A High-Order Kernel Method for Diffusion and Reaction-Diffusion Equations on Surfaces

@article{Fuselier2013AHK,
  title={A High-Order Kernel Method for Diffusion and Reaction-Diffusion Equations on Surfaces},
  author={Edward J. Fuselier and Grady B. Wright},
  journal={Journal of Scientific Computing},
  year={2013},
  volume={56},
  pages={535-565}
}
  • E. Fuselier, G. Wright
  • Published 31 May 2012
  • Computer Science, Mathematics
  • Journal of Scientific Computing
In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in $$\mathbb{R }^d$$. For two-dimensional surfaces embedded in $$\mathbb{R }^3$$, these types of problems have received growing interest in biology, chemistry, and computer graphics to model such things as diffusion of chemicals on biological cells or membranes, pattern formations in biology, nonlinear chemical… 
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