Owing to the co-existence of multiple physical scales, wave propagation through highly heterogeneous (random) media is an inherently complex physical phenomenon. In the context of laser propagation through turbulent atmospheres, the phase screen method is routinely used for numerical simulations. Phase screen methods are analogous to time splitting methods for random Schrödinger equations, and surprisingly work well even for very large step sizes. In this talk, I will provide an analysis for such methods, and show that one obtains only first order accuracy in the pathwise sense, even while using centered splitting schemes, while errors in the statistical averages converge much faster. This is joint work with Guillaume Bal.

Biography: Anjali Nair is a William H. Kruskal instructor at the University of Chicago. Prior to this, she obtained a Ph.D. in Mathematics from the University of Wisconsin-Madison and a bachelor's degree in Engineering Physics from the Indian Institute of Technology Madras. Her research interests include applied analysis and computation for partial differential equations, applied probability, inverse problems and optimization with a focus on wave propagation through complex media and kinetic theory.