Main innovation: first multirate fully explicit method with no step size restriction (even for stiff problems)
We accomplished the design of a PinT explicit stabilised method with applications to cardiac electrophysiology. The method has a multirate and a non multirate version, is used in combination with the multilevel spectral deferred correction framework, is fully explicit, and does not have any step size restrictions. Preliminary results are promising. However, more time is needed to analyse the method and, eventually, optimise it. We are currently implementing the methods in the pySDC library, where we plan to employ the PFFAST technology for efficient PinT integration. Finally, for the cardiac electrophysiology applications, we are tightly cooperating with another EuroHPC project (MICROCARD).
In the example below, we solve the monodomain equation for electrophysiology with our two explicit stabilised methods (non multirate and multirate) and compare their efficiency against a standard explicit method: explicit Euler (EE). In the left figure we remark that the new non multirate method HSRKU based on Chebshev polynomials achieves similar errors as EE, but progressively and at a significantly lower cost. In the right picture we compare the same method HSRKU against its multirate version mHSRKU and see that the cost is reduced even further.
- G. Rosilho de Souza, S. Pezzuto, R. Krause, “Parallel-in-Time Multirate explicit stabilized method for the monodomain model in cardiac electrophysiology”, Proceedings of the CMBE2021 conference, 27–29 June 2022, Italy. ISSN 2227-9385.