学术报告20251217：Stabilized enhancement for large time computation using exponential spectral process method

报告人：王翔 教授 吉林大学

报告题目：Stabilized enhancement for large time computation using exponential spectral process method

摘 要：We propose an exponential spectral process (ESP) method for time discretization of spatial-temporal equations. The proposed ESP method uses explicit iterations at each time step, which allows us to use simple initializations at each iteration. This method has the capacity to obtain high accuracy (up to machine precision) with reasonably large time step sizes. Theoretically, the ESP method is proved to be unconditionally energy stable for arbitrary iteration steps for the case of using two spectral points. It is worth mentioning that, a operator matrix is introduced in the energy stability analysis, which avoids the problem of combinatorial explosion in multi-stage time discretizations. To demonstrate the advantages of the ESP method, we consider two applications which have stability difficulties in large time simulations. One of them is the Allen-Cahn equation with the symmetry breaking problem faced by most of the existing time discretizations, and the second one is about the complex Ginzburg-Landau equation which also suffers from large time instability.

报告人简介：王翔教授，吉林大学数学学院，博士生导师。主要从事偏微分方程的高精度时空离散算法研究，在有限体积元法的最佳L2构造理论与超收敛性质，以及相场模型时间指数谱过程方法等方面做出了系列工作，在《SIAM J. Numer. Anal.》《Math. Comp.》《J. Comput. Phys.》《Sci. China Math.》《J. Sci. Comput.》《Adv. Comput. Math.》等期刊发表论文十余篇。主持国家自然科学基金面上项目、青年科学基金项目、国家重点研发计划校内子课题等项目。

报告时间：2025年12月17日，10:00--13:00

报告地点：腾讯会议（会议号：480-988-131）

欢迎广大师生参加！

内蒙古大学数学科学学院

2025年12月11日