应用数学青年讨论班(午餐会)--A high-accurate and efficient numerical homogenization method for quasiperiodic multiscale problems
报告人：李蒙(湘潭大学)
时间：2026-04-02 12:00-13:30
地点：智华楼四元厅
摘要：Quasiperiodic multiscale problems are prevalent in materials science and physics. Quasiperiodic homogenization theory is a powerful tool for analyzing such problems. However, accurately and efficiently solving the corrector equation in the whole space and computing the quasiperiodic homogenized coefficients pose major numerical challenges. Based on the projection method, we develop a highly efficient and accurate quasiperiodic numerical homogenization method for quasiperiodic multiscale elliptic equations. The proposed approach effectively overcomes Diophantine errors arising from the approximation of irrational numbers by rational ones. The numerical analysis establishes spectral convergence. Moreover, we numerically verify the convergence from the multiscale solution to the homogenized limit, consistent with homogenization theory, thus confirming the effectiveness of our method. The proposed framework has been extended to quasiperiodic parabolic and Hamilton–Jacobi equations, offering an accurate computational approach for a range of quasiperiodic multiscale PDEs.
报告人简介：李蒙，湘潭大学数学与计算科学学院博士，师从蒋凯教授。主要研究方向为准周期多尺度问题的计算与理论分析，专注于高精度准周期数值均匀化方法。博士期间入选中国科协青年科技人才培育工程博士生专项计划，荣获国家奖学金，并主持湖南省研究生科研创新项目一项。
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