High order ADI method for separable generalized Helmholtz equations

Advances in engineering software

Volumn 31, Issue 8, 2000, Pages 585-591

  Zhuang, Y ^a   Sun, X H ^a,b  

^a Louisiana State University   (United States)

^b Illinois Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DATA STRUCTURES; LAPLACE TRANSFORMS; MATHEMATICAL OPERATORS;

ALTERNATING DIRECTION IMPLICIT (ADI) METHODS; HELMHOLTZ EQUATIONS; HIGH-ORDER DISCRETIZATION;

FINITE DIFFERENCE METHOD;

EID: 0342409507     PISSN: 09659978     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0965-9978(00)00026-0     Document Type: Article

References (14)

1. Birkhoff G., Varga R.S. Implicit alternating direction methods. Trans. AMS. 92:1959;13-24.
2. Boisvert R.F. A fourth-order-accurate Fourier method for the Helmholtz equation in three dimensions. ACM Trans. Math. Software. 13:1987;221-234.
3. Collatz L. The numerical treatment of differential equations. 1960;Springer, Berlin.
4. Douglas J. Alternating direction implicit methods for three space variables. Numer. Math. 4:1962;41-63.
5. Hirsh R. Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique. J. Comput. Phys. 19:1975;90-109.
6. Hockney R. A fast direct solution of Poisson's equation using Fourier analysis. J. ACM. 12:1965;95-113.
7. Kreiss H, Oliger J. Methods for the approximate solution of time dependent problems. GARP Report No. 10, 1973.
8. Lee Q.-Y., Wang N.-C., Yi D.-Y. Numerical analysis. 3rd ed :1986;Central China Institute of Technology Press.
9. Lynch R.E., Rice J.R., Thomas D.H. Tensor product analysis of partial differential equations. Bull. Am. Math. Soc. 70:1964;378-384.
10. Peaceman D.W., Rachford J.H.H. The numerical solution of parabolic and elliptic differential equations. J. SIAM. 3:1955;28-41.
11. Sun X-H, Zhuang Y. A high-order direct solver for Helmholtz equations with Neumann boundary conditions. NASA ICASE Technical Report No. 97-11, NASA Langley Research Center, Hampton, VA 23681-0001, 1997.
12. Wachspress EL. CURE: a generalized two-space-dimension multigroup coding for the IBM 704. Knolls Atomic Power Laboratory Report No. KAPL 1724, General Electric Co., Schenectady, NY, April 1957.
13. Wachspress E.L., Habetler G.J. An alternating direction implicit iteration technique. J. SIAM. 8:1960;403-424.
14. Xu J. Ainsworth M., Levesley J., Light W.A., Marletta M. An introduction to multilevel methods. Wavelets, multilevel methods and elliptic PDEs. 1997;213-302 Oxford Science, Oxford.