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 predictor-corrector method 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 the electric field and the electric flux expansion coefficients at the predictor and the corrector stages of the time integration method. 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：提出了一种时域电场体积分方程（TD-EFVIE）求解器，用于分析具有克尔非线性的介质物体的电磁散射。该求解器利用描述散射体内部电场与电通量之间非线性本构关系的方程作为辅助方程，与TD-EFVIE互补。基于Schaubert-Wilton-Glisson（SWG）离散化的TD-EFVIE所生成的常微分方程组，采用预估-校正法对电场未知展开系数进行时间积分。通过SWG离散化非线性本构关系及其基于Padé逼近的逆矩阵所得的矩阵系统，在时间积分方法的预估和校正阶段实现电场与电通量展开系数的显式更新。所提出的显式时间步进（MOT）方案无需任何牛顿型非线性求解器，仅需在每一步求解稀疏且良态的格拉姆矩阵系统。数值结果表明，与传统用于分析非线性物体瞬态电磁散射的时域有限差分法相比，本文提出的基于显式MOT的TD-EFVIE求解器具有更高的精度。