The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.
Aalto

On the Implementation and Formulation of the Electromagnetic Surface Integral Equations

Matti Taskinen

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Electrical and Communications Engineering for public examination and debate in Auditorium S4 at Helsinki University of Technology (Espoo, Finland) on the 7th of April, 2006, at 12 o'clock noon.

Overview in PDF format (ISBN 951-22-8123-6)   [1053 KB]
Dissertation is also available in print (ISBN 951-22-8120-1)

Abstract

Surface integral equation method is one of the most popular numerical methods in the computational electromagnetics. In this thesis three problem areas in the implementation and formulation of the frequency domain surface integral equation methods are studied.

First, a recursive technique is developed to evaluate the singular integrals arising from the electromagnetic surface integral equation methods. The technique is based on singularity subtraction method in which the most singular terms are extracted and evaluated analytically. A similar recursive algorithm is also developed for higher order basis functions. The technique is efficient and easy to apply for different surface integral equation formulations and polynomial basis functions.

The second problem is how to model the electromagnetic fields in complex structures. A procedure is developed for this junction problem to model the fields separately in each region and to properly enforce the electromagnetic boundary conditions on the interfaces of the regions. The developed method is very simple and independent of the surface integral equation formulation and thus makes it easy to apply to different formulations.

The third and most important problem is the choice of the electromagnetic surface integral equation formulation. Various traditional type of formulations are developed in this thesis and their behavior is studied especially with respect to the iterative methods.

The most significant part of this thesis is the new type of a surface integral equation formulation and new techniques developed for it. The main idea in this new formulation is to use the surface charge densities as unknowns in addition to the traditional surface current densities. The formulation does not have problems with the low frequencies, it is well-balanced and the convergence of the iterative methods is fast for a very wide frequency range. The new formulation seems to be the first well-conditioned, truly broadband formulation that can be used from static to high frequencies in a general case of composite metallic and dielectric structures.

The relation between the new formulation and the Picard's extended Maxwell system is also studied.

This thesis consists of an overview and of the following 8 publications:

  1. Pasi Ylä-Oijala and Matti Taskinen. Calculation of CFIE impedance matrix elements with RWG and n × RWG functions. IEEE Transactions on Antennas and Propagation, 51 (8): 1837-1846, August 2003.
  2. Seppo Järvenpää, Matti Taskinen, and Pasi Ylä-Oijala. Singularity extraction technique for integral equation methods with higher order basis functions on plane triangles and tetrahedra. International Journal for Numerical Methods in Engineering, 58 (8): 1149-1165, October 2003.
  3. Seppo Järvenpää, Matti Taskinen, and Pasi Ylä-Oijala. Singularity subtraction technique for high-order polynomial vector basis functions on planar triangles. IEEE Transactions on Antennas and Propagation, 54 (1): 42-49, January 2006.
  4. Pasi Ylä-Oijala, Matti Taskinen, and Jukka Sarvas. Surface integral equation method for general composite metallic and dielectric structures with junctions. Progress In Electromagnetics Research (PIER), 52: 81-108, 2005.
  5. Pasi Ylä-Oijala and Matti Taskinen. Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects. IEEE Transactions on Antennas and Propagation, 53 (3): 1168-1173, March 2005.
  6. Pasi Ylä-Oijala and Matti Taskinen. Well-conditioned Müller formulation for electromagnetic scattering by dielectric objects. IEEE Transactions on Antennas and Propagation, 53 (10): 3316-3323, October 2005.
  7. Pasi Ylä-Oijala, Matti Taskinen, and Seppo Järvenpää. Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods. Radio Science, 40 (6): RS6002 1-19, November 2005.
  8. Matti Taskinen and Pasi Ylä-Oijala. Current and charge integral equation formulation. IEEE Transactions on Antennas and Propagation, 54 (1): 58-67, January 2006.

Keywords: electromagnetic surface integral equations, singular integrals, low frequency problem

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© 2006 Helsinki University of Technology

Last update 2011-05-26