哈尔滨工业大学（深圳）学术讲座

演讲人Speaker：  邱建贤  

题目Title: High-order conservative positivity-preserving DG-interpolation for deforming meshes and application to moving mesh DG simulation of radiative transfer

时间Date：   2023年 10月 27 日    Time：15:00 -16:00

地点Venue：   H栋 403室

内容摘要Abstract： 

Solution interpolation between deforming meshes is an important component for several applications in scientific computing, including indirect arbitrary-Lagrangian-Eulerian and rezoning moving mesh methods in numerical solution of partial differential equations. In this presentation, a high-order, conservative, and positivity-preserving interpolation scheme is developed based on the discontinuous Galerkin solution of a linear time-dependent equation on deforming meshes. The scheme works for bounded but otherwise arbitrary mesh deformation from the old mesh to the new one. The cost and positivity preservation (with a linear scaling limiter) of the DG-interpolation are investigated. Numerical examples are presented to demonstrate the properties of the interpolation scheme. The DG-interpolation is applied to the rezoning moving mesh DG solution of the radiative transfer equation, an integro-differential equation modeling the conservation of photons and involving time, space, and angular variables. Numerical results obtained for examples in one and two spatial dimensions with various settings show that the resulting rezoning moving mesh DG method maintains the same convergence order as the standard DG method, is more efficient than the method with a fixed uniform mesh, and is able to preserve the positivity of the radiative intensity.

个人简介(About the speaker):

邱建贤，厦门大学数学科学学院特聘教授、博士生导师，闽江学者，从事计算流体力学及微分方程数值解法的研究工作，担任《Journal of Computational Physics》、《Numerical Mathematics: Theory, Methods and Applications》、《Advances in Applied Mathematics and Mechanics》等杂志的编委。在间断Galerkin有限元（DG）和加权本质无振荡（WENO）方法的研究及其在计算流体力学及工程界的应用方面取得出色成果，发表了一百四十多篇SCI论文，主持两项国家自然科学基金重点项目。参与欧盟第六框架特别研究项目,是项目组中唯一非欧盟的成员，多次应邀在国际会议上作大会报告。获2020年度教育部自然科学奖二等奖，2021年度福建省自然科学奖二等奖各一项。