应兰州大学数学与统计学院邀请，兰州大学聂大鑫博士后将于2024年12月9日作学术报告。

报告题目:A physics-informed finite difference method for d-dimensional fractional Poisson equation on arbitrary bounded domain

时 间：2024年12月9日14：30

地 点：理工楼402

报告摘要：Inspired by the idea of `walk-on-sphere' algorithm, we propose a novel finite difference framework for solving the fractional Poisson equation under the help of the Feynman-Kac representation of its solution, i.e., physics-informed finite difference scheme. By choosing suitable basis functions in interpolatory quadrature and using graded meshes, the convergence rates can achieve up to $O(h^{2})$ in arbitrary $d$-dimensional bounded Lipschitz domain satisfying the exterior ball condition, where $d>1$; while the convergence rate can reach $O(h^{10})$ in one-dimensional bounded domain under some regularity assumptions on the source term $f$. Furthermore, we propose a concise convergence analysis and several numerical examples in different domains, including circle, L-shape, and pentagram, are provided to illustrate the effectiveness of the above built scheme.

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报告人简介

聂大鑫，兰州大学博士后。研究方向主要为非局部偏微分方程数值解、多尺度模型算法及分析等。获得国家自然科学基金青年基金、中国博士后科学基金面上项目、中央高校基本科研业务费博士后创新项目等资助。在SINUM、Numer. Math.、ESAIM Math. Model. Numer. Anal.等期刊上发表论文多篇。

数学与统计学院

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2024年12月6日