Asymptotic expansion of the free-space green's function for the discrete 3-D poisson equation

SIAM Journal on Scientific Computing

Volumn 18, Issue 4, 1997, Pages 1142-1162

  Burkhart, Richard H ^a  

^a BOEING COMPANY   (United States)

Author keywords

Absorbing boundary condition; Asymptotic expansion; Fourier series; Green's function; Poisson equation

Indexed keywords

ABSORBING BOUNDARY CONDITION; ASYMPTOTIC EXPANSION; FREE SPACE GREEN FUNCTION; POISSON EQUATION; TAYLOR SERIES; TRANAIR PROGRAM;

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; FAST FOURIER TRANSFORMS; GREEN'S FUNCTION; POISSON RATIO; THREE DIMENSIONAL;

NONLINEAR EQUATIONS;

EID: 0031173546     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827594261589     Document Type: Article

References (23)

1. R. P. AGARWAL AND B. S. LALLI, Discrete polynomial interpolation, Green's functions, maximum principles, error bounds, and boundary value problems, Comput. Math. Appl., 25 (1993), pp. 3-39.
2. O. BUNEMAN, Analytic inversion of the five-point Poisson operator, J. Comput. Phys., 8 (1971), pp. 500-505.
3. R. H. BURKHART AND D. P. YOUNG, GMRES Acceleration and Optimization Codes, Tech. report ETA-TR-88, Boeing Computer Services, Seattle, WA, 1989.
4. R. H. BURKHART, G. SENGUPTA, F. T. JOHNSON, J. E. BUSSOLETTI, D. P. YOUNG, R. G. MELVIN, S. S. SAMANT, AND M. B. BIETERMAN, Numerical prediction of scattering of acoustic waves by an aircraft, in Computational Acoustics: Scattering, Gaussian Beams, and Aeroacoustics, Vol. 2, D. Lee, A. Cakmak, and R. Vichnevetsky, eds., North-Holland, Amsterdam, 1990, pp. 207-226.
5. R. H. BURKHART, J. E. BUSSOLETTI, F. T. JOHNSON, S. S. SAMANT, AND D. P. YOUNG, Solution of the Discrete Free-Space 3-D Poisson Equation, Tech. report BCSTECH-94-015, Boeing Computer Services, Seattle, WA, 1994.
6. D. C. CHAMPENEY, Handbook of Fourier Theorems, Cambridge University Press, London, 1987.
7. R. E. EDWARDS, Integration and Harmonic Analysis on Compact Groups, Cambridge University Press, London, 1972.
8. D. GIVOLI, A spatially exact non-reflecting boundary condition for time dependent problems, Comput. Methods Appl. Mech. Engrg., 95 (1992), pp. 97-113.
9. T. HAGSTROM, Asymptotic boundary conditions for dissipative waves: General theory, Math. Comp., 56 (1991), pp. 589-606.
10. R. L. HIGDON, Numerical absorbing boundary conditions for the wave equation, Math. Comp., 49 (1987), pp. 65-90.
11. J. B. KELLER AND D. GIVOLI, An exact non-reflecting boundary condition, J. Comput. Phys., 82 (1988), pp. 172-192.
12. D. H. MUGLER, Green's functions for the finite difference heat, Laplace, and wave equations, in Anniversary Volume on Approximation Theory and Functional Analysis, Birkhauser, Basel, Switzerland, 1984, pp. 543-554.
13. D. H. MUGLER AND R. A. SCOTT, Fast Fourier transform method for partial differential equations, case study: The 2-D diffusion equation, Comput. Math. Appl., 16 (1988), pp. 221-228.
14. P. E. RUBBERT, J. E. BUSSOLETTI, F. T. JOHNSON, K. W. SIDWELL, W. S. ROWE, S. S. SAMANT, G. SENGUPTA, W. H. WEATERILL, R. H. BURKHART, B. L. EVERSON, D. P. YOUNG, AND A. C. Woo, A new approach to the solution of boundary value problems involving complex configurations, in Computational Mechanics - Advances and Trends, American Society of Mechanical Engineers, New York, A. K. Noor, ed., 1986, pp. 49-70.
15. W. RUDIN, Fourier Analysis on Groups, Interscience, New York, 1962.
16. V. S. RYABEN'KII, Boundary equations with projections, Russian Math. Surveys, 40 (1985), pp. 147-183.
17. S. V. TSYNKOV, Artificial Boundary Conditions Based on the Difference Potentials Method, NASA Langley Research Center, Hampton, VA, 1995.
18. V. S. RYABEN'KII AND S. V. TSYNKOV, Artificial boundary conditions for the numerical solution of external viscous flow problems, SIAM J. Numer. Anal., 32 (1995), pp. 1355-1389.
19. TRANAIR Computer Code - Theory Document, Boeing Technical Report, NASA contract report NAS2-11851, Seattle, WA, 1987, Appendix D.
20. L. B. WIGTON, N. J. Yu, AND D. P. YOUNG, GMRES Acceleration of Computational Fluid Dynamics Codes, AIAA Paper 85-1494, Washington, DC, 1985.
21. D. P. YOUNG, R. G. MELVIN, M. B. BIETERMAN, F. T. JOHNSON, S. S. SAMANT, AND J. E. BUSSOLETTI, A locally refined rectangular grid finite element method: Applications to computational fluid dynamics and computational physics, J. Comput. Phys., 92 (1991), pp. 1-66.
22. A. ZYGMUND, Trigonometric Series, Vol. II, Cambridge University Press, London, 1968.
23. A. ZEMLA, On the fundamental solutions for the difference Helmholtz operator, SIAM J. Numer. Anal., 32 (1995), pp. 560-570.