Jing Gao, Associate Professor, Xi'an Jiaotong University

Yifa Tang, Professor

A framework for stable spectral methods in d-dimensional unit balls

14:00-15:00 May 11(Sunday), N702

The subject of this talk is the design of efficient and stable spectral methods for time-dependent partial differential equations in unit balls. We commence by sketching the desired features of a spectral method, which is defined by a choice of an orthonormal basis acting in the spatial domain. We continue by considering in detail the choice of a W-function basis in a disc in R^2. This is a nontrivial issue because of a clash between two objectives: skew symmetry of the differentiation matrix and the correct behaviour at the origin. We resolve it by representing the underlying space as an affine space and splitting the underlying functions. This is generalised to any dimension d\geq2 in a natural manner and the talk is concluded with numerical examples that demonstrate how our choice of basis attains the best outcome out of a number of alternatives.

报告人简介：高静，西安交通大学数学与统计学院副教授、研究生导师，英国剑桥大学博士后。主要致力于谱方法、高振荡现象及其计算、渐近分析和微积分方程数值算法的研究。在Mathematics of Computation、Journal of Computational Physics、BIT Numerical Mathematics、IEEE Transactions on Geoscience and Remote Sensing、Nonlinear Analysis、Science China Mathematics等国内外重要学术期刊杂志上发表论文30多篇。同时，主持完成国家自然科学基金2项和教育部博士点专项1项、陕西省工业攻关项目和自然科学基金等各类科研项目4项。