This minisymposium presents recent developments on large-scale biomechanical simulations of the human body. We invite contributions from a broad range of topics, including the development of novel discretization schemes for solving partial differential equations, the development of advanced mathematical algorithms for solving linear systems, involving both iterative methods with geometric, polynomial and algebraic multigrid schemes, physics-based block preconditioners as well as sparse direct solvers with novel low-rank factorizations. Furthermore, algorithm implementations on modern high-performance platforms, especially for GPU systems, are at the core of this minisymposium. This includes method development to best utilize these systems, such as matrix-free methods, mixed-precision algorithms, or the embeddeding into modern software packages. The minisymposium is primarily driven by the European Centre of Excellence (CoE) dealii-X [1], an initiative hosted in four European countries and spanning mathematical development, biomechanical applications, and hardware-driven algorithm design. It covers mathematical abstractions using the deal.II finite element library and various modern third-part packages, such as PSCToolkit and MUMPS, all the way to applications. Contributions in related fields are explicitly invited, and it is planned to present a mix of contributions of the dealii-X CoE as well as other research. We also invite contributions from biomedical applications or progress on biomedical code development, to participate in the minisymposium.