统计与数学学院数学讲座
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发布时间：2021-07-03
统计与数学学院数学讲座
报告题目：
Analysis-based fast algorithms for convolution-type nonlocal potential in Nonlinear Schr?dinger equation
报告人： 张勇 （奥地利维也纳大学与美国克朗数学研究所）博士后
报告时间与地点：2017年5月5日（星期五）15:00点-16:00点 卓远楼统数学院307会议室
报告主持人：王汉权 统计与数学学院副院长、教授
报告内容摘要：
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.
报告参考文献：
[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.
报告人简介：
张勇博士后2012年于清华大学数学学院取得博士学位后一直于奥地利维也纳大学Wolfgang Pauli研究所与美国著名的数学研究所--克朗数学研究所等地做博士后。他最近在快速算法设计与相关物理应用取得不少先进的研究成果。
报告题目：
Analysis-based fast algorithms for convolution-type nonlocal potential in Nonlinear Schr?dinger equation
报告人： 张勇 （奥地利维也纳大学与美国克朗数学研究所）博士后
报告时间与地点：2017年5月5日（星期五）15:00点-16:00点 卓远楼统数学院307会议室
报告主持人：王汉权 统计与数学学院副院长、教授
报告内容摘要：
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.
报告参考文献：
[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.
报告人简介：
张勇博士后2012年于清华大学数学学院取得博士学位后一直于奥地利维也纳大学Wolfgang Pauli研究所与美国著名的数学研究所--克朗数学研究所等地做博士后。他最近在快速算法设计与相关物理应用取得不少先进的研究成果。
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