主题：Efficient and accurate stochastic methods for high dimensional PDEs with jump
时间：12月12日 14:00-15:30
地点：腾讯会议（会议号：902-399-901）
主持人：邵文婷
报告人简介：
盛长滔，上海财经大学数学学院副教授，博士生导师，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。主要研究方向为谱与谱元法以其应用、非局部问题和奇性问题的高精度数值方法、高维偏微分方程的随机算法等。目前为止，在SIAM系列, Math. Comp.等知名国内外期刊上发表SCI论文20余篇。
讲座简介：
In this talk, we will introduce efficient Monte Carlo methods for solving a class of high-dimensional PDEs on irregular domains. The key idea of these stochastic algorithms is the probabilistic representation, also known as the Feynman-Kac formula, which reformulates the solution of PDEs into an expectation form, thereby enabling the solution to be obtained through the simulation of stochastic paths. The proposed algorithm bypasses the need to solve linear systems and proves remarkably efficient in solving high-dimensional PDEs, as it only requires the evaluation of expectation-form integrals over a series of inside balls with the known Green function and Poisson kernel. Consequently, we can overcome the curse of dimensionality and demonstrate that the proposed method is well-suited for solving PDEs over irregular domains. Moreover, we introduce the spectral Monte Carlo iterative method, which effectively integrates multiple computational techniques, including interpolation based on orthogonal polynomials/functions, space-time spectral collocation methods, control variates, and the novel walk-on-sphere method. Extensive numerical results are provided to demonstrate the accuracy and efficiency of the proposed method, validating the theoretical findings.
