## 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. | |

Dissertation for the degree of Doctor of Science in Technology to be presented
with due permission for public examination and debate in Auditorium S4 at
Helsinki University of Technology (Espoo, Finland) on the
26^{th} of May 2001 at 12 o'clock noon.

Overview in PDF format (ISBN 951-22-5491-3) [574 KB]

Dissertation is also available in print (ISBN 951-22-5473-5)

This thesis deals with the development and application of two simulation methods commonly used in radio engineering, namely the Finite-Difference Time-Domain method (FDTD) and the Finite Element Method (FEM). The main emphasis of this thesis is in FDTD.

FDTD has become probably the most popular computational technique in radio engineering. It is a well established, fairly accurate and easy-to-implement method. Being a time-domain method, it can provide wide-band information in a single simulation. It simulates physical wave propagation in the computational volume, and is thus especially useful for educational purposes and for gaining engineering insight into complicated wave interaction and coupling phenomena.

In this thesis, numerical dispersion taking place in the FDTD algorithm is analyzed, and a novel dispersion reduction procedure is described, based on artificial anisotropy. As a result, larger cells can be used to obtain the same accuracy in terms of dispersion error. Simulation experiments suggest that typically the dispersion reduction allows roughly doubling the cell size in each coordinate direction, without sacrificing the accuracy. The obtainable advantage is, however, dependent on the problem. In the open literature, a few other procedures are also presented to reduce the dispersion error. However, the rather dominating effect of unequal grid resolution along different coordinate directions has been neglected in previous studies.

The so-called Perfectly Matched Layer (PML) has proven to be a very useful absorbing boundary condition (ABC) in FDTD simulations. It is reliable, works well in wide frequency band and is easy to implement. The most notable deficiency of PML is that it enlarges the computational volume - in open 3-D structures easily by a factor of two. However, due to its advantages, PML has become a standard ABC. In this thesis, the operation of PML in FDTD has been studied theoretically, and some interesting properties of it not known before are uncovered. For example, it is shown that, surprisingly, PML can absorb perfectly (i.e. with zero reflection) plane waves propagating towards almost arbitrary given direction at given frequency. Optimizing the conductivity profile allows reduction of the PML thickness.

A typical application of the FDTD method is the design of a mobile handset antenna. An improved coaxial probe model has been developed for antenna simulations. The well-known resistive voltage source (RVS) model has also been discussed. A reference plane transformation is proposed to correct the simulated input impedance.

A popular thin-wire model in 2-D FDTD is discussed, and it is shown to be based on erroneous reasoning. The error has been corrected by a simple procedure, and the corrected model has been demonstrated to simulate infinite long thin wires much better than the commonly used model.

A novel way to implement singular basis functions in FEM is discussed. It is shown theoretically and demonstrated by examples that if a waveguide propagation mode contains field singularities, then explicit inclusion of singularities in finite element analysis is crucial in order to obtain accurate cut-off wavenumbers.

This thesis consists of an overview and of the following 6 publications:

- Jaakko Juntunen, Theodoros D. Tsiboukis: Reduction of numerical dispersion in FDTD algorithm through artificial anisotropy. IEEE Transactions on Microwave Theory and Techniques, Vol. 48, No. 4, 2000, pp. 582-588. © 2000 IEEE. By permission.
- Jaakko Juntunen, Nikolaos V. Kantartzis, Theodoros D. Tsiboukis: Zero reflection coefficient in discretized split-field PML. IEEE Microwave and Wireless Components Letters, Vol. 11, No. 4, 2001, pp. 155-157. © 2001 IEEE. By permission.
- Jaakko Juntunen, Outi Kivekäs, Jani Ollikainen, Pertti Vainikainen: FDTD simulation of a wide-band half volume DRA. Proceedings of the Fifth International Symposium on Antennas, Propagation and EM Theory (ISAPE 2000), Beijing, 2000, pp. 223-226. © 2000 Publishing House of Electronics Industry. By permission.
- Jaakko Juntunen: Note on the S11-parameter and input impedance extraction in antenna simulations using FDTD. Microwave and Optical Technology Letters, Vol. 28, No. 1, 2001, pp. 8-11.
- Riku Mäkinen, Jaakko Juntunen, Markku Kivikoski: An accurate 2D hard-source model for FDTD. IEEE Microwave and Wireless Components Letters, Vol. 11, No. 2, 2001, pp. 74-76. © 2001 IEEE. By permission.
- Jaakko Juntunen, Theodoros D. Tsiboukis: On the FEM treatment of wedge singularities in waveguide problems. IEEE Transactions on Microwave Theory and Techniques, Vol. 48, No. 6, 2000, pp. 1030-1037. © 2000 IEEE. By permission.

**Keywords:**
computational electromagnetics, FDTD, FEM, numerical methods, PML,
numerical dispersion

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© 2001 Helsinki University of Technology

Last update 2011-05-26