主題：Efficient and accurate stochastic methods for high dimensional PDEs with jump

時間：12月12日 14:00-15:30

地點：騰訊會議（會議號：902-399-901）

主持人：邵文婷

報告人簡介：

盛長滔，上海財經(jīng)大學(xué)數(shù)學(xué)學(xué)院副教授，博士生導(dǎo)師，2018年于廈門大學(xué)獲得理學(xué)博士學(xué)位，之后在新加坡南洋理工大學(xué)從事博士后研究。主要研究方向為譜與譜元法以其應(yīng)用,、非局部問題和奇性問題的高精度數(shù)值方法、高維偏微分方程的隨機算法等,。目前為止,，在SIAM系列, Math. Comp.等知名國內(nèi)外期刊上發(fā)表SCI論文20余篇。

講座簡介：

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.