| 报告题目： | Compact implicit integration factor method for a class of high order differential equations |
| 报 告 人： | 刘新峰 |
| University of South Carolina | |
| 报告时间： | 06月24日（周二）上午10:30-11:30 |
| 报告地点： | 九龙湖数学系第一报告厅 |
| 相关介绍： | 摘要：When developing efficient numerical methods for solving parabolic types of equations, severe temporal stability constraints on the time step are often required due to the high-order spatial derivatives and/or stiff reactions. The implicit integration factor (IIF) method, which treats spatial derivative terms explicitly and reaction terms implicitly, can provide excellent stability properties in time with nice accuracy. One major challenge for the IIF is the storage and calculation of the dense exponentials of the sparse discretization matrices resulted from the linear differential operators. The compact representation of the IIF (cIIF) can overcome this hortcoming and greatly save computational cost and storage. In this talk, by treating the discretization matrices in diagonalized forms, we will present an efficient cIIF method for solving a family of semilinear fourth-order parabolic equations, in which the bi-Laplace operator is explicitly handled and the computational cost and storage remain the same as to the classic cIIF for second-order problems. In particular, the proposed method can deal with not only stiff nonlinear reaction terms but also various types of homogeneous or inhomogeneous boundary conditions.。 刘新峰，现为美国University of South Carolina终身副教授。 1997年复旦大学本科，2000年东南大学硕士，2006年美国纽约州立大学石溪分校博士。2006－2009年美国加州大学尔湾分校访问助理教授。2009－2013年南卡罗来纳大学助理教授，2013年－至今南卡罗来纳大学终身副教授。已发表20多篇学术论文，单独主持两项美国自然科学基金项目，单独主持一项南卡大学基金项目，共同主持两项南卡州立基金项目。现致力于计算与生物数学，偏微分方程与数值解，自由边界问题，计算流体及大型数值模拟计算等方面的研究。 |
