Simulation of one heart beat which faithfully account for biophysical details involved in cardiac electro-physiology and mechanics are still far away from real time performance, even when employing several thousands of compute nodes. Therefore, a simpler model based on the Eikonal equation will be considered. This model could be of great utility as a tool for generating activation and repolarisation sequences and its concomitant electrocardiogram by replacing the PDE part of the bi-domain equations with the Eikonal equations, while retaining the ODE parts to account for the full mechanistic detail relevant to ECG computation. Further, the approach can be extended to use Eikonal-based activation sequences as a driver for mechanical contraction models. We will address the implementation of an Eikonal solver for Shared Memory (OpenMP) with a low memory footprint. This solver will be transferred for a coarse model onto a tablet computer and other handheld devices for clinical use. dimensional meshes it is needed to build efficient and fast algorithms. Due to the splitting of the wave front (described by the Eikonal equations), the parallel version results in a slightly different convergence history and in minor differences in the solution. A future CUDA implementation of the parallel algorithm will reduce the run time further such that also interactive simulations will be possible.