In this talk, we will present a highly parallel method for simulating the elastodynamics of a patient-specific, four-chamber human heart. Using a finite element method for spatial discretization and a fully implicit adaptive method for temporal discretization, our scalable domain decomposition algorithm solves the nonlinear algebraic systems. The model captures complex deformations of cardiac muscles due to realistic geometry, heterogeneous hyperelasticity, and myocardial fibers with active stresses. Key muscle movements, such as atrial diastole, atrial systole, isovolumic contraction, ventricular ejection, isovolumic relaxation, and ventricular filling, are simulated with a fine spatial-temporal mesh. Our two-level time-stepping strategy combines a uniform baseline time step for accuracy and adaptive time-stepping for convergence. Numerical experiments evaluate performance based on material coefficients, fiber orientations, mesh sizes, and time step sizes. On an unstructured tetrahedral mesh with over 200 million degrees of freedom, our method scales efficiently across 16,384 processor cores for a complete cardiac cycle. This work lays the foundation for developing a comprehensive cardiac electro-mechanics coupling scheme.