Efficiency of parallel anisotropic mesh adaptation for the solution of the bidomain model in cardiac tissue

Electrocardiology models are nonlinear reaction-diffusion type systems, where the numerical simulation requires extremely fine meshes to accurately compute the heart's electrical activity. Anisotropic mesh adaptation methods have been proven to be efficient for simulating cardiac dynamic by many authors and showed a considerable improvement in the numerical accuracy while reducing the computational expenses. However, the efficiency of these techniques in parallel computing environments has not been shown yet, especially when compared to the performance of parallel uniform meshes. In this paper, we demonstrate the efficiency of a parallel anisotropic mesh adaptation method for the solution of the bidomain model in cardiac tissue. The technique is based on an efficient error estimator appropriate for second or higher order numerical solutions. To demonstrate the effectiveness of the developed methodology, comparisons between the numerical simulations on parallel adapted meshes with those on parallel uniform meshes are presented. The computational efficiency is assessed by computing spiral and scroll waves in cardiac tissue.