报告人：盛长滔

邀请人：刘文杰

报告题目：Stochastic methods for PDEs driven by \alpha-stable Lévy process

摘要：In this talk, we introduce the Monte Carlo methods for solving high dimensional PDEs driven by \alpha-stable Lévy process, also known as PDEs involving integral fractional Laplacian (IFL). We first introduce the Feynman-Kac representation based on the Green function for the IFL on the unit ball in arbitrary dimensions. The proposed algorithm finds it remarkably efficient in solving fractional PDEs: it only needs to evaluate the integrals of expectation form over a series of inside ball tangent boundaries with the known Green function. Moreover, we carry out the error estimates of the proposed method for complex domain in high dimensions. Ample numerical results are presented to demonstrate the robustness and effectiveness of the proposed method. Finally, we extended the proposed algorithm to solve linear and semi-linear parabolic PDEs in high dimensions.

报告时间：2023年12月23 日10：00—11：00 

报告地点：理学楼609

报告人简介：盛长滔，上海财经大学，2018年于厦门大学获得理学博士学位，之后在新加坡南洋理工大学从事博士后研究。主要研究方向为谱方法和谱元法以其应用、高维偏微分方程的随机算法等。主持国家自然科学青年基金和上海市浦江人才计划。目前为止，在SIAM J. Numer. Anal., Math. Comp., ESAIM M2AN.等知名国内外期刊上发表论文20篇。