报告人：李焕荣 （重庆工商大学）

时间：2021年6月16日15:30开始

地点：理科楼LA106

摘要:The Allen-Cahn equation has been widely used in all kinds of fields, such as image processing, materials science, and fluid dynamics. Therefore, it is indispensable to propose some efficient and accurate numerical schemes to solve the Allen-Cahn equation. The reduced-order finite difference (ROFD) method and reduced-order finite element (ROFE) method are proposed to simulate the Allen-Cahn equation, based on the proper orthogonal decomposition (POD) method with the snapshot technique. We first derive the FD and FE formulations of the Allen-Cahn equation and compute its FD and FE solutions, from which we choose a few solutions as snapshots. Based on the POD technique, we establish the low-order numerical models of ROFD and ROFE formulations for the Allen-Cahn equation. We also prove error estimates of the ROFD and ROFE solutions of the Allen-Cahn equation.  Finally, some numerical results are provided to test the validity of the reduced-order numerical formulations.

简介:李焕荣，重庆工商大学数学与统计学院教授，硕士生导师， 研究方向为偏微分方程数值解。在《Appl. Math. Comput.》，《Appl. Math. Model.》，《Comput. Math. Appl.》，《Numer.Meth.Part.D.E.》等期刊发表学术论文多篇，主持和参与完成三项国家自然科学基金项目，主持完成多项重庆市自然科学基金项目和重庆市教委项目，主持完成一项中科院重点实验室(LASG)开放课题，荣获萧玉丽优秀教师奖。

邀请人：王坤

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