讲座题目：Accurate and efficient computation of some nonlocal potentials based on Gaussian-sum approximation

主讲人：张勇博士（维也纳大学）

主持人：陈秀卿教授

时 间：2015年3月5日（周四）上午10:00-11:00

地 点：主楼1214

主要内容：

We introduce an accurate and efficient method for the evaluation of a class of free space nonlocal potentials, such as the free space Coulomb and Poisson potential in 2D/3D and dipolar potential in 2D/3D. Starting from the convolution formulation, for smooth and fast decaying densities, we make a full use of the Fourier pesudospectral (plane wave) approximation of the density and a separable Gaussian sums approximation of the kernel in an interval where the singularity point (the origin) is excluded. Hence, the potential is split into a regular integral and a correction integral, and the latter is well resolved utilising a low-order Taylor expansion of the density. Both can be computed with fast Fourier transforms (FFT). The method is accurate (14-16 digits), efficient (O (N log N) complexity), low in storage, easily adaptable to other different kernels, applicable for anisotropic densities and highly parallel able.

主讲人简介：

Yong ZHANG，Wolfgang Pauli Institute，Ph.D. in Mathematics, Tsinghua University。

Research Interests：

• Fast algorithms and their applications

• Computational electromagnetic

• Numerical methods and analysis of differential equations

• Highly oscillatory system

• Bose-Einstein Condensate