Efficient simulation of cardiac electrical propagation using high-order finite elements II: Adaptive p-version

Our results using two-dimensional domains of varying complexity demonstrate that significant improvements in efficiency are possible over the standard linear FEM in our single-thread studies, and our preliminary three-dimensional results suggest that improvements are also possible in 3D. We do not work in parallel or investigate the challenges for adaptivity such as dynamic load-balancing which are associated with parallelisation. However, based upon recent work demonstrating that in some circumstances and with moderate processor counts parallel h-adaptive methods are efficient, and upon the claim that p-adaptivity will outperform h-adaptivity, we argue that p-adaptivity should be investigated for efficiency in parallel for simulation on moderate numbers of processors.