On Multiple Domain Basis Functions and Their Application to Wire Radiators
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The Method of Moments (MoM) is a general method for solving linear problems, including electromagnetic problems, such as radiation and scattering of electromagnetic waves. The applications of the method include analysis and design of antennas and scatterers and electromagnetic compatibility. This work develops several new extensions to the traditional framework of the method of moments, addressing memory savings, problem conditioning, and acceleration of computations. The MoM’s groundwork in this thesis is based on the works by Professor B.M. Kolundzija. The theory from his books and papers was implemented in a Matlab programming code, within the thin-wire kernel. Several new features, core to this thesis, were then devised, including an improvement to the condition number of impedance matrix, analytical computation of radiation pattern, and piecewise-linearly interpolating multiple domain basis functions (MDBF). This work includes a study into new possibilities to minimize the impedance matrix’s condition number with non-to-little computational overhead. The approach devised involves an appropriate selection of a common/reference wire at a junction with multiple wires attached. It is shown that the choice is frequency dependent. Several solutions with different degrees of optimality and complexity are introduced. A proposed simplistic method ensures that the maximum condition number is never encountered. On the other extreme, another new but more computationally demanding method minimizes the condition number. The technique proposed has demonstrated an order of magnitude reduction in the condition number. The work also proposed a novel method for an accelerated computation of radiation patterns. The method is based on analytical techniques. At low frequencies, the method employs Taylor’s expansion of the oscillating exponential term. At higher frequencies, the method uses integration by parts. Estimates for errors are derived and used to establish the boundary between the Taylor's expansion and the integration by parts. At this boundary, the method has a limitation on the best achievable accuracy. However, this limit is found to be sufficient for most practical applications. The speed and accuracy of a Matlab realization of the method were found matching commercial software, indicating further acceleration potential through coding in a lower level programming language. The bulk of this thesis is on the realisation of multiple domain basis functions (MDBF). MDBF are be defined over a chain of several wire segments. The proposed extension to the traditional MoM decouples the requirements for the mesh of the geometrical model from the requirements for the representation of current distribution. This separation permits to treat curved structures more efficiently, as well as also extends the boundaries of the thin wire approximation. The presented treatment of the problem includes the development and testing of several original automatic algorithms for generating appropriate meshes of chains of wires. The concept of linearly interpolated MDBFs is developed, implemented and tested on piecewise linear (PWL) and piecewise sinusoidal (PWS) MDBFs. Several examples ranging from a short monopole to a resonant coil-loaded antenna were used to illustrate the techniques devised. The application of the technique to the latter example has shown an order of magnitude improvement in the number of the unknowns, as compared to a traditional MoM formulation. This translates into two orders of magnitude in memory savings. Furthermore, a theoretical basis for applying higher order polynomial basis functions to chains of wire segments has been developed, and can be readily extended onto other shapes of basic geometrical element than wire segments. An estimate for computational complexity associated with the higher order hierarchical polynomial basis functions has been derived, quantifying the available potential for a reduction in the number of unknowns. A composition of these individual improvements covers the wide spectrum of a MoM based solution to a multitude of practical problems. It is expected to provide a next step in the reduction of the time and other resources required to solve large problems, towards a numerical electromagnetic synthesis of antennas.
SeriesDoctoral Theses at NTNU, 1503-8181; 2010:102
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