Selected developments in computational electromagnetics for radio engineering

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.reviewe

Efficient Wave-based Sound Propagation and Optimization for Computer-Aided Design

Acoustic phenomena have a large impact on our everyday lives, from influencing our enjoyment of music in a concert hall, to affecting our concentration at school or work, to potentially negatively impacting our health through deafening noises. The sound that reaches our ears is absorbed, reflected, and filtered by the shape, topology, and materials present in the environment. However, many computer simulation techniques for solving these sound propagation problems are either computationally expensive or inaccurate. Additionally, the costs of some methods are dramatically increased in design optimization processes in which several iterations of sound propagation evaluation are necessary. The primary goal of this dissertation is to present techniques for efficiently solving the sound propagation problem and related optimization problems for computer-aided design. First, we propose a parallel method for solving large acoustic propagation problems, scalable to tens of thousands of cores. Second, we present two novel techniques for optimizing certain acoustic characteristics such as reverberation time or sound clarity using wave-based sound propagation. Finally, we show how hybrid sound propagation algorithms can be used to improve the performance of acoustic optimization problems and present two algorithms for noise minimization and speech intelligibility improvement that use this hybrid approach. All the algorithms we present are evaluated on various benchmarks that are computer models of architectural scenes. These benchmarks include challenging environments for existing sound propagation algorithms, such as large indoor or outdoor scenes, structural complex scenes, or the prevalence of difficult-to-model sound propagation phenomena. Using the techniques put forth in this dissertation, we can solve many challenging sound propagation and optimization problems on the scenes in an efficient manner. We are able to accurately model sound propagation using wave-based approaches up to \SI{10}{\kilo\hertz} (the full range of human speech) and for the full range of human hearing (22kHz) using our hybrid approach. Our noise minimization methods show improvements of up to 13dB in noise reduction on some scenes, and we show a 71\% improvement in speech intelligibility using our algorithm.Doctor of Philosoph

Impedance Transformers

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Optimal 25-Point Finite-Difference Subgridding Techniques for the 2D Helmholtz Equation

We present an optimal 25-point finite-difference subgridding scheme for solving the 2D Helmholtz equation with perfectly matched layer (PML). This scheme is second order in accuracy and pointwise consistent with the equation. Subgrids are used to discretize the computational domain, including the interior domain and the PML. For the transitional node in the interior domain, the finite difference equation is formulated with ghost nodes, and its weight parameters are chosen by a refined choice strategy based on minimizing the numerical dispersion. Numerical experiments are given to illustrate that the newly proposed schemes can produce highly accurate seismic modeling results with enhanced efficiency