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Dr. Franzniska Weber
University of Maryland
An angular momentum method for approximating wave maps into the sphere
April 13, 2018
2-3 PM, 646A PGH
Abstract
The wave map equation into the sphere is one of the simplest hyperbolic nonlinear geometric equations and it has been studied by mathematicians to gain further insight into singularity formation of more complicated equations, as for example the Einstein equations.
In addition, it is related to mathematical models for applications such as liquid crystals or ferromagnetics, where the solution of the corresponding partial differential equation satisfies a length constraint.
In this talk, I will present an efficient finite difference method for approximating wave maps into the sphere. The method is based on a reformulation of the second order wave map equation as a first order system by using the angular momentum as an auxiliary variable. This enables us to preserve the length constraint as well as the energy inherit in the system of equations at the discrete level. The method will be shown to converge to a weak solution of the wave map equation as the discretization parameters go to zero. The performance of the method will be illustrated by numerical experiments.
The method can be extended to a convergent scheme for the damped wave map equation and the heat map flow. I will also discuss possible extensions of the method to applications for liquid crystal dynamics.
David H. Wagner University of Houston
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Last modified: September 26 2017 - 05:42:22
