报告人：邵嗣烘（北京大学）

时间：2022年07月20日10:30-

报告地点：理科楼LD202

摘要：Unbounded domain problems arise in many scientific applications and adaptive numerical methods are needed on many occasions. Despite adaptive methods in bounded domains have witnessed numerous advances in their efficiency and accuracy, there are few adaptive methods that apply in unbounded domains. In this talk, we first propose a scaling technique and a moving technique to adaptively cluster enough collocation points in a region of interest in order to achieve fast spectral convergence.  Our scaling algorithm employs an indicator in the frequency domain that is used to determine when scaling is needed and informs the tuning of a scaling factor to redistribute collocation points to adapt to the diffusive behavior of the solution. Our moving technique adopts an exterior-error indicator and moves the collocation points to capture the translation. Then, we propose a frequency-dependent p-adaptive technique that adaptively adjusts the expansion order based on a frequency indicator.  Using this $p$-adaptive technique, combined with the scaling and moving techniques, we are able to devise an adaptive spectral method in unbounded domains that can capture and handle diffusion, advection, and oscillations.

简介：邵嗣烘，北京大学数学科学学院副教授，毕业于北京大学数学科学学院并获得理学学士和博士学位，先后到访过北卡罗莱那大学夏洛特分校，香港科技大学，普林斯顿大学、塞维利亚大学和香港中文大学等。主要开展面向智能、量子和计算的交叉融合研究，落脚点在基础的数学理论和高效的算法设计，强调离散数学结构的设计、分析和应用。具体研究领域包括：高维问题的数值方法、组合优化、计算量子力学、图（网络）上的数学及其算法、微分方程数值解和脑科学等，获国家自然科学基金青年基金、面上项目和优秀青年基金连续资助。2019年入选北京智源人工智能研究院“智源青年科学家”。2020年获北京大学优秀博士学位论文指导老师。2021年获北京大学黄廷芳/信和青年杰出学者奖。曾获中国计算数学学会优秀青年论文一等奖，北京大学学术类创新奖，北京大学优秀博士学位论文三等奖，宝洁教师奖和北京大学优秀班主任等。

邀请人：王坤

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