Harichandran, R. S., and Ye, B. (1993). "A method of deriving parallel
algorithms for direct integration in structural dynamics."
Computing Systems in Engineering, 4(4-6), 415-420.
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 uni-processors. It appears that the
parallel algorithms can be made to maintain the property of
unconditionally 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 the 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 q method and is called the "parallel
Wilson q 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.