A family of second-order boundary dampers for finite element analysis of two and three-dimensional problems in transient exterior acoustics

International Journal for Numerical Methods in Engineering

Volumn 48, Issue 6, 2000, Pages 925-948

  Manoj, K G ^a   Bhattacharyya, S K ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

Author keywords

Boundary damper; Exterior acoustics; Finite element method; Transient; Unsymmetric solver

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER AIDED ANALYSIS; COMPUTER SOFTWARE; DAMPING; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS;

BAYLISS-GUNSBURGER-TURKEL (BGT) BOUNDARY CONDITIONS; DIRICHLET BOUNDARY CONDITIONS; NEUMANN BOUNDARY CONDITIONS; TRANSIENT EXTERIOR DAMPERS;

ACOUSTICS;

EID: 0033716708     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(20000630)48:6<925::AID-NME915>3.0.CO;2-0     Document Type: Article

References (26)

1. Bayliss A, Turkel E. Radiation boundary conditions for wave like equations. Communications on Pure Applied Mathematics 1980; 33:707-725.
2. Bayliss A, Gunzburger M, Turkel E. Boundary conditions for the numerical solution of elliptic equations in exterior regions. SIAM Journal of Applied Mathematics 1982; 42:430-451.
3. Bando K, Bettess P, Emson C. The effectiveness of dampers in the analysis of exterior scalar wave diffraction by cylinders and ellipsoids. International Journal for Numerical Methods in Fluids 1984; 4:599-617.
4. Keller B, Givoli D. Exact non-reflecting boundary conditions. Journal of Computational Physics 1989; 82:172-192.
5. Keller B, Givoli D. Finite element method for large domains. Computer Methods in Applied Mechanics and Engineering 1989; 76:41-66.
6. Givoli D, Keller JB. Nonreflecting boundary conditions for elastic waves. Wave Motion 1990; 12:261-279.
7. Givoli D. A finite element method for large domain problems. PhD Thesis, Stanford University, Stanford, CA, 1988.
8. Givoli D. Numerical methods for problems in infinite domains. Studies in Applied Mechanics, vol. 33. Elsevier, North-Holland: Amsterdam, 1992.
9. Grote MJ, Keller JB. On nonreflecting boundary conditions. Journal of Computational Physics 1995; 122:231-243.
10. Grote MJ, Keller JB. Exact nonreflecting boundary conditions for the time dependent wave equation, SIAM Journal of Applied Mathematics 1995; 55:280-297.
11. Givoli D, Patlashenko I, Keller JB. High-order boundary conditions and finite elements for infinite domains. Computer Methods in Applied Mechanics and Engineering 1997; 143:13-39.
12. Engquist B, Majda A. Absorbing boundary conditions for the numerical simulation of waves. Mathematics of Computation 1977; 31:629-651.
13. Engquist B, Majda A. Radiation boundary conditions for acoustic and elastic wave calculations. Communications on Pure and Applied Mathematics 1977; 32:312-358.
14. Lee CF, Shin RT, Kong JA, McCartin BJ. Absorbing boundary conditions on circular and elliptical boundaries. In Finite Elements for Wave Electromagnetics-Methods and Techniques. Silvester PP, Pelori G (eds). IEEE Press: New York, 1994; 450-462.
15. Harari I. Computational methods for problems of acoustics with particular reference to exterior domains. PhD Thesis, Department of Mechanical Engineering, Stanford University, CA, 1991.
16. Harari I, Hughes TJR. Finite element method for Helmholtz equation in an exterior domain: model problems, Computer Methods in Applied Mechanics and Engineering 1991; 87:59-96.
17. Prabavathi C. Analysis of acoustic scattering using independent finite element method and eigenfunction expansion. PhD Thesis, I.I.T. Madras, India, 1995.
18. Vendhan CP, Prabavati C. Determination of far-field pattern of rigid scatterers using independent finite element method and eigenfunction expansion, Part 1: Axisymmetric scattering. ASME, Transactions Journal of Vibration and Acoustics 1996; 118:575-582.
19. Prabavati C, Vendhan CP. Determination of far-field pattern of rigid scatterers using independent finite element method and eigenfunction expansion, Part 2: Nonaxisymmetric scattering. ASME, Transactions Journal of Vibration and Acoustics 1996; 118:583-590.
20. Bossut R, Decarpigny JN. Finite element modeling of radiating structures using dipolar elements. Journal of the Accoustical Society of America 1989; 86:1234-1244.
21. Wright JP. Numerical approach to far-field acoustic wave propagation from a prolate spheroidal surface. ASME, Transactions Journal of Vibration and Acoustics 1993; 115:448-451.
22. Pinsky PM, Abboud NN. Finite element solution of the transient exterior structural acoustics problem based on the use of radially asymptotic boundary operators. Computer Methods in Applied Mechanics and Engineering 1991; 85:311-348.
23. Pinsky PM, Thompson LL, Abboud NN. Local high-order radiation boundary conditions for the two-dimensional time dependant structural acoustics. Journal of the Accoustical Society of America 1992; 91:1321-1335.
24. Thompson LL, Pinsky PM. A space-time finite element method for the exterior acousics problem. Journal of the Accoustical Society of America 1996; 99:3297-3311.
25. Malhotra M, Pinsky PM. A matrix-free interpretation of the non-local dirichlet-to-neumann radiation boundary condition. International Journal for Numerical Methods in Engineering 1996; 39:3705-3713.
26. Manoj KG, Bhattacharyya SK. A block solver for large, unsymmetric, sparse banded matrices with symmetric profile. International Journal for Numerical Methods in Engineering 1997; 40:3279-3295.