Extrapolation multigrid methods for solving large linear system arising from the discretizations of PDEs

Abstract

The multigrid method is an efficient iterative method for solving discrete partial differential equations. The geometric multigrid method has the nested mesh required for Richardson extrapolation. We propose two extrapolation multigrid methods: extrapolation cascadic multigrid method (EXCMG), extrapolation full multigrid method (EXFMG), and show the superoptimality of the EXCMG method for solving second-order elliptic problems. Finally, some numerical experiments include second-order and fourth-order elliptic problems and fractional diffusion equations are given to show the efficiency of the EXCMG method.

Biography

Prof. Pan is a professor and the vice dean of School of Mathematics and Statistics, Central South University, China. He got his PhD degree in Fudan University in 2009. His research area include multigrid method, finite difference method for solving nonlinear PDEs, and finite element methods.