Mathematics

Talk 1 Title: A Sequential Operator Splitting Method for Maxwell's Equations in Debye Dispersive Media

Speaker: Aubrey Leung

Abstract: We consider Maxwell's equations in dispersive media of Debye type. We present an operator splitting scheme in one dimension that decouples fast and slow moving processes in the problem to develop separate sub-problems. We demonstrate that the scheme is unconditionally stable, first order accurate and perform a numerical stability and dispersion analysis. We provide comparisons of our operator splitting scheme with the Yee finite difference time domain method and demonstrate the advantages of operator splitting.

Talk 2 Title: The Implicit Derivative Method for Maxwell's Equations in Heterogeneous Media

Speaker: Anna Kirk

Abstract: This talk will focus on the finite difference time domain (FDTD) method as a forward solver for Maxwell's equations in one dimensional complex materials. FDTD methods have the advantage of being easy to implement, however, across a material interface these methods lose accuracy. We will introduce an Implicit Derivative Matching method that introduces fictitious points to modify FDTD schemes in complex dielectric materials.