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報告題目：
Analysis-based fast algorithms for convolution-type nonlocal potential in Nonlinear Schr?dinger equation

報告人： 張勇 （奧地利維也納大學(xué)與美國克朗數(shù)學(xué)研究所）博士后

報告時間與地點(diǎn)：2017年5月5日（星期五）15:00點(diǎn)-16:00點(diǎn) 卓遠(yuǎn)樓統(tǒng)數(shù)學(xué)院307會議室

報告主持人：王漢權(quán) 統(tǒng)計與數(shù)學(xué)學(xué)院副院長、教授

報告內(nèi)容摘要：

Convolution-type potential are common and important in many science and engineering
fields. E_cient 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 potentials that are generated by isotropic and anisotropic smooth and fast-decaying density. 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 efficiency. The state-of-art fast algorithms includeWavelet 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.


報告參考文獻(xiàn)：
[1] W. Bao, S. Jiang, Q. Tang and Y. Zhang, Computing the ground state and dynamics of the nonlinear Schr?dinger equation with nonlocal interactions via the nonuniform FFT, J. Comput. Phys., 296 (2015), pp. 72–89.
[2] L. Exl, N.J.Mauser and Y. Zhang, Accurate and e_cient computation of nonlocal potentials based on Gaussian-sum approximation, J. Comput. Phys., 327 (2016), pp. 629–642.
[3] X. Antoine, Q.L. Tang and Y. Zhang, On the ground states and dynamics of space fractional nonlinear Schr?dinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions, J. Comput. Phys., 325 (2016), pp. 74–97.

報告人簡介：
張勇博士后2012年于清華大學(xué)數(shù)學(xué)學(xué)院取得博士學(xué)位后一直于奧地利維也納大學(xué)Wolfgang Pauli研究所與美國著名的數(shù)學(xué)研究所--克朗數(shù)學(xué)研究所等地做博士后。他最近在快速算法設(shè)計與相關(guān)物理應(yīng)用取得不少先進(jìn)的研究成果。