On Multiple Domain Basis Functions and Their Application to Wire Radiators

This work introduces several advances to the method of moments (MoM) in a thin wire formulation, considered in the context of computational electromagnetics. The main focus in the thesis has been placed on the following original studies and methods: (a) improvement to the condition number of the impedance matrix, (b) analytical computation of radiation pattern, and (c) interpolating multiple domain basis functions (MDBF). The condition number of the impedance matrix due to the MoM has been studied for a junction of several wires. It has been shown that the condition number can be reduced by an appropriate frequency-dependent choice of basis function assignment. Several new methods have been introduced, permitting various degree of control over the condition number. The examples considered have shown a ten-fold reduction in the condition number. Another part of the work establishes a novel method for an accelerated computation of radiation patterns. The method devised is intended for higher order polynomial basis functions. It uses Taylor’s expansion at lower frequencies and integration by parts at higher frequencies. The error estimates have been derived and used to optimize the computations. The speed and accuracy of a Matlab realization of the method have been found to match and potentially exceed those of commercial software. The main focus in the thesis has been on a realization of the novel multiple domain basis functions (MDBF). These functions are a profiled linear combination of common basis functions (BF), such as piecewise linear (PWL). Such a weighted aggregation over a chain of multiple wire segments enables an efficient treatment of curved structures, which is also backward compatible with most of the existing MoM codes. This method also permits to extend the boundaries of the thin wire approximation. The method has been introduced, implemented and tested using PWL and piecewise sinusoidal (PWS) weight profiles. The implementation has included several original automatic algorithms for meshing of wire structures. These algorithms has been extensively studied and compared against several references. The method realizing MDBFs has been applied to several examples, demonstrating an order of magnitude reduction in the number of unknowns required. This translates into a hundred-fold memory saving. Furthermore, a theoretical basis for applying higher order polynomial basis functions to chains of interconnected wire segments has been introduced. An estimate for computational complexity associated with the higher order hierarchical polynomial basis functions has been derived, quantifying an available potential for a reduction in the number of unknowns. Most of the methods introduced in the thesis, including the approaches portrayed in above, are applicable to more complex geometrical elements than wire segments, with only minor modifications.