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A High-Order Kernel Method For Diffusion And Reaction-Diffusion Equations On Surfaces, Edward J. Fuselier, Grady B. Wright

Grady Wright

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 R^d . For two-dimensional surfaces embedded in R³ , 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 oscillators in excitable media, and texture mappings. Our kernel method is based on radial basis functions and uses a semi-discrete approach (or the method-of-lines) in which the surface derivative operators that …