Despite a steep increase in available compute power, in‐silico experimentation with highly detailed models of the heart remains to be challenging due to the high computational cost involved. It is hoped that next generation high performance computing (HPC) resources lead to significant reductions in execution times to leverage a new class of in‐silico applications. However, peformance gains with these new platforms can only be achieved by engaging a much larger number of compute cores, necessitating strongly scalable numerical techniques. So far strong scalability has been demonstrated only for a moderate number of cores, orders of magnitude below the range required to achieve the desired performance boost.In this study, strong scalability of currently used techniques to solve the bidomain equations is investigated. Benchmark results suggest that scalability is limited to 512–4096 cores within the range of relevant problem sizes even when systems are carefully load‐balanced and advanced IO strategies are ...