A Structured Grid Method for the Singularly Perturbed Reaction-Diffusion Equation from Computational Cardiology

The monodomain equation in computational cardiology, which describes the electrical activity of the heart, is a singularly perturbed reaction-diffusion equation. In this talk, I will introduce a structured grid method for solving the problem. The method applies the technique of operator splitting to integrate the linear diffusion part separately from the nonlinear reaction part. The split linear diffusion equation is solved with the recently developed kernel-free boundary integral method on a Cartesian grid, which does not need to know the kernel of the boundary and volume integrals involved, while the split diffusion equation on a Cartesian grid itself is a stiff problem and integrated with an L-stable second-order accurate time integration method, called the composite backward differentiation formula. Numerical results for the problem in both two and three-space dimensions will be presented. To the best of my knowledge, this is the first Cartesian/structured grid-based method for singularly perturbed reaction-diffusion equations (In the literature, there are structure-based methods for parabolic PDEs but not for singularly perturbed reaction-diffusion equations).

Event Topic

Stochastic & Multiscale Modeling and Computation