# Qing Xia: Multiscale analysis and high-order schemes for nonlinear multilevel Maxwell–Bloch equations

**Time: **
Thu 2021-11-04 14.00 - 15.00

**Location: **
KTH, 3721, Lindstedsvägen 25 (and also Zoom: 632 9929 3349)

**Lecturer: **
Qing Xia (KTH)

**Abstract:** In this talk, we will consider nonlinear dispersive models for active media with material interfaces in 2D and 3D arbitrary geometry. The considered nonlinear multilevel systems in the formulation of rate equations are experimental generalizations of two-level atomic systems. A multiscale analysis of the Maxwell–Bloch equations based on asymptotic expansions will be presented. The resulting reduced envelope equations (or slow equations) capture amplitude dynamics of the underlying solutions accurately and efficiently. In addition, we will discuss efficient and high-order schemes for arbitrary multilevel systems with any number of polarization vectors in high dimensional complex geometry, with or without material interfaces, using overlapping grids in the Overture framework. The developed schemes allow compact stencils in time integration, large CFL numbers, and point-wise update of the numerical solutions. It is also shown that the multilevel systems have bounded growth in the energy estimate. Additionally, numerical evidences, including convergence results and simulations, are provided for planar and curved interfaces in both 2D and 3D.