A Hybrid Preconditioned Iterative Framework for Large-Scale Multibody Dynamics

Multibody dynamics (MBD) simulations involving hundreds to thousands of bodies give rise to large-scale, sparse, and structurally indefinite linear systems. Traditional direct solvers incur prohibitive memory and computational costs, while iterative methods suffer from slow convergence due to severe ill-conditioning. This paper proposes HPI-MBD, a hybrid preconditioned iterative framework. It combines an algebraic multigrid (AMG) for global error smoothing with a block Jacobi preconditioner tailored to the kinematic constraint graph. The framework exploits graph topology to construct a block-diagonal Schur complement approximation, incorporates Tikhonov regularisation for redundant constraints, and maintains O(n) work per iteration, where n is the number of degrees of freedom. A rigorous spectral analysis supports the problem-size independent convergence of the Minimal Residual (MINRES) solver. Evaluated on five benchmark systems with 104 to 106 degrees of freedom, the HPI-MBD achieves speedups up to 12.7× and memory reductions up to 68% against MA57, with comparable gains against PARDISO. All solutions maintain relative residuals below 10−6. Comparisons against ILU(0)-preconditioned Generalised Minimal Residual (GMRES), Finite Element Tearing and Interconnecting method (FETI-1), and a block-Jacobi-only variant confirm the essential role of AMG. The framework exhibits near-linear scalability and strong parallel efficiency on up to 32 processors, along with robust performance under redundant constraints and varying time step sizes. These results position HPI-MBD as a scalable, memory-efficient alternative for real-time simulation in virtual prototyping, robotics, and biomechanics.