Images and plane waves : efficient field computation in electromagnetics and acoustics

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Doctoral thesis (article-based)
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Electromagnetic theory, computational electromagnetics
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37, [111]
Electromagnetics Laboratory report series, 472
In some simple or canonical problems, analytical solutions offer the most efficient way to compute the electromagnetic or acoustic fields. For arbitrary geometries, efficient numerical methods are needed. This thesis contains new or improved solutions of classical electrostatic problems and some further developments of a variant of the fast multipole method (FMM). In the first part, the electrostatic problems of pairs of both orthogonally intersecting and non-intersecting conducting spheres are solved using Kelvin's image theory. A new efficient method for evaluating the polarizability of two non-intersecting spheres is presented. Novel analytical solutions, and also computationally efficient approximative solutions, are obtained by applying Kelvin's inversion to the electrostatic image solution of a conducting wedge. Integral equation methods are popular for both electrodynamic and acoustic scattering problems. However, to be able to use very large number of unknowns, fast iterative methods, such as the fast multipole method, must be used. In the second part of this thesis, a new broadband variant of the multilevel fast multipole algorithm (MLFMA) is described and used for both acoustic and electromagnetic scattering problems. In particular, the implementation overcomes the low-frequency breakdown of the MLFMA using a combination of the spectral representation of the Green's function and Rokhlin's translation formula.
image theory, Kelvin's inversion, fast multipole method (FMM), sub-wavelength breakdown, speglingsteori, Kelvins inversion, snabba multipolmetoden (FMM), lågfrekvens-sammanbrott
Other note
  • I. V. Lindell, K. H. Wallén, and A. H. Sihvola, Electrostatic image theory for two intersecting conducting spheres, Journal of Electromagnetic Waves and Applications, vol. 17, no. 11, pp. 1643-1660, 2003. [article1.pdf] © 2003 VSP International Science Publishers. By permission.
  • H. Wallén and A. Sihvola, Polarizability of conducting sphere-doublets using series of images, Journal of Applied Physics, vol. 96, no. 4, pp. 2330-2335, Aug. 2004. [article2.pdf] © 2004 American Institute of Physics. By permission.
  • K. Nikoskinen and H. Wallén, Application of Kelvin's inversion to static conducting wedge problems, Helsinki University of Technology, Electromagnetics Laboratory Report Series, Report 467, Espoo, Finland, 16 pages, Jan. 2006. IEE Proceedings - Science, Measurement and Technology, submitted for publication.
  • H. Wallén and J. Sarvas, Translation procedures for broadband MLFMA, Progress in Electromagnetics Research, vol. PIER 55, pp. 47-78, 2005. [article4.pdf] © 2005 EMW Publishing. By permission.
  • H. Wallén, S. Järvenpää, and P. Ylä-Oijala, Broadband multilevel fast multipole algorithm for acoustic scattering problems, Journal of Computational Acoustics, 21 pages, accepted for publication, 2006.
  • H. Wallén, S. Järvenpää, P. Ylä-Oijala, and J. Sarvas, Broadband Müller-MLFMA for electromagnetic scattering by dielectric objects, Helsinki University of Technology, Electromagnetics Laboratory Report Series, Report 465, Espoo, Finland, 19 pages, Jan. 2006. IEEE Transactions on Antennas and Propagation, submitted for publication.
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