Efficient parallelizable algorithm for computer simulation of multibody dynamical systems

A new parallelizable hybrid direct-iterative algorithm (HDIA) for computer simulation of motion behaviors of multibody dynamical systems is introduced. Specifically, the formation of the equations of motion, with their solution for system state derivatives and subsequent temporal integration is performed on parallel computing systems for multi-body systems with chain and tree structures. The method is based on cutting certain system interbody joints so that a system of largely independent multibody subchains is formed. These subchains interact with one another through associated unknown constraint forces with constraint equation at the cut joints. The increased parallelism is obtainable through cutting joints and the explicit determination of associated constraint forces combined with a sequential O(n) procedure. Consequently, the sequential O(n) procedure is carried out within each subchain to form and solve the equations of motion, while parallel strategies are performed between the subchains to form and solve constraint equations concurrently.;The joint cutting creates a need to solve a large system of sparse linear equations (Ax = b) associated with the constraint equation at each integration step. This linear system can be difficult to solve when the matrix A may be ill-conditioned or with poor properties due to widely varying magnitudes of its coefficients. In addition, solution of this linear sparse system may take a significant part of the total computational time when a parallel iterative solver is selected improperly. In this work five different Krylov subspace parallel linear iterative solvers have been integrated with the HDIA to improve its computational efficiency and to broaden its application. The algorithm has been implemented on IBM 1350 cluster through the integration of Krylov subspace iterative solvers in Aztec (A Massively Parallel Iterative Solver Library for Solving Sparse Linear Systems). Numerical programs based on the algorithm are further presented for validation, and along with typical case studies and performance comparison.