Computational models of the human heart play a vital role in understanding cardiac function and guiding patient-specific treatment. However, modeling accuracy must be balanced with computational efficiency, especially for time-critical applications. This study evaluates two spatial discretization methods - conforming Galerkin (CG) and enriched Galerkin (EG) - in the context of electro-mechanical cardiac simulations using active strain to model cardiac contraction and Rayleigh damping to suppress non-physiological oscillations.
A realistic bi-ventricular geometry was modeled with the transversely iso\-tropic Guccione material model complemented with a volumetric penalty functional to approximate incompressibility. For coupling mechanical deformation and electrophysiology we employed a staggered scheme. We compared CG and EG discretizations across multiple mesh resolutions using both linear and quadratic elements. Key metrics included cavity volumes, computational cost, and numerical robustness.
CG discretization showed locking effects with coarse meshes and linear elements, negatively impacting deformation accuracy. EG mitigated these artifacts while introducing only one additional degree of freedom per element. Although EG simulations were slightly more computationally demanding, they demonstrated enhanced numerical stability and robustness without excessive damping. Moreover, EG improved the local volume change by ca. 10 \% compared with CG. Both methods performed comparably on fine meshes using quadratic elements.
The EG method offers a favorable balance between numerical accuracy and computational efficiency for cardiac electro-mechanical simulations. In combination with active strain and Rayleigh damping, EG provides improved deformation behavior and greater numerical robustness compared to the standard CG method. These results suggest that EG is a promising approach for realistic and efficient cardiac modeling.