报告人：仲杏慧教授

报告题目：An improved simple WENO limiter for discontinuous Galerkin methods solving hyperbolic systems on unstructured meshes

报告摘要：

(1) Discontinuous Galerkin (DG) method is a class of finite element methods that has gained popularity in recent years due to its flexibility for arbitrarily unstructured meshes, with a compact stencil, and with the ability to easily accommodate arbitrary h-p adaptivity. In this talk, we improve the simple WENO limiter designed for DG methods for solving hyperbolic systems on unstructured meshes. The major improvement is reducing the number of polynomials transformed to the characteristic fields for each direction. For the triangular mesh, this new simple WENO limiter transforms only two polynomials to the characteristic fields for each direction, while the original simple WENO limiter uses four polynomials. Thus the improved simple WENO limiter reduces the computational cost and improves the efficiency. It provides a simpler and more practical and efficient way to the characteristic-wise limiting procedure, while still simultaneously maintaining uniform high-order accuracy in smooth regions and controlling spurious nonphysical oscillations near discontinuities.      

(2) We also apply this improved simple WENO limiter to a high order method constructed for solving hyperbolic conservation laws on arbitrarily distributed point clouds, where polygonal meshes are constructed based on the random points and the traditional DG method was adopted on the constructed polygonal mesh. For such a complex polygonal mesh, this limiter still transforms only two polynomials to the characteristic fields. Thus the simplicity and efficiency of this new limiter is more evident in this case. Numerical results are provided to illustrate the accuracy and effectiveness of this procedure. For some examples, the improved limiter has less smearing and higher resolution than the original one.

报告时间：2022年10月29日上午8:00-11:00

报告形式：腾讯会议；会议号：451-707-526

获取会议密码请发邮件至：mathgzc@hit.edu.cn

报告人简介：仲杏慧于2007年获中国科学技术大学学士学位，2012年获美国布朗大学博士学位，导师为舒其望教授。2012-2016分别在密歇根州立大学和犹他大学从事博士后研究工作。现任浙江大学百人计划研究员、博士生导师。2016年入选中组部高层次青年人才计划。研究方向为数值分析，科学计算，不确定性量化等领域，主要研究工作包括间断有限元方法的算法设计及其分析、动理学传输方程的数值模拟及其在等离子体物理中的应用、不确定量化及随机计算算法及应用等方面。