A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for analyzing electromagnetic scattering from dielectric objects with Kerr nonlinearity. The nonlinear constitutive relation that relates electric flux and electric field induced in the scatterer is used as an auxiliary equation that complements TD-EFVIE. The ordinary differential equation system that arises from TD-EFVIE's Schaubert-Wilton-Glisson (SWG)-based discretization is integrated in time using a PE(CE)m scheme for the unknown expansion coefficients of the electric field. Matrix systems that arise from the SWG-based discretization of the nonlinear constitutive relation and its inverse obtained using the Pade approximant are used to carry out explicit updates of electric field and electric flux expansion coefficients at the predictor (PE) and the corrector (CE) stages. The resulting explicit marching-on-in-time (MOT) scheme does not call for any Newton-like nonlinear solver and only requires solution of sparse and well-conditioned Gram matrix systems at every step. Numerical results show that the proposed explicit MOT-based TD-EFVIE solver is more accurate than the finite-difference time-domain method that is traditionally used for analyzing transient electromagnetic scattering from nonlinear objects.
翻译:提出一个时间域电场体积整体方程式(TD-EFVIE)求解器,用于分析用Kerr非线性分析来自电磁物体的电磁散射。在散射器中引发的电通和电场的非线性构成关系,用作辅助方程式,补充TD-EFVIE。基于TD-EFVIE的Schaaubert-Wilton-Glisson(SWG)的普通差异方程式系统,由基于TD-EFVIE的Schaubert-Wilton-Glisson(SWG)基于SWG的非线性电场扩展系数(PE(CE)m)的离散分布。基于SWG的非线性离散的矩阵系统及其使用Pade aproximant的反向电通电流和电通量扩张系数,用来在预测器(PEPEPE) 和校正(CEE) 阶段进行清晰的电流扩张。由此产生的直径矩阵系统要求任何类似于牛顿型非线性非线性溶解解解解解解解解解解解解的矩阵系统,只需要磁分析结果比传统平平平平平平平平平平平平平平平平平平平平平平平平平平平平的磁法。