A Kernel-Independent Uniform Fast Multipole Method Based on Barycentric Rational Interpolation      

主讲人：梁江丽（广西民族大学）

摘要：The original uniform fast multipole method (UFMM) based on Lagrange interpolation at equispaced grids allows the moment-to-local (M2L) translation to be accelerated by FFT, but it suffers from the Runge phenomenon as the number of interpolation nodes increases, leading to instability and loss of accuracy. This talk presents a kernel-independent UFMM based on the Floater–Hormann barycentric rational interpolant, which preserves the FFT-accelerated M2L operators while significantly improving the stability and accuracy of the scheme for high-order interpolation. A modified smooth-UFMM is further introduced for sufficiently smooth kernels, in which the interactions of nearby cells are also transferred through local expansions. Numerical experiments on the pressure and velocity computations arising from the method of regularized Stokeslets, as well as on the inverse quadratic kernel, demonstrate that the proposed methods outperform the original UFMM in accuracy, stability and efficiency.

主讲人简介：梁江丽，广西民族大学数学科学学院讲师。主要从事计算数学方向的研究，研究兴趣包括快速多极子方法、快速边界元方法、重心有理插值与多项式逼近，及其在积分方程数值解、Stokes 流等科学计算问题中的应用。相关研究成果发表于 Numerical Algorithms、Computers & Mathematics with Applications 等期刊。   

邀请人：王海永

时间：10月24号下午14:30-16:30

地点： 腾讯会议室：759-936-598