论文标题
时域体积积分方程求解器，以分析非线性介电对象的电磁散射
A Time Domain Volume Integral Equation Solver to Analyze Electromagnetic Scattering from Nonlinear Dielectric Objects
论文作者
论文摘要
提出了时间域电场音量积分方程（TD-EFVIE）求解器，用于分析具有Kerr非线性介电对象的电磁散射。与散射器中诱导的电通和电场相关的非线性本构关系用作补充TD-EFVIE的辅助方程。由TD-Efvie的Schaubert-Wilton-Glisson（SWG）离散化产生的普通微分方程系统，使用预测器 - 矫正器方法及时整合了电场的不明膨胀系数。由基于SWG的非线性本构之间的离散化及其使用板近似值获得的逆矩阵系统用于进行电场的明确更新，并在预测指标和时间整合方法的正确阶段进行电场的显式更新。由此产生的显式前进（MOT）方案不要求任何类似牛顿的非线性求解器，只需要在每个步骤都需要解决稀疏且条件良好的革兰氏矩阵系统。数值结果表明，所提出的基于MOT的TD-FEFVIE求解器比有限差异时域方法更准确，该方法传统上用于分析非线性对象的瞬时电磁散射。
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.
