The increasing demand for personalized healthcare solutions has brought biomechanical simulations to the forefront of medical diagnostics and treatment planning. Fast and accurate simulations are critical for clinical applications, where timely decision-making can significantly impact treatment outcomes. Biomechanical models, however, are inherently complex, involving multiphysics such as fluid-structure interaction (FSI) and structure-electrical interaction. These models are highly nonlinear, and the corresponding discretized systems are often large and ill-conditioned, posing significant challenges for numerical solution techniques. In this talk, we present some parallel scalable domain decomposition methods for patient-specific biomechanics simulations. These methods enable the efficient and accurate solution of large-scale computational models that capture the complex dynamics of biological systems. By significantly improving computational efficiency and scalability, our approach makes these simulations feasible for real-world clinical applications in personalized medicine. We will also discuss applications of this methodology in cardiovascular simulations, where patient-specific data are used to predict surgical outcomes and optimize treatment strategies, demonstrating the potential for improving patient care.