An optimal iterative process for the Johnson-Nedelec method of coupling boundary and finite elements, SIAM J. Numer. Anal., 35 (1998), pp. 1393-1415.
16. S. MEDDAHI, M. GONZÁLEZ, AND P. PÉREZ, On a FEM-BEM formulation for an exterior quasilinear problem in the plane, SIAM J. Numer. Anal., 37 (2000), pp. 1820-1837.
17. S. MEDDAHI AND A. MARQUEZ, A combination of spectral and finite elements methods for an exterior problem in the plane, Appl. Numer. Math., 43 (2002), pp. 275-295.
18. S. MEDDAHI AND F.-J. SAYAS, A fully discrete BEM-FEM for the exterior Stokes problem in the plane, SIAM J. Numer. Anal., 37 (2000), pp. 2082-2102.
19. S. MEDDAHI AND A. MARQUEZ, New implementation techniques for the exterior Stokes problem in the plane, J. Comput. Phys., 172 (2001), pp. 685-703.
20. A. KIRSCH AND P. MONK, An analysis of the coupling of finite-element and Nyström methods in acoustic scattering, IMA J. Numer. Anal., 14 (1994), pp. 523-544.
21. J. SARANNEN AND G. VAINIKKO, Periodic Integral and Pseudodifferential Equations with Numerical Approximation, Springer-Verlag, New York, 2002.
22. R. SCOTT, Interpolated boundary conditions in the finite element method, SIAM J. Numer. Anal., 12 (1975), pp. 404-427.
23. G. STRANG, Variational crimes in the finite element method, in The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A. Aziz, ed., Academic Press, New York, 1972, pp. 689-710.
24. A. ŽENÍŠEK, Nonlinear Elliptic and Evolution Problems and Their Finite Element Approximations, Academic Press, London, 1990.
25. M. ZLÁMAL, Curved elements in the finite element method I, SIAM J. Numer. Anal., 10 (1973), pp. 229-240.