Techniques for Numerically Efficient Analysis of Multi-Scale Problems in Computational Electromagnetics

Authors: Kapil Sharma

Source: FERMAT, Volume 25, Communication 9, Jan.-Feb., 2018

Abstract: Multi-scale problems in numerical electromagnetics are becoming increasingly common with the advent and widespread usage of compact mobile phones, body area networks, small and nano antennas, sensors, high-speed interconnects, integrated circuits and complex electronic packaging structures, to name just a few commercial applications. Numerical electromagnetic modeling and simulation of structures with multi-scale features is highly challenging due to the fact that electrically small as well as large features are simultaneously present in the model which demands for discretization of the computational domain such that the number of degrees of freedom is very large, thus, levying a heavy burden on computational resources. The multi-scale nature of a given problem also exacerbates the challenge of generating very fine meshes which do not introduce instabilities or ill-conditioned behaviors.

In this work we introduce a hybrid technique, which combines frequency domain and time domain techniques in a manner such that the fine features (electrically small) of the object being modeled are handled by the Method of Moments (MoM) technique while the electrically large parts of the structure are dealt with by using the Finite-Difference Time-Domain (FDTD) technique in order to reduce the computational burden. Recently, structures with multi-scale features have been simulated by using the dipole moment (DM) approach combined with the FDTD technique to handle fine features in a multi-scale geometry. However, when the size of the scatterer becomes larger in terms of the wavelength and the quasi-static assumption becomes invalid, extensive modifications of the DM/FDTD hybrid approach are needed resulting in a high computational cost.

The research proposes a novel hybrid FDTD technique, which combines the Method of Moments and the Finite-Difference Time-Domain techniques directly in the time domain circumventing the need to carry out frequency transform calculations as required in the DM approach when the object size is not small (size>λ/20). The proposed technique utilizes piecewise sinusoidal basis functions to represent the currents on arbitrarily shaped wires with fine features, and modified RWG basis function for surfaces. The fields scattered by the object with fine features in MoM region are computed in the time domain on a planar interface. The time domain fields obtained at the planar interface are then combined with the FDTD update equations. In contrast to the existing techniques used to handle this type of problems, the proposed technique is both efficient as well as stable.

Index Terms: MoM, FDTD, DM, RWG, DoF, TDIE, EFIE, MFIE, CFIE, Matrix, RHS, Finite Difference, Lagrange Quadratic Interpolation, Modified RWG

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Techniques for Numerically Efficient Analysis of Multi-Scale Problems in Computational Electromagnetics