报告题目：GoFD and Meshfree GoFD method for the fractional Laplacian on arbitrary bounded domains
报 告 人： 沈金叶 副教授 西南财经大学
报告时间：2024年4月16日 9:30-10:30
报告地点：#腾讯会议：268-515-977，会议密码：20857
校内联系人： wxjldx@jlu.edu.cn
报告摘要：A grid-overlay finite difference method (GoFD) was proposed and developed for the numerical solution of homogeneous Dirichlet boundary value problems of the fractional Laplacian on arbitrary bounded domains. It was shown to have advantages of both finite difference and finite element methods, including its efficient implementation through the fast Fourier transform and ability to work for complex domains and with mesh adaptation. The purpose of this talk is to introduce GoFD and GoFD in a meshfree setting. GoFD method uses an unstructured simplicial mesh and an overlay uniform grid for the underlying domainand constructs the approximation based on a uniform-grid finite difference approximation and a data transfer from the unstructured mesh to the uniform grid. It is shown that its stiffness matrix is similar to a symmetric and positive definite matrix and thus invertible if the data transfer has full column rank and positive column sums. Moreover, a key of meshfree GoFD is to construct the data transfer matrix from a given point cloud to a uniform grid. Two approaches are proposed, one based on the moving least squares fitting and the other based on the Delaunay triangulation and piecewise linear interpolation. Numerical results obtained for examples with convex and concave domains and various types of point clouds are presented.
报告人简介： 沈金叶，副教授，西南财经大学必威硕士生导师。研究兴趣：金融期权定价模型的数值算法，Bernoulli 自由边界问题的自适应算法，非线性发展方程的差分方法，分数阶模型的数值算法。主持国家自然科学基金青年基金项目1项，参与完成国家自然科学基金面上项目2项。近5年在国际主流计算数学，金融数学杂志上发表学术论文20余篇。长期从事《数值分析》《偏微分方程数值解》等课程的教学工作。
