Mathematical cardiocirculatory models play a crucial role in cardiology by providing valuable insights into diagnostics and the effects of cardiovascular diseases. A wide range of models has been developed to represent different components of the heart and the cardiovascular system, spanning from purely time dependent (0D) formulations to fully three dimensional spatial descriptions. We focus on a 3D-0D full heart electromechanical model composed of several coupled submodels designed to represent the different physics occurring within the heart: electrophysiology, active force generation, mechanics and circulation [1]. These physics are characterized by distinct spatial and temporal scales, which necessitate a multiscale modeling approach. Accurately capturing the contribution of each physical component requires a sufficiently fine computational mesh, which, together with the model complexity, results in a high computational cost, even when simulations are performed in parallel. In matrix-based implementations, processors store and communicate portions of the system matrices during the simulation. However, during communication phases, the hardware computational resources are not fully exploited, leading to increased computational demand. In contrast, matrix-free algorithms avoid explicit matrix assembly by recomputing matrix entries at each iteration, thereby enabling a more efficient use of hardware resources, that allows for a reduction in computational time for higher polynomial degrees of the finite element space [2]. Within the 3D–0D full-heart electromechanical model, the electrophysiology and mechanics submodels represent the most computationally demanding components. Previous studies on left ventricle electrophysiology simulations have already shown substantial reductions in computational time when switching from matrix-based to matrix-free algorithms [3]. We investigate the impact of matrix-free algorithms on electromechanical simulations, focusing on how these algorithms affect both computational efficiency and resource utilization. By quantifying these effects, we aim to provide insights into the advantages and limitations of matrix-free approaches in multiscale and multiphysics cardiac simulations. We acknowledge the project Horizon Europe-JU-RIA dealii-X, 2024-2026, CORDIS ID: 101172493, “Dealii-X: an Exascale Framework for Digital Twins of the Human Body”.