Table 1.

Homogenisation represents significant time savings for cardiac electrophysiology. Runtimes for the generation of a single activation map for an example 2D tissue slice of fibrotic tissue (20% of sites marked obstructed at random). As expected, reducing the number of nodes and elements represents a huge reduction in computation time, and the time required to construct homogenised models (solving (9) for each coarse grid element) is minor compared to the time required for simulating on the finescale. Time required to homogenise is non-monotonic with respect to gridsize owing to a balance between the size of each closure problem, and the number of closure problems to be solved.

Mesh spacing	Homogenisation time	Simulation time	Total time	Speedup factor
10  µm	–	10 594.2 s	10 594.2 s	–
50  µm	29.4 s	186.8 s	216.2 s	49.0
100  µm	16.6 s	39.5 s	56.1 s	188.8
250  µm	21.6 s	5.8 s	50.5 s	209.8
500  µm	28.9 s	2.1 s	31.0 s	341.7