Talks by Dr. Wan: "Talk 2: Multigrid Methods: from Elliptic, Hyperbolic to Nonlinear Partial Differential Equations"
July 27th (Thursday), 11:00-12:00 am
National Institute of Informatics
Room: 12F, 1212
Multigrid Methods: from Elliptic, Hyperbolic to Nonlinear Partial Differential Equations
Dr. Justin W.L. Wan
Canada Research Chair in Scientific Computing,
Associate Professor, SciCom group in the David R. Cheriton School of Computer Science at University of Waterloo, Canada,
Director of the Centre for Computational Mathematics in Industry and Commerce (CCMIC).
Multigrid methods have been well known solvers for their mesh independent convergence. They are efficient for Poisson-type problems as well as smooth coefficient elliptic partial differential equations (PDEs). However, when the coefficients exhibit jumps, for instance, in interface problems, the convergence can be slow. For non-elliptic problems such as hyperbolic equations as well as nonlinear PDEs, standard multigrid methods do not work well. In this talk, we will present efficient and robust multigrid methods for solving different types of PDEs. We explore different techniques for constructing interpolation, restriction, and coarse grid operators. They are so designed to capture the properties of the underlying PDE problems so that they will result in fast convergence. We will present numerical results to demonstrate the effectiveness of the multigrid methods.
Ken Hayami (hayami(at)nii.ac.jp)