Debye sources and the numerical solution of the time harmonic maxwell equations

Communications on Pure and Applied Mathematics

Volumn 63, Issue 4, 2010, Pages 413-463

  Epstein, Charles L ^a   Greengard, Leslie ^b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77952823014     PISSN: 00103640     EISSN: 00103640     Source Type: Journal    
DOI: 10.1002/cpa.20313     Document Type: Article

References (38)

1. Adams, R. J. Combined field integral equation formulation for electromagnetic scattering from convex geometries. IEEE Trans. Antennas Propag. 52 (2004), no. 5, 1294-1303.
2. Alouges, F.; Borel, S.; Levadoux, D. P. A stable well-conditioned integral equation for electromagnetic scattering. J. Comput. Appl. Math. 204 (2007), no. 2, 440-451.
3. Axelsson, A. Transmission problems for Maxwell's equations with weakly Lipschitz interfaces. Math. Methods Appl. Sci. 29 (2006), no. 6, 665-714.
4. Blank, A. A; Friedrichs, K. O.; Grad, H. Notes on magneto-hydrodynamics V: Theory of Maxwell's equations without displacement current. 1957. Courant Institute of Mathematical Sciences, New York University, Doc. NYO-6486-V. Available at: http://www.cims.nyu.edu/~schmitt/.
5. Bouwkamp, C. J.; Casimir, H. B. G. On multipole expansions in the theory of electromagnetic radiation. Physica 20 (1954), no. 1-6, 539-554.
6. Bruno, O.; Elling, T.; Paffenroth, R.; Turc, C. Electromagnetic integral equations requiring small numbers of Krylov-subspace iterations. J. Comput. Phys. 228 (2009), no. 17, 6169-6183.
7. Christiansen, S. H.; Nédélec, J.-C.. A preconditioner for the electric field integral equation based on Calderon formulas. SIAM J. Numer. Anal. 40 (2002), no. 3, 1100-1135 (electronic).
8. Colton, D. L.; Kress, R. Integral equation methods in scattering theory. Reprint. Krieger, Malabar, Fla., 1992.
9. Colton, D.; Kress, R. Inverse acoustic and electromagnetic scattering theory. Applied Mathematical Sciences, 93. Springer, Berlin, 1992.
10. Contopanagos, H.; Dembart, B.; Epton, M.; Ottusch, J. J.; Rokhlin, V.; Visher, J. L.; Wandzura, S. M. Well-conditioned boundary integral equations for three-dimensional electromagnetic scattering. IEEE Trans. Antennas Propag. 50 (2002), no. 12, 1824-1830.
11. Cools, K.; Andriulli, F. P.; Olyslager, F.; Michielssen, E. Nullspaces of MFIE and Calderon preconditioned EFIE operators applied to toroidal structures. IEEE Trans. Antennas Propag. 57 (2009), 3205-3215.
12. Debye, P. Der Lichtdruck auf Kugeln von beliebigen Material. Ann. Phys. (Leipzig) 30 (1909), 57-136.
13. Griffiths, P.; Harris, J. Principles of algebraic geometry. Pure and Applied Mathematics. Wiley-Interscience, New York, 1978.
14. Gülzow, V. An integral equation method for the time-harmonic Maxwell equations with boundary conditions for the normal components. J. Integral Equations Appl. 1 (1988), no. 3, 365-384.
15. Jackson, J. D. Classical electrodynamics. 3rd ed. Wiley, New York, 1999.
16. Jiang, S.; Rokhlin, V. Second kind integral equations for the classical potential theory on open surfaces. II. J. Comput. Phys. 195 (2004), no. 1, 1-16.
17. Kress, R. On an exterior boundary value problem for the time-harmonic Maxwell equations with boundary conditions for the normal components of the electric and magnetic field. Math. Methods Appl. Sci. 8 (1986), no. 1, 77-92.
18. Lorenz, L. V. Lysvevxgelsen i og uden for en af plane lysbolger belyst kugle. K. Dan. Vidensk. Selsk. Forh. 6 (1890), 1-62.
19. Maue, A.-W. Zur Formulierung eines allgemeinen Beugungsproblems durch eine Integralgleichung. Z. Physik 126 (1949), 601-618.
20. Mautz, J. R.; Harrington, R. F. A combined-source solution for radiation and scattering from a perfectly conducting body. IEEE Trans. Antennas Propag. 27 (1979), no. 4, 445-454.
21. Mie, G. Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen. Ann. Phys. (Leipzig) 25 (1908), no. 3, 377-445.
22. Morita, N.; Kumagai, N.: Mautz, J. R. Integral equation methods for electromagnetics. Artech House, Boston, 1990.
23. Nédélec, J.-C. Acoustic and electromagnetic equations. Integral representations for harmonic problems. Applied Mathematical Sciences, 144. Springer, New York, 2001.
24. Papas, C. H. Theory of electromagnetic wave propagation. Dover, New York, 1988.
25. Picard, R. Zur Lösungstheorie der zeitunabhängigen Maxwellschen Gleichungen mit der Randbedingung n B= n D = 0 in anisotropen, inhomogenen Medien. Manuscripta Math. 13 (1974), no. 1, 37-52.
26. Picard, R. Ein Randwertproblem für die zeitunabhängigen Maxwellschen Gleichungen mit der Randbedingung n εE = n μH = 0 in beschränkten Gebieten beliebigen Zusammenhangs. Applicable Anal. 6 (1976/1977), no. 3, 207-221.
27. Poggio, A. J.; Miller, E. K. Integral equation solutions of three-dimensional scattering problems. Computer Techniques for Electromagnetics, 159-264. Pergamon, Oxford-New York, 1973.
28. Scharstein, R. W. Helmholtz decomposition of surface electric current in electromagnetic scattering problems. Proc. 23rd Southeastern Symposium on System Theory, March, 1991, 424-426.
29. Taskinen, M.; Ylä-Oijala, P. Current and charge integral equation formulation. IEEE Trans. Antennas Propag. 54 (2006), no. 1, 58-67.
30. Vick, J. W. Homology theory. An introduction to algebraic topology. Pure and Applied Mathematics, 53. Academic, New York-London, 1973.
31. Warner, F. W. Foundations of differentiable manifolds and Lie groups. Scott, Foresman, Glenview, Ill.-London, 1971.
32. Werner, P. On an integral equation in electromagnetic diffraction theory. J. Math. Anal. Appl. 14 (1966), no. 3, 445-462.
33. Wilton, D. R.; Glisson, A. W. On improving the electric field integral equation at low frequencies. URSI Radio Science Meeting Digest (Los Angeles, CA), 24, 1981.
34. Wu, W.; Glisson, A. W.; Kajfez, D. A study of two numerical solution procedures for the electric field integral equation at low frequency. Appl. Comput. Electromagnet. Soc. J. 10 (1995), no. 3, 69-80.
35. Yaghjian, A. D. Augmented electric-and magnetic-field integral equations. Radio Sci. 16 (1981), no. 12, 987-1001.
36. Yee, K. S. Uniqueness theorems for an exterior electromagnetic field. SIAM J. Appl. Math. 18 (1970), no. 1, 77-83.
37. Zhang, Y.; Cui, T. J.; Chew, W. C.; Zhao, J.-S. Magnetic field integral equation at very low frequencies. IEEE Trans. Antennas Propag. 51 (2003), no. 8, 1864-1871.
38. Zhao, J.-S.; Chew, W. C. Integral equation solution of Maxwell's equations from zero frequency to microwave frequencies. IEEE Trans. Antennas Propag. 48 (2000), no. 10, 1635-1645.