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Algorithmic Issues for Electromagnetic Scattering in Layered Media: Green's Functions, Current Basis, and Fast Solver

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In this paper, we will address three computational issues for electromagnetic scattering in layered media: fast algorithm of calculating dyadic Green's functions, high order RWG current basis and fast solver for layered media. Numerical results will be included.

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References

  1. M.I. Aksun, A robust approach for the derivation of closed-form Green's functions, IEEE Trans. Microwave Theory Tech. 44 (May 1996) 651-658.

    Google Scholar 

  2. L.S. Andersen and J.L. Volakis, Development and application of a novel class of hierarchical tangential vector finite elements for electromagnetics, IEEE Trans. Antennas Propag. 47(1) (1999).

  3. W. Cai, High order current basis functions for electromagnetic scattering of curved surfaces, J. Sci. Comput. 14(1) (1999) 73-105.

    Google Scholar 

  4. W. Cai and T.J. Yu, Fast calculation of dyadic Green's functions for electromagnetic scattering in a multilayered medium, J. Comput. Phys. 165 (2000) 1-21.

    Google Scholar 

  5. W. Cai, T.J. Yu, H. Wang and Y. Yu, High order mixed RWG basis functions for electromagnetic applications, IEEE Trans. Microwave Theory Tech. 49 (July 2001) 1295-1303.

    Google Scholar 

  6. W.C. Chew, Waves and Fields in Inhomogeneous Media, 2nd ed. (IEEE Press, New York, 1995).

    Google Scholar 

  7. Y.L. Chow, J.J. Yang, D.G. Fang and G.E. Howard, A closed form spatial Green's function for the thick microstrip substrate, IEEE Trans. Microwave Theory Tech. 39 (March 1991) 588-592.

    Google Scholar 

  8. T.J. Cui and W.C. Chew, Fast evaluation of Sommerfeld integrals for EM scattering and radiation by three-dimensional buried objects, Research Report No. CCEM-34-97, University of Illinois, Urbana, IL (December 1997).

    Google Scholar 

  9. I. Daubechies, Ten Lectures on Wavelets, Conference Board of the Mathematical Sciences Series, Vol. 61 (SIAM, Philadelphia, 1992).

    Google Scholar 

  10. L. Demkowicz, L. Vardapetyan and W. Rachowicz, Hp-adaptive edge finite elements for Maxwell equations, in: ACES '98, Monterey, CA, 16-20 March 1998.

  11. L. Greengard and V. Rokhlin, A fast algorithm for particle simulation, J. Comput. Phys. 73 (1987) 325-348.

    Google Scholar 

  12. R.F. Harrington, Time Harmonic Electromagnetic Fields (McGraw-Hill, New York, 1961).

    Google Scholar 

  13. R.F. Harrington, Field Computation by Moment Methods (Macmillian, New York, 1968).

    Google Scholar 

  14. R.F. Harrington, Characteristic modes for antennas and scatters, in: Numerical and Asymptotic Techniques in Electromagnetics, ed. R. Mittra, Topics in Applied Physics, Vol. 3 (Springer, Berlin, 1975).

    Google Scholar 

  15. B. Hu and W.C. Chew, Fast inhomogeneous plane wave algorithm for electromagnetic solution in layered medium structures: two-dimensional case, Radio Sci. 35(1) (2000) 31-43.

    Google Scholar 

  16. D. Kopriva, S.L. Woodruff and M.Y. Hussaini, Discontinuous spectral elment approximation of Maxwell's equation, in: Proc. of the Internat. Symposium on Discontinuous Galerkin Methods, eds. B. Cockburn, G. Karniadakis and C.-W. Shu (Springer, New York, 2000).

    Google Scholar 

  17. E. Kreyszig, Differential Geometry (Dover, New York, 1991).

    Google Scholar 

  18. K. Michalski and J.R. Mosig, Multilayered media Green's functions in the integral equation formulations, IEEE Trans. Antennas Propag. 35(11) (1987) 1299-1301.

    Google Scholar 

  19. E. Michielssen and W.C. Chew, The fast steepest descent path algorithm for analyzing scattering from two dimensional objects, Radio Sci. 31(5) (1996) 1215-1224.

    Google Scholar 

  20. J.R. Mosig, Integral equation technique, in: Numerical Techniques for Microwave and Millimeter-Wave Passive Structure, ed. T. Itoh (Wiley, New York, 1989) pp. 133-213.

    Google Scholar 

  21. C. Muller, Foundation of the Mathematical Theory of Electromagnetic Waves (Springer, Berlin, 1969).

    Google Scholar 

  22. K. Nabors and J. White, Fastcap: A multipole accelerated 3-D capacitance extraction program, IEEE Trans. Comput.-Aided Design Integrated Circuits Systems 10 (1991) 1447-1459.

    Google Scholar 

  23. J.C. Nedelec, Computation of Eddy current on a surface in R 3 by finite element methods, SIAM J. Numer. Anal. 15(3) (1978) 580-594.

    Google Scholar 

  24. Y.C. Pan and W.C. Chew, A hierachical fast multipole method for strated media, Microwave Optic. Technol. Lett. 27(1) (2000).

  25. B.D. Popovic and B.M. Kolundzija, Analysis of Metallic Antennas and Scatters (IEE Press, London, 1994).

    Google Scholar 

  26. P.A. Raviart and J.M. Thomas, A mixed finite element method for 2nd order elliptic problems, in: Lecture Notes in Mathematics, Vol. 606 (Springer, Berlin/New York, 1977) pp. 292-315.

    Google Scholar 

  27. S.M. Rao, D.R. Wilton and A.W. Glisson, Electromagnetic scattering by surfaces of arbitrary shape, IEEE Trans. Antennas Propag. 30 (May 1982) 409-418.

    Google Scholar 

  28. V. Rokhlin, Diagonal forms of translation operators for the Helmholtz equation in three dimensions, Appl. Comput. Harmonic Analysis 1 (1993) 82-93.

    Google Scholar 

  29. V. Rokhlin, Rapid solution of integral equations of scattering theory in two dimensionals, J. Comput. Phys. 36(2) (1990) 414-439.

    Google Scholar 

  30. Y. Saad and M.H. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear system, SIAM J. Sci. Statist. Comput. 7 (1986) 856-869.

    Google Scholar 

  31. M.I. Sancer, R.L. McClary and K.J. Glover, Electromagnetic computation using parametric geometry, Electromagnetics 10(1/2) (1990) 85-103.

    Google Scholar 

  32. T.B. Senior and J.L. Volakis, Approximate Boundary Conditions in Electromagnetics (The Institute of Electrical Engineers, Bath, England, 1994).

    Google Scholar 

  33. P.P. Silvester and R.L. Ferrari, Finite Elements for Electrical Engineer (Cambridge Univ. Press, Cambridge, 1996).

    Google Scholar 

  34. J.M. Song and W.C. Chew, Moment method solutions using parametric geometry, J. Electromagnetic Waves Appl. 9(1/2) (1995) 71-83.

    Google Scholar 

  35. J.A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

    Google Scholar 

  36. B. Szabo and I. Babuska, Finite Element Analysis (Wiley, New York, 1991).

    Google Scholar 

  37. J. Van Bladel, Singular Electromagnetic Fields and Sources (IEEE Press, New York, 1991).

    Google Scholar 

  38. R.L. Wagner and W.C. Chew, A ray-propagation fast multipole algorithm, Microwave Optic. Technol. Lett. 7(10) (1994) 435-438.

    Google Scholar 

  39. S. Wandzura, Electric current basis functions for curved surfaces, Electromagnetics 12 (1992) 77-91.

    Google Scholar 

  40. T. Warburton, Application of the discontinuous Galerkin method to Maxwell equations using unstructured polymorphic hp-finite elments, in: Proc. of the Internat. Symposium on Discontinuous Galerkin Methods, eds. B. Cockburn, G. Karniadakis and C.-W. Shu (Springer, New York, 2000).

    Google Scholar 

  41. J.P. Webb, Edge elements and what they can do for you, IEEE Trans. Magn. 29 (March 1993) 1460-1465.

    Google Scholar 

  42. D.L. Wilkes and C.-C. Cha, Method of moments solution with parametric curved triangular patches, in: 1991 Internat. IEEE AP-S Symposium Digest, London, ON, 1991, pp. 1512-1515.

  43. K.S. Yee, Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media, IEEE Trans. Antennas Propag. 14 (May 1966) 302-307.

    Google Scholar 

  44. T.J. Yu and W. Cai, High-order window functions and fast algorithms for calculating dyadic electromagnetic Green's functions in multilayered media, Radio Sci. 36(4) (2001) 559-570.

    Google Scholar 

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Cai, W. Algorithmic Issues for Electromagnetic Scattering in Layered Media: Green's Functions, Current Basis, and Fast Solver. Advances in Computational Mathematics 16, 157–174 (2002). https://doi.org/10.1023/A:1014429611757

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