| Fri, Dec 02, 2022
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Colloquium
3:30 PM
MSCS 101 | | The MMPDE moving mesh method and applications
Weizhang Huang, University of Kansas
Host: Xu Zhang
| | | Abstract: The MMPDE moving mesh method is a dynamic mesh adaptation method for use in the numerical solution of partial differential equations. It employs a partial differential equation (MMPDE) to move the mesh nodes continuously in time and orderly in space while adapting to evolving features in the underlying problem. The MMPDE is formulated as the gradient flow equation of a meshing functional that is typically designed based on geometric, physical, and/or accuracy considerations. In this talk, I will describe the MMPDE method and a new discretization of the method. This new discretization gives the mesh velocities explicitly, analytically, and in a compact matrix form, which in turn leads to a simple, efficient, and robust implementation of the MMPDE method. In particular, it works for convex or nonconvex domains in any dimension and is guaranteed for mesh nonsingularity (free of mesh tangling). Applications of the method will be discussed, including bulk and surface mesh smoothing (to improve mesh quality), generation of anisotropic polygonal meshes, and the numerical solution of the porous medium equation, the regularized long-wave equation, the phase-field modeling of brittle fracture, shallow water equations, and moving and free boundary problems. |
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