A succinct way to diagonalize the translation matrix in three dimensions

Microwave and Optical Technology Letters

Volumn 15, Issue 3, 1997, Pages 144-147

  Chew, W C ^a   Koc, S ^a   Song, J M ^a   Lu, C C ^a   Michielssen, E ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

Integral equation; Numerical methods; Translation matrix

Indexed keywords

ACOUSTICS; ELECTRODYNAMICS; ELECTROMAGNETIC WAVE SCATTERING; INTEGRAL EQUATIONS; ITERATIVE METHODS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; NUMERICAL METHODS;

FAST MULTIPOLE METHOD; HELMHOLTZ EQUATION; TRANSLATION MATRICES;

ELECTROMAGNETIC FIELD THEORY;

EID: 0031167993     PISSN: 08952477     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2760(19970620)15:3<144::AID-MOP7>3.0.CO;2-G     Document Type: Article

References (17)

1. V. Rokhlin, "Rapid Solution of Integral Equations of Scattering Theory in Two Dimensions," J. Comput. Phys., Vol. 36, No. 2, 1990, pp. 414-439.
2. R. Coifman, V. Rokhlin, and S. Wandzura, "The Fast Multipole Method for the Wave Equation: A Pedestrian Prescription," IEEE Antennas Propagat. Mag., Vol. 35, No. 3, 1993, pp. 7-12.
3. C. C. Lu and W. C. Chew, "A Fast Algorithm for Solving the Hybrid Integral Equation," IEE Proc. Pt. H, Vol. 140, No. 6, 1993, pp. 455-460.
4. R. Coifman, V. Rokhlin, and S. Wandzura, "Faster Single-Stage Multipole Method for the Wave Equation," 10th Annual Review of Progress in ACES, 1994, pp. 19-24.
5. R. L. Wagner and W. C. Chew, "A Ray-Propagation Fast Multipole Algorithm," Microwave Opt. Technol. Lett., Vol. 7, No. 10, 1994, pp. 435-438.
6. J. M. Song and W. C. Chew, "Fast Multipole Method Solution Using Parametric Geometry," Microwave Opt. Technol. Lett., Vol. 7, No. 16, 1994, pp. 760-765.
7. V. Rokhlin, "Diagonal Forms of Translation Operators for the Helmholtz Equation in Three Dimensions," Appl. Comp. Harmon. Anal., Vol. 1, 1993, pp. 82-93.
8. M. Epton and B. Dembart, "Multipole Translation Theory for the Three-Dimensional Laplace and Helmholtz Equations," SIAM J. Sci. Comput., Vol. 16, No. 4, 1995, pp. 865-897.
9. C. C. Lu and W. C. Chew, "A Multilevel Algorithm for Solving Boundary-Value Scattering," Microwave Opt. Technol. Lett., Vol. 7, No. 10, 1994, pp. 466-470.
10. J. M. Song and W. C. Chew, "Multilevel Fast-Multipole Algorithm for Solving Combined Field Integral Equations of Electromagnetic Scattering," Microwave Opt. Technol. Lett., Vol. 10, No. 1, 1995, pp. 14-19.
11. W. C. Chew, C. C. Lu, and Y. M. Wang, "Review of Efficient Computation of Three-Dimensional Scattering of Vector Electromagnetic Waves," J. Opt. Soc. Am. Ser. A, Vol. 11, 1994, pp. 1528-1537.
12. B. Dembart and E. Yip, "A 3D Fast Multipole Method for Electromagnetics with Multiple Levels," 11th Annual Review of Progress in Applied Computational Electromagnetics, 1995, p. 621.
13. L. R. Hamilton, J. J. Ottusch, M. A. Stalzer, R. S. Turley, J. L. Visher, and S. M. Wandzura, "The Fast Multipole Method for Large 2D Scatterers," 11th Annual Review of Progress in Applied Computational Electromagnetics, p. 606, 1995.
14. S. Stein, "Addition Theorems for Spherical Wave Functions," Q. Appl. Math., Vol. 19, No. 1, 1961, pp. 15-24.
15. W. C. Chew, Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, New York, 1990, reprinted by IEEE Press, 1995.
16. W. K. Tung, Group Theory in Physics, World Scientific Publishing Co., Singapore, 1984.
17. J. A. Stratton, Electromagnetic Theory, McGraw-Hill, New York, 1941.