Computational electromagnetic methods for multiphysics simulations

Abstract

In this thesis, novel numerical algorithms rooted in computational electromagnetic methods are developed for multiphysics simulations. Due to multidisciplinary scientific advances, conventional electromagnetic methods face many new challenges that involve more physics beyond electromagnetics. It could start with extreme frequencies, periodicity, new materials or nonlinearities. When the frequency is low, the circuit physics dominates the field coupling results. Hence, a new electric field integral equation (EFIE) method is proposed to describe both circuit and wave physics at low frequency. It is formulated by using the Coulomb-gauge Green’s function of quasi-static approximation. Integrated with loop-tree decomposition, frequency normalization and basis rearrangement techniques, the developed Coulomb-gauge EFIE approach shows the capability of solving low-frequency problems. By analyzing the properties of surface and Bloch modes inside finite periodic structures (FPSs), a novel method is proposed to calculate large FPSs efficiently and accurately. Thanks to the fast decay feature of surface waves, the performance of large FPSs is accurately predicted from the information of surface waves and Bloch waves inside small FPSs. The proposed method captures the edge effects meanwhile saves considerable computer resources. Furthermore, a general homogenization methodology is proposed to simplify the modeling and design of devices containing FPSs. To answer the nonlinear simulation request for nanoparticles, a surface integral equation (SIE) method is developed to model nonlinear optics problems. The second-harmonic radiation from metal nanoparticles with arbitrary shapes is evaluated. The mutual coupling between fundamental and second-harmonic fields is captured to take the depletion of fundamental field into account. With this method, a novel compact nonlinear Yagi-Uda antenna is designed to direct second-harmonic radiation. Simultaneously spectral and spatial isolations are achieved between scattered second-harmonic waves and incident fundamental waves. The developed SIE method is efficient with a surface discretization; and can employ experimentally tabulated linear susceptibility and nonlinear surface susceptibility tensor of metals directly. Finally, to handle the measured data for radio frequency and microwave nonlinear devices, a systematic and general-purpose method is proposed to generate blackbox macro-models of nonlinear circuits based on the Volterra series representation of X-parameters. The generated macro-models include memory effects automatically and can support transient simulation with arbitrary input. It constitutes a powerful supplement to existing blackbox macro-modeling methods for nonlinear circuits. The above proposed methods are demonstrated by various examples. The accuracy, efficiency, and robustness of these methods are clearly observed.