The EOS Formulation for Linear and Nonlinear Transient Scattering Problems

Abstract

This thesis developed the EOS formulations of solving nonlinear transient scatterings, both for 1D case and 3D Maxwell's equations. This method can be accurately and stably implemented using one particular choice of numerical scheme for the inside of the objects and for the required integral representations of the boundary values. For a stable numerical solution, the time step needs to be confined in some range, where we have found that for 1D case, this range is determined by the internal domain-based method while for the 3D case, this range is both determined by the the internal domain-based method and the boundary integral part. Specifically, in 3D case, the lower limit of the interval is highly depended on the properties of the materials while the upper limit is determined by the internal domain-based method. This finding is believed to be related with the popular late time stabilities in community of computational electromagnetics.