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

Research output: Contribution to journalArticle

Original languageEnglish
Article numberN/A
Pages (from-to)443-470
Number of pages28
Issue numberN/A
Publication statusPublished - 15 Nov 2013

King's Authors


We present a computationally efficient method of simulating cardiac electrical propagation using an adaptive high-order finite element method to automatically concentrate computational effort where it is most needed in space on each time-step. We drive the adaptivity using a residual-based error indicator, and demonstrate using norms of the error that the indicator allows us to control it successfully.

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.

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