Adaptive spectral deferred correction methods for cardiac simulation

by · Sep 26, 2014 · 1 402 views ·

Zuse-Institut Berlin, Berlin, Germany A quantitative understanding of human heart function is necessary for understanding disease mechanisms and for individual therapy planning, but is hampered by the significant computational effort needed for numerical simulation. The electrical excitation is described by a reaction-diffusion equation coupled to pointwise ODEs and exhibits a wide range of temporal and spatial scales. One way to address the challenge is to devise efficient adaptive algorithms exploiting the locality of solutions in space and time. In this talk we will investigate the use of spectral deferred correction (SDC) methods for time integration, and their interplay with different forms of adaptivity. SDC methods are fixed point solvers for collocation systems. Their iterative nature allows to interleave the SDC convergence with mesh refinement, operator splitting, and inexact linear solveres, and thus provides many possibilities for adapting the overall algorithm to the problem at hand. We will look at some of those options and work out corresponding adaptive algorithms, illustrating their efficiency at numerical examples. 51

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