数学与信息科学学院学术报告（20170526-2）
 发布时间：2017-05-23 浏览次数：
 数学与信息科学学院学术报告 （20170526-2） 题 目: Efficient and accurate spectral methods for PDEs with weakly singular solutions 时 间：2017年5月26日(星期五)下午15:00 报告人：Jie Shen教授(Purdue University，厦门大学) 地 点：先骕楼数信学院四楼3425多媒体报告厅 摘要：The usual spectral methods will provide high-order accuracy for problems with smooth solutions. However, they may not work well for problems with singular solutions due to various facts such as corner singularities, non-matching boundary conditions, non-smooth coefficients. If the form of the singular expansion for the solution is known, we develop a Muntz Galerkin method which is based on specially tuned Muntz polynomials to deal with the singular behaviors of the underlying problems, and show that it provide optimal error estimates. On the other hand, if the Muntz Galerkin method is not applicable or efficient, we present a new extended spectral-Galerkin method which allows us to split it into two separate problems: one is to find an approximation for the smooth part by a usual spectral method, the other is to determine an approximation to the singular part with $k$ terms by solving a $k\times k$ system. So the new method is very easy to implement, very efficient and is capable of providing very accurate approximations for a class of singular problems. We will present ample numerical results for a variety of problems with singular solutions, including fractional PDEs, to demonstrate the effectiveness of our approaches.   报告人简介： 沈洁教授：江西人，美国普渡大学应用数学和计算中心主任，美国数学会会士，厦门大学数学学院教授，中组部“千人计划”入选者。沈教授1982年毕业于北京大学，1987年在巴黎南大学获得计算数学博士学位。先后在美国宾西州立大学和中弗罗里达大学任职，2002年至今在普渡大学任职。     沈老师是多个国际重要数学杂志的编辑，发表论文170余篇，出版专著2部。主要研究谱方法及其在流体动力学和材料科学中的应用。