A Parallel Block Iterative Scheme Applied to Computations in Structural Analysis
Robert J. Plemmons · SIAM Journal on Algebraic and Discrete Methods · 1986
In this paper it is shown how a block cyclic successive overrelaxation direct-iterative method can be applied to the parallel solution of certain large-scale linear equality-constrained quadratic programming problems. The scheme is similar in nature to those studied recently by de Pillis, Niethammer and Varga and by Markham, Neumann and Plemmons for solving large sparse least squares problems. It is based upon a partitioning strategy of the fundamental matrix into a block consistently ordered 2-cyclic form where the nonzero eigenvalues of the Jacobi matrix are all pure imaginary. The method is shown to be globally convergent and convergence rates are established. Applications of the algorithm are discussed for large-scale structural analysis computations where it is shown how the algorithm can be adapted to the simultaneous computation of the system forces and the nodal displacements. Here, advantage can be taken of the special forms of the matrices involved. In particular, it is shown that much of the algorithm lends itself to efficient implementation on pipelined vector machines and on multiprocessors.