Algorithms for Wave Scattering of Random Media: Fast Multipole Method in Layered Media and a Phase Shift Deep Neural Network for Wideband Learning


Wei Cai, Dept. of Math, Southern Methodist University


2019.06.03 14:00-15:00


Room 306,No. 5, Science Building


In this talk, we will present two algorithms and numerical results for solving electromagnetic wave scattering of random meta-materials. Firstly, a fast multipole method for 3-D Helmholtz equation for layered media will be presented based on new multipole expansion (ME) and multipole to local translation (M2L) operators for layered media Green’s functions. Secondly, a parallel phase shift deep neural network (PhaseDNN) is proposed for wideband data learning. In order to achieve uniform convergence for low to high frequency content of data, phase shifts are used to convert high frequency learning to low frequency learning. Due to the fast learning of many DNNs in the low frequency range, PhaseDNN is able to learn wideband data uniformly in all frequencies.


[1] B.Wang, W.Z. Zhang, W. Cai, Fast Multipole Method For 3-D Helmholtz Equation In Layered Media, arXiv:1902.05132

[2] W. Cai, X.G. Li, L.Z. Liu, PhaseDNN - A Parallel Phase Shift Deep Neural Network for Adaptive Wideband Learning , arXiv:1905.01389


Prof. Wei Cai obtained his B.S. and M.S. in Mathematics from the University of Science and Technology of China in 1982 and 1985, respectively, and his Ph.D. in Applied Mathematics at Brown University in 1989. Currently, he is the Clements Chair professor of applied mathematics at SMU. Before he joined SMU, he was an assistant and then associate professor at the University of California at Santa Barbara during 1995-96, and a full Professor at the University of North Carolina after 1999. He also taught and conducted research at Peking University, Fudan University, Shanghai Jiaotong University, and Beijing Computational Science Research Center in China. His research interest focuses on the development of deterministic and stochastic numerical methods for studying electromagnetic and quantum phenomena with applications in meta-materials, nano-photonics, nano-electronics, biological systems, and quantum systems. He has published over 110 refereed articles in top international journals and is the author of the book “Computational Methods for Electromagnetic Phenomena: electrostatics in solvation, scattering, and electron transport” published by Cambridge University Press, 2013.