ABSTRACT

This talk consists of two major topics. The first part is on the fast multipole method (FMM) in layered media. The FMM in homogeneous free space medium, invented by L. Greengard and V. Rokhlin in the 1980s, has been a revolutionary development in modern computational algorithms for many-body interactions, which reduces the O(N 2 ) cost of computing long-range interactions to O(N log N) or O(N). We will show our recent results on the FMM in layered media for wave and charge source interactions, made possible by newly developed far-field multipole expansions (MEs) for Green's functions in layered media, together with rigorous analysis of the MEs’ exponential convergence. The second part is on solving high-dimensional partial differential equations using deep neural networks (DNN). In order to overcome the curse of dimensionality, we present a DNN solver to approximate the solutions to high-dimensional quasilinear parabolic PDEs using forward-backward stochastic differential equations based on the Pardoux-Peng theory.

Registration URL

https://cityu.zoom.us/meeting/register/tJcsd-GsrT0sHdTC_wastacDaCzb09mcfmuY

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