报告题目：An efficient Fourier-Legendre spectral-Galerkin method for problems in 2D complex geometries

报 告 人：王中庆教授（上海理工大学）

报告时间：2022年12月8日  14:30

报告地点：腾讯会议（362206288）

报告摘要：

A polar coordinate transformation is introduced, which transforms the complex gcomectrics into a unit disc and plays an important role in designing spectral-Galerkin methods for various differential equations in two-dimensional complex geometries. Some basic properties of the polar coordinate transformation are given. As applications, we consider the Helmholtz equation in two-dimensional complex geometries. The existence and uniqueness of the weak solution are proved, the Fourier-Legendre spectral-Galerkin scheme is constructed and the optimal convergence of numerical solutions under SH^ 1$-norm is analyzed. The proposed method is very effective and easy to implement for problems in 2D complex geometries. Numerical results are presented to demonstrate the high accuracy.

报告人简介：

王中庆，上海理工大学教授、博导，上海市曙光学者。主要从事偏微分方程谱方法的研究工作，在《Found. Comput. Math.》《SIAM J. Numer. Anal.》和《Math. Comp.》等国内外学术期刊上发表论文90余篇，主持和参与科研项目20余项。