High-Order Operator-Splitting Methods for Cardiac Tissue Simulations
Professor Raymond Spiteri, U. Sask
Cardiac tissue simulations often use the bidomain or monodomain model to describe the electrophysiology of cardiac tissue. These models take the form of multi-scale reaction-diffusion partial differential equations that couple the dynamic behaviour on the cellular scale with that on the tissue scale. The systems of differential equations associated with these models are large and strongly non-linear, but they also have a distinct structure due to their multi-scale nature. Operator-splitting methods attempt to take advantage of this structure to efficiently produce numerical solutions. The focus of this presentation is on operator-splitting methods with order higher than two. Such methods require backward time integration in each operator and historically have been considered unstable for solving deterministic parabolic systems. The stability and performance of operator-splitting methods of up to order four to solve the bidomain and monodomain models are demonstrated on several examples arising in the field of cardiovascular modelling.
Wednesday, March 14 at 1:05 pm to 1:55 pm
Fisher Hall, 222
1400 Townsend Drive, Houghton, MI 49931