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报告题目: MCMS-RBM: Multi-Component Multi-State Reduced Basis Method toward Rapid Generation of Phase Diagrams for the Lifshitz-Petrich Model
报告人：纪丽洁 讲师 上海大学 理学院数学系
报告时间：2025年12月4日上午10:00-11:00
报告地点：红瓦楼726
报告内容简介：Due to quasicrystals having long-range orientational order but without translational symmetry, traditional numerical methods usually suffer when applied as is. In the past decade, the projection method has emerged as a prominent solver for quasiperiodic problems. Transforming them into a higher dimensional but periodic ones, the projection method facilitates the application of the fast Fourier transform. However, the computational complexity inevitably becomes high which significantly impedes the generation of the phase diagram.To address the computational challenge of quasiperiodic problems based on the projection method, this talk introduces a multi-component multi-state reduced basis method (MCMS-RBM). Featuring multiple components with each providing reduction functionality for one branch of the problem induced by one part of the parameter domain, the MCMS-RBM does not resort to the parameter domain configurations (e.g. phase diagrams) a priori. It enriches each component in a greedy fashion via a phase-transition guided exploration of the multiple states inherent to the problem. Adopting the empirical interpolation method, the resulting online-efficient method vastly accelerates the generation of a delicate phase diagram to a matter of minutes for a parametrized two-turn-four dimensional Lifshitz-Petrich model with two length scales. Moreover, it furnishes surrogate and equally accurate field variables anywhere in the parameter domain.
报告人简介：纪丽洁，上海大学数学系讲师。2021年博士毕业于上海交通大学，导师徐振礼教授。2019年至2020年在马萨诸塞大学达特茅斯分校访学一年。2021年至2023年，在上海交通大学博士后流动站从事博士后研究。主要研究方向为电荷输运问题的理论和数值分析、参数化偏微分方程的模型降阶算法、等离子体物理的数值算法以及黑盒优化问题等。在SIAM J. Appl. Math., SIAM J. Sci. Comput., J. Comput. Phys.，J. Sci. Comput.等期刊发表论文。获得2021年上海市超级博士后奖励计划资助，主持过中国博士后科学基金面上1项，现主持国家自然科学基金青年基金1项。
报告邀请人：方礼冬
