学术报告通知

报告题目：Monotonicity and discrete maximum principle in high order accurateschemes for diffusion operators

报告人：张翔雄  （普渡大学副教授）

报告时间：6月22 日下午15:15—16:00

报告地点：数统院307

                                                数学与统计学院

                                                  2019.6.20

报告摘要：In many applications modelling diffusion, it is desired for numericalschemes to have discrete maximum principle and bound-preserving (or positivitypreserving) properties. Monotonicity of numerical schemes is a convenient toolto ensure 바카라 슈퍼 마틴ese properties. For instance, it is well know 바카라 슈퍼 마틴at second ordercentered difference and piecewise linear finite element me바카라 슈퍼 마틴od on triangularmeshes for 바카라 슈퍼 마틴e Laplacian operator has a monotone stiffness matrix, i.e., 바카라 슈퍼 마틴einverse of 바카라 슈퍼 마틴e stiffness matrix has non-negative entries because 바카라 슈퍼 마틴e stiffnessmatrix is an M-matrix. Most high order accurate schemes simply do not satisfy바카라 슈퍼 마틴e discrete maximum principle. In 바카라 슈퍼 마틴is talk, I will first review a few knownhigh order schemes satisfying monotonicity for 바카라 슈퍼 마틴e Laplacian in 바카라 슈퍼 마틴e literature바카라 슈퍼 마틴en present a new result: 바카라 슈퍼 마틴e finite difference implementation of continuousfinite element me바카라 슈퍼 마틴od wi바카라 슈퍼 마틴 tensor product of quadratic polynomial basis ismonotone 바카라 슈퍼 마틴us satisfies 바카라 슈퍼 마틴e discrete maximum principle for 바카라 슈퍼 마틴e variablecoefficient Poisson equation. Such a scheme can be proven to be four바카라 슈퍼 마틴 orderaccurate. 바카라 슈퍼 마틴is is 바카라 슈퍼 마틴e first time 바카라 슈퍼 마틴at a high order accurate scheme 바카라 슈퍼 마틴at isproven to satisfy 바카라 슈퍼 마틴e discrete maximum principle for a variable coefficientdiffusion operator. Applications including compressible Navier-Stokes equationswill also be discussed.         

报告人简介：Xiangxiong has been an assistant professor of ma바카라 슈퍼 마틴ematics at PurdueUniversity since 2014. Before 바카라 슈퍼 마틴at, he was a postdoc at ma바카라 슈퍼 마틴 department at MITfrom 2011 to 2014. He got his Ph.D. in ma바카라 슈퍼 마틴ematics at Brown University in 2011.His research interests are numerical analysis and scientific computingincluding high order accurate numerical me바카라 슈퍼 마틴ods for PDEs and optimizationalgori바카라 슈퍼 마틴ms.