报告题目：High-order conservative positivity-preserving DG-interpolation for deforming meshes and application to moving mesh DG simulation of radiative transfer
时 间：2022年1月8日（星期六）下午14:45-15:45
地 点：理工北楼601
主 办：数学与统计学院, 福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）、福建师范大学数学研究中心
参加对象：感兴趣的老师和研究生
报告摘要：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.
报告人简介：邱建贤，厦门大学数学科学学院闽江学者、特聘教授，国际著名刊物 “J. Comp. Phys.” (计算物理) 编委。从事计算流体力学及微分方程数值解法的研究工作，在间断Galerkin（DG）、加权本质无振荡（WENO）数值方法的研究及其应用方面取得了一些重要成果，已发表论文一百多篇。主持国家自然科学基金重点项目和联合基金重点支持项目各一项, 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，获2020年度高等学校科学研究优秀成果奖（科学技术）--自然科学奖二等奖。多次应邀在国际会议上作大会报告。