Dear friends,
There is a mathmatics colloquium tomorrow in MSCS 101 at 3:30PM.
Refreshments will be at 4:30 in the department lounge.
The speaker is Professor Weizhang Huang of the University of Kansas
and his title is
The MMPDE moving mesh method and applications
His abstract may be found below.
Please join us for this talk on an interesting numerical method for
solving partial differential equations.
Best wishes,
David Wright
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.
