Analysis of a Diagonal Form of the Fast Multipole Algorithm for Scattering Theory

BIT Numerical Mathematics

Volumn 39, Issue 4, 1999, Pages 585-602

  Amini, S ^a   Profit, A T J ^a  

^a UNIVERSITY OF SALFORD   (United Kingdom)

Author keywords

Fast multipole method; Helmholtz equation; Hypersingular equation; Integral equation

Indexed keywords

EID: 0038049725     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022331021899     Document Type: Article

References (14)

1. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover, New York, 1974.
2. S. Amini and A. T. J. Profit, Analysis of the truncation errors in the fast multipole method for scattering problems, Tech. Rep. CMS-98-05, Dept. of Computer and Mathematical Sciences, University of Salford, Salford, M5 4WT, UK, 1998. To appear in J. Comp. Appl. Math.
3. S. Bindiganavale and J. L. Volakis, Comparison of three FMM techniques for solving hybrid FE-BE systems, IEEE Antennas and Propagation Magazine, 39 (1997), pp. 47-60.
4. A. J. Burton and G. F. Miller, The application of integral methods for the numerical solution of boundary value problems, Proc. Royal Society of London, A232 (1971), pp. 201-210.
5. J. Carrier, L. Greengard, and V. Rokhlin, A fast adaptive multipole algorithm for particle simulations, SIAM J. Sci. Stat. Comput., 9 (1988), pp. 669-686.
6. W. Chew, J. Jin, C. Lu, E. Michielssen, and J. Song, Fast solution methods in electromagnetics, IEEE Transactions on Antennas and Propagation, 45 (1997), pp. 533-543.
7. M. Epton and B. Dembart, Multipole translation theory for the three-dimensional Laplace and Helmholtz equations, SIAM J. Sci. Comput, 16 (1995), pp. 865-897.
8. W. Hackbusch and Z. P. Nowak, On the fast matrix multiplication in the boundary element method by panel clustering, Numer. Math., 54 (1989), pp. 436-491.
9. C. Lu and W. Chew, A multilevel algorithm for solving a boundary integral equation of wave scattering, Microwave and Optical Technology Letters, 7 (1994), pp. 466-470.
10. J. Rahola, Diagonal forms of the translation operators in the fast multipole algorithm for scattering problems, BIT, 36:2 (1996), pp. 333-358.
11. R. Coifman, V. Rokhlin, and S. Wandzura, The fast multipole method for the wave equation: A pedestrian prescription, IEEE Antennas and Propagation Magazine, 35 (1993), pp. 7-12.
12. V. Rokhlin, Rapid solution of integral equations of classical potential theory, J. Comp. Physics, 60 (1985), pp. 187-207.
13. V. Rokhlin, Rapid solution of integral equations of scattering theory in two dimensions, J. Comp. Physics, 86 (1990), pp. 414-439.
14. R. Wagner and W. Chew, A study of wavelets for the solution of electromagnetic integral equations, IEEE Transactions on Antennas and Propagation, 43 (1995), pp. 802-810.