A localized meshless method for diffusion on folded surfaces
| Autor: | Steven J. Ruuth, Ka Chun Cheung, Leevan Ling |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Surface (mathematics)
Numerical Analysis Regularized meshless method Partial differential equation Physics and Astronomy (miscellaneous) Discretization Applied Mathematics Mathematical analysis Image processing Solver Computer Science Applications Computational Mathematics Modeling and Simulation Fluid dynamics Radial basis function Mathematics |
| Zdroj: | Journal of Computational Physics. 297:194-206 |
| ISSN: | 0021-9991 |
| Popis: | Partial differential equations (PDEs) on surfaces arise in a variety of application areas including biological systems, medical imaging, fluid dynamics, mathematical physics, image processing and computer graphics. In this paper, we propose a radial basis function (RBF) discretization of the closest point method. The corresponding localized meshless method may be used to approximate diffusion on smooth or folded surfaces. Our method has the benefit of having an a priori error bound in terms of percentage of the norm of the solution. A stable solver is used to avoid the ill-conditioning that arises when the radial basis functions (RBFs) become flat. |
| Databáze: | OpenAIRE |
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