Experience with the conjugate gradient method for stress analysis on a data parallel supercomputer

The storage requirements and performance consequences of a few different data parallel implementations of the finite element method for domains discretized by three-dimensional brick elements are reviewed. Letting a processor represent a nodal point per unassembled finite element yields a concurrency that may be one to two orders of magnitude higher for common elements than if a processor represents an unassembled finite element. The former representation also allows for higher order elements with a limited amount of storage per processor. A totally parallel stiffness matrix generation algorithm is presented. The equilibrium equations are solved by a conjugate gradient method with diagonal scaling. The results from several simulations designed to show the dependence of the number of iterations to convergence upon the Poisson ratio, the finite element discretization and the element order are reported. The domain was discretized by three-dimensional Lagrange elements in all cases. The number of iterations to convergence increases with the Poisson ratio. Increasing the number of elements in one special dimension increases the number of iterations to convergence, linearly. Increasing the element order p in one spatial dimension increases the number of iterations to convergence as p^α, where α is 1·4–1·5 for the model problems.