A method of deriving parallel algorithms for direct integration in structural dynamics

Abstract

A method of deriving parallel algorithms from well-established conventional direct integration algorithms such as the Wilson θ method, Newmark β method etc. is presented. The new algorithms are able to effectively exploit the power of parallel computers for the dynamic analysis of large-scale structures, and may be more efficient than the conventional methods, even on uniprocessors. It appears that the parallel algorithms can be made to maintain the property of unconditional stability displayed by the conventional methods. The parallel algorithms are derived by splitting the stiffness, damping and mass matrices such that the dynamic equations of motion can be cast in block diagonal form. The splitting of the matrices corresponds to physical subdomains of the structure. Each set of block diagonal equations can be solved independently of the others and therefore the computations can be performed in parallel. However, a predictor-corrector approach requiring iterations within a time step must be used for acceptable accuracy. The method described in this paper is derived from the Wilson θ method and is called the “parallel Wilson θ method.” A simple numerical example is used to illustrate the accuracy of the parallel method, which is comparable to the conventional method when a sufficient number of iterations is used. Preliminary computations were performed on a BBN GP-1000 distributed-memory parallel computer to assess the performance of the parallel algorithm. The proposed method is especially suited for large-scale non-linear structural dynamics problems.