An efficient implementation of an implicit FEM scheme for fractional-in-space reaction-diffusion equations
Year: 2011
Type: report
Abstract: Fractional differential equations are becoming increasingly used as a modelling tool for processes with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time fractional) or nonlocality (space fractional) issues, which impose a number of computational constraints. In this paper we develop efficient, scalable techniques for solving fractional-in-space reaction diffusion equations using the finite element method on both structured and unstructured grids, and robust techniques for computing the fractional power of a matrix times a vector. Our approach is show-cased by solving the fractional Fisher and fractional Allen-Cahn reaction-diffusion equations in two and three spatial dimensions, and analysing the speed of the travelling wave and size of the interface in terms of the fractional power of the underlying Laplacian operator.
Authors: Kevin Burrage, Nicholas Hale, David Kay
Institution: University of Oxford
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G551029724
OpenAlex ID: W635609117