Computing on surfaces with the Closest Point Method
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Thu, 09/06/2011 16:00 |
Colin B MacDonald (University of Oxford) |
Differential Equations and Applications Seminar  |
DH 1st floor SR |
| Solving partial differential equations (PDEs) on curved surfaces is important in many areas of science. The Closest Point Method is a new technique for computing numerical solutions to PDEs on curves, surfaces, and more general domains. For example, it can be used to solve a pattern-formation PDE on the surface of a rabbit. A benefit of the Closest Point Method is its simplicity: it is easy to understand and straightforward to implement on a wide variety of PDEs and surfaces. In this presentation, I will introduce the Closest Point Method and highlight some of the research in this area. Example computations (including the in-surface heat equation, reaction-diffusion on surfaces, level set equations, high-order interface motion, and Laplace–Beltrami eigenmodes) on a variety of surfaces will demonstrate the effectiveness of the method. | |||