搜索:
 
 当前位置:>首页 -> 学术报告
9-11天元基金几何与随机分析及其应用交叉讲座之79【Jaap van der Vegt】
题目: Positivity Preserving Limiters for Discontinuous Galerkin Discretizations
报告人: Professor Jaap van der Vegt
Department of Applied Mathematics, University of Twente

时间: 2017年9月11日  下午 15:30~16:30

地点: 管理科研楼1218

摘要:
In the numerical solution of partial differential equations, it is frequently necessary to ensure that certain variables remain positive; otherwise unphysical solutions will be obtained that might result in the failure of the numeral algorithm. Positivity of certain variables is generally ensured using positivity preserving limiters, which locally modify the solution to ensure that the constraints are satisfied.
The combination of (positivity preserving) limiters and implicit time integration methods results, however, in serious problems. Many limiters have a complicated, non-smooth formulation that is difficult to linearize, which seriously hampers the use of standard Newton methods to solve the nonlinear algebraic equations of the implicit time discretization.
In this presentation, we will discuss a different approach to ensure that the numerical solution satisfies the positivity constraints. Instead of using a limiter, we impose the positivity constraints directly on the algebraic equations resulting from a discontinuous Galerkin method by reformulating the DG equations with constraints using techniques from mathematical optimization theory. The resulting algebraic equations are then solved using a semi-smooth Newton method that is well suited to deal with the resulting nonlinear complementarity problem. This approach allows the direct imposition of constraints in implicit discontinuous Galerkin discretizations, without the construction of complicated limiters, and results in more efficient solvers for the implicit discretization.
 

  科大主页 | 国家数学与交叉科学中心(合肥) | 中科院吴文俊数学重点实验室 |
中科院数学与系统科学研究院 | 北京国际数学研究中心 | 安徽省数学会