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An efficient Fourier-Legendre spectral-Galerkin method for problems in 2D complex geometries

主讲人：王中庆

摘要：A polar coordinate transformation is considered, which transforms the complex geometries into a unit disc. 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 $HA1$-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 of our spectral-Galerkin method.

主讲人简介：王中庆，上海理工大学教授、博导，长期从事微分方程数值方法的研究工作，在《Found. Comput. Math.》、《SIAM J. Numer. Anal.》、《Math. Comp.》、《IMA J. Numer. Anal.》以及《J. Comput. Phys.》等国内外学术期刊上发表论文八十余篇。

邀请人：王海永

时间：2022年12月13日（星期二）10:00-12：00

地点：腾讯会议室    ID:          908 932 224