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Efficient Higher Order VIE Method with Taylor Series Expansion for Wideband Frequency EM Scattering Analysis of Dielectric Objects

In this paper, an efficient volume integral equation (VIE) method with Taylor series expansion (TSE) and higher order hierarchical vector (HOHV) basis functions is developed for fast electromagnetic scattering analysis over a wideband frequency of dielectric objects. In this VIE, the impedance matrix elements can be divided into the frequency dependent item (FDT) and geometric structure dependent term (GSDT), where only GSDT is required to be calculated and stored in advance. Then, during frequency sweeping process, the impedance matrix can be generated by combining the precomputed matrices GSDT and FDT. Besides, due to the hierarchy of the HOHV bases, only one coarse mesh corresponding to the lowest frequency of the given frequency band is generated, and the pre-computed matrices corresponding to the highest order basis are need to be computed. Based on those, the EM scattering corresponding into high frequency point can be calculated simply by adjusting the order of the HOHV bases. This saves much work in geometrical modeling and further improves computational efficiency. In contrast to the conventional scheme for fast EM scattering analysis over a wideband frequency, this HO-TSE-VIE method requires much less computational time while the accuracy remains at the same level. Numerical results are provided to demonstrate its accuracy and efficiency.