Fast simulations of waves in three-dimensional excitable media

A fast numerical scheme based on the model of Barkley [Physica 49D (1991), 61] is extended to three space dimensions (3D). The original time-stepping scheme is improved to provide greater accuracy and a Is-point approximation for the Laplacian operator in 3D is shown to have significant advantages over the commonly used 7-point formula. Simulations are coupled to a state-of-the-art surface rendering algorithm such that the combined code allows real-time interactive simulations of 3D waves on a desktop workstation. Results are presented from simulations over a range of spatio-temporal resolutions, from coarse cellular-automaton type simulations to fully resolved simulations of the underlying partial differential equations.