Victory Obieke was selected for a fully funded participation to give a Poster Presentation at the SIAM MDS24 through the Sustainable Horizon Institute(SHI). https://www.siam.org/conferences-events/siam-conferences/mds24/

Title: Compatible Energy Preserving Discretizations for Nonlinear Optical Wave Propagation: The Maxwell-Duffing Approach

Authors: Victory Obieke and Prof. Vrushali Bokil.

Abstract: This talk explores the modeling and numerical discretization of Maxwell's equations in nonlinear optical media, specifically focusing on the Maxwell-Duffing model. We present the constitutive laws governing electromagnetic wave propagation in non-magnetic, non-conductive media, describing the material's response using a nonlinear cubic Duffing model coupled with Maxwell's equations. The presentation includes the derivation of energy relations for the one-dimensional nonlinear Maxwell model.

We introduce a high-order spatial discretization method based on fully discrete leap-frog finite-difference time-domain (FDTD) methods and operator splitting methods designed for the accurate and stable simulation of nonlinear wave propagation. Numerical simulations highlight the effectiveness of these methods in capturing the complex dynamics of electromagnetic waves in nonlinear media. Special attention is given to the implementation of the Second order in time and higher order in space leap-frog scheme and its application to traveling wave solutions.

We prove Energy Stability of the Higher Order Yee FDTD Schemes for the cubic Maxwell-Duffing Model and demonstrate these results through Numerical Simulations.

This work provides critical insights into the mathematical and computational challenges of modeling nonlinear optical materials, offering robust techniques for advancing research in nonlinear photonics.

This is a continuation of a talk she gave in an ICERM Workshop In Brown University over the summer https://icerm.brown.edu/program/topical_workshop/tw-24-edmc from July 22 – Aug 2.

Title: Energy Stable Yee-Finite Difference Time Domain Methods for Maxwell Duffing Models.