学术报告一
报告人:冯新龙教授 (新疆大学)
报告题目:A positivity preserving characteristic FEM for solving the convection-diffusion-reaction equations on general surfaces
报告时间:9月22日15:00-16:00
报告地点:25教14楼学术报告厅
参加人员:教师、研究生、本科生
报告摘要:In this talk, a positivity preserving characteristic FEM is presented to solve the transport and convection-diffusion-reaction equations on general surfaces. The FEM applied in this work is the surface FEM which solves a variation problem by the linear FEM on a approximate triangulated surface. For the backtracking in characteristic derivative discretization, unlike the cases on the two-dimensional plane, the foots of approximate characteristics may locate in the outer domain of the surface. To determine the value of solution at the foots of characteristics, a new strategy which permits larger time steps is designed instead of the discrete closest point mapping method which has a strict time step restriction. Via the mass lumping technique, the proposed numerical scheme is positivity preserving. The proposed method can also be extended to the problems with nonlinear convection terms. Various numerical examples are performed to demonstrate the validity and accuracy of the proposed method.
报告人简介:冯新龙,教授,博士生导师,工作单位:新疆大学数学与系统科学学院;研究领域:科学计算、不确定性量化、计算流体力学、图像处理与数据分析、保险精算等。1998年毕业于新疆大学基础数学专业,获学士学位; 2001年毕业于新疆大学计算数学专业,获硕士学位; 2007年毕业于西安交通大学数学专业,获博士学位。先后在韩国首尔国立大学、香港浸会大学、巴西巴拉那联邦大学、加拿大阿尔伯塔大学从事博士后研究工作和短期访问。
拥有中国准精算团队格,曾担任中国核学会计算物理学会理事、中国计算数学学会理事,目前担任中国数学会理事。曾荣获教育部高等院校青年教师奖、自治区科学技术进步奖以及新疆青年科技奖等。曾入选教育部新世纪优秀人才支持计划、自治区杰出青年科技创新人才培养人选等。主持完成10余项国家级和省部级科研项目。已在SISC、MCOM、CMAME、JCP、IJNME、JSC、DCDS、NMPDE等国际著名期刊合作发表SCI论文100余篇。
学术报告二
报告人:王坤副教授 (重庆大学)
报告题目:Time discretization scheme based on non-uniform mesh for the problem with singularity near the initial time
报告时间:9月22日16:00-17:00
报告地点:25教14楼学术报告厅
参加人员:教师、研究生、本科生
报告摘要:In this talk, we study a time discretization scheme based on a non-uniform mesh for the problem with singularity near the initial time. Due to the weak singularity of the solution near the initial time, the classical scheme based on a uniform mesh can not reach the ideal convergence rate when approximating this kind of problems. As an improvement, a new kind of non-uniform meshes (the tanh meshes) in time is proposed. The new scheme is proved to be unconditionally stable and reach the ideal convergence rate by suitably choosing the parameter. Some numerical tests are also carried out to confirm the theoretical prediction.
报告人简介:王坤,重庆大学星际电子在线副教授,硕士生导师,中国数学会计算数学分会委员。主要从事偏微分方程数值解方面的研究,包括复杂流体力学方程、大波数Helmholtz方程的数值模拟等。2011年获西安交通大学博士学位,2013年获陕西省优秀博士论文。2012.1——2014.1在加拿大Alberta大学从事博士后研究(加拿大PIMS基金资助),曾应邀多次访问香港理工大学、Alberta大学等。主持和参与国家自然科学基金、国家重大研究计划重点项目多项,在Journal of Computational Physics, Communications in Computational Physics 等杂志上发表SCI论文30余篇。