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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:

Dr. Yong Zhang,Wolfgang Pauli Institute, University of Vienna

 

 

 

Inviter: 刘歆
Title:
Fast convolution-type nonlocal potential solvers in Nonlinear Schr?dinger equation and Lightning simulation
Time & Venue:
2017.11.16 14:00-15:00 N702
Abstract:

Convolution-type potential are common and important in many science and engineering fields. Ecient and accurate evaluation of such nonlocal potentials are essential in practical simulations. In this talk, I will focus on those arising from quantum physics/chemistry and lightning-shield protection, including Coulomb, dipolar and Yukawa potential that are generated by isotropic and anisotropic smooth and fast-decaying density, as well as convolutions defined on a one-dimensional adaptive finite di erence grid. The convolution kernel is usually singular or discontinuous at the origin and/or at the far field, and density might be anisotropic, which together present great challenges for numerics in both accuracy and eciency. The state-of-art fast algorithms include Wavelet based Method( WavM), kernel truncation method(KTM), NonUniform-FFT based method(NUFFT) and Gaussian-Sum based method(GSM). Gaussian-sum/exponential-sum approximation and kernel truncation technique, combined with finite Fourier series and Taylor expansion, finally lead to a O(N log N) fast algorithm achieving spectral accuracy. Applications to NLSE are reviewed. Tree-algorithm to compute the onedimensional convolutions in lighting-shield simulation is also covered in the last section.

 

 

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