Accelerating implicit integration in multi-body dynamics using GPU computing

A new direct linear equation solver is proposed for GPUs. The proposed solver is applied to mechanical system analysis. In contrast to the DFS post-order traversal which is widely used for conventional implementation of supernodal and multifrontal methods, the BFS reverse-level order traversal has been adopted to obtain more parallelism and a more adaptive control of data size. The proposed implementation allows solving large problems efficiently on many kinds of GPUs. Separators are divided into smaller blocks to further improve the parallel efficiency. Numerical experiments show that the proposed method takes smaller factorization time than CHOLMOD in general and has better operational availability than SPQR. Mechanical dynamic analysis has been carried out to show the efficiency of the proposed method. The computing time, memory usage, and solution accuracy are compared with those obtained from DSS included in MKL. The GPU has been accelerated about 2.5-5.9 times during the numerical factorization step and approximately 1.9-4.7 times over the whole analysis process, compared to an experimental CPU device.