Element order and convergence rate of the conjugate gradient method for data parallel stress analysis

A data parallel formulation of the finite element method is described. The data structures and the algorithms for stiffness matrix generation and the solution of the equilibrium equations are presented briefly. The generation of the elemental stiffness matrices requires no communication, even though each finite element is distributed over several processors. The conjugate gradient method with a diagonal preconditioner has been used for the solution of the resulting sparse linear system. This formulation has been implemented on the Connection Machine® model CM-2. The simulations reported in this article investigate the influence of the mesh discretization and the interpolation order on the convergence behavior of the conjugate gradient method. A linear dependence of the convergence behavior on the mesh discretization parameter is observed. In addition, the convergence rate depends on the interpolation order p as (p1.6). The peak floating point rate (single-precision) for the evaluation of the stiffness matrix is approximately 2.4 Gflops s-1. The iterative solver peaks at nearly 850 Mflops s-1.