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Fast Multipole Methods For Wave And Charge Source Interactions In Layered Media And Deep Neural Network Algorithms For High-Dimensional Pdes, Wenzhong Zhang
Fast Multipole Methods For Wave And Charge Source Interactions In Layered Media And Deep Neural Network Algorithms For High-Dimensional Pdes, Wenzhong Zhang
Mathematics Theses and Dissertations
In this dissertation, we develop fast algorithms for large scale numerical computations, including the fast multipole method (FMM) in layered media, and the forward-backward stochastic differential equation (FBSDE) based deep neural network (DNN) algorithms for high-dimensional parabolic partial differential equations (PDEs), addressing the issues of real-world challenging computational problems in various computation scenarios.
We develop the FMM in layered media, by first studying analytical and numerical properties of the Green's functions in layered media for the 2-D and 3-D Helmholtz equation, the linearized Poisson--Boltzmann equation, the Laplace's equation, and the tensor Green's functions for the time-harmonic Maxwell's equations and the …