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

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.