Time-Domain Boundary Element Method Incorporating Strongly Nonlinear Conductivity for Application in the Modeling of 2D Devices

Jay Prakash, Mark T. Greenaway, Kristof Cools
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Abstract

In this work, a time-domain surface integral equation with a strongly nonlinear Resistive Boundary Condition is formulated and approximately solved using the march on in time scheme. The discretization of the nonlinear relation between the surface current density and the electric field is approximated such that the final system of equations to be solved are linear. It is applied to solve scattering of a Gaussian plane wave by a sphere possessing a strongly nonlinear conductivity relation. This solver is developed to specifically model the effects due to the region of negative differential conductivity in the conductivity relation, which is expected in graphene superlattice structures. Numerical results demonstrate the stability and convergence of the method and the ability to enforce the constitutive relation within controllable error bounds.
含强非线性电导率的时域边界元法在二维器件建模中的应用
本文建立了一个具有强非线性电阻性边界条件的时域曲面积分方程,并采用时间格式进行了近似求解。对表面电流密度与电场之间的非线性关系进行了离散化处理,使最终待解方程组为线性方程组。将其应用于求解具有强非线性电导率关系的球对高斯平面波的散射。该求解器的开发是为了专门模拟电导率关系中负微分电导率区域的影响,这在石墨烯超晶格结构中是预期的。数值结果证明了该方法的稳定性和收敛性,以及在可控误差范围内强制执行本构关系的能力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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