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【10月19日、10月26日、11月2日】数学学术系列讲座

】【打印】【关闭窗口 来源:统计与数学学院 作者:统计与数学学院 编辑:张薇 发布时间:2020-10-19
  报告题目:Fast algorithm for convolution-type potential evaluation in quantum mechanics and engineering problems(系列讲座)
  主讲人:张勇教授(天津大学应用数学中心)
  时间:
  系列讲座之一:2020年10月19日(周一)10:30 a.m.
  系列讲座之二:2020年10月26日(周一)10:30 a.m.
  系列讲座之三:2020年11月2日(周一)10:30 a.m.
  形式:线上讲座
  主办单位:统计与数学学院
   会议链接:
  系列讲座之一:https://meeting.tencent.com/s/S2218JFQTYCq
  系列讲座之二:https://meeting.tencent.com/s/UjDyv201PWNB
  系列讲座之三:https://meeting.tencent.com/s/UjDyv201PWNB
  摘要:
Convolution-type potential are common and important in many science and engineering fields. Efficient and accurate evaluation of such nonlocal potentials are essential in practical simulations. In this serial-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 difference 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 efficiency. 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) algorithm achieving spectral accuracy. For the one-dimensional convolutions, we shall introduce the tree and sum-of-exponential based fast algorithm.
  Part I:The series topic will cover the following topics
                   Spectral method on bounded domain and PDE-based algorithm
       
  Part II:The series topic will cover the following topics
                  (1)NUFFT-based fast convolution solver and related application
                  (2) GauSum approximation and Fast Convolution Solver

  Part III:
The series topic will cover the following topics
                     1) Kernel truncation method and Anisotropic Kernel Truncation method 
                     2) Fast one-dimensional Solver based on Sum-Of-Exponentials
 


  主讲人简介:
  张勇,男,天津大学应用数学中心。2012年于清华大学数学学院取得博士学位后,于奥地利维也纳大学Wolfgang Pauli研究所、美国著名的数学研究所——克朗数学研究所等地进行博士后研究。近年来,张勇博士在快速算法设计与相关物理应用取得了不少先进的研究成果。