Finite element applications on a shared-memory multiprocessor: Algorithms and experimental results

We describe strategies for parallelizing finite element applications on a shared-memory multiprocessor. The applications studied include the convection-diffusion equation, and the Stokes equations of low Reynolds number hydrodynamics. The overall approach that we use is standard, but with significant restructuring for efficient parallel computation. The primary focus is on parallel methods for solving the linear systems of algebraic equations generated by the finite element discretization using polynomial iterative solvers preconditioned by incomplete factorizations. The challenging issue is the parallelization of the preconditioner, especially for the unstructured matrices obtained from finite element discretizations, and we describe the algorithms developed for this purpose. Specific experimental results obtained with our programs on ACE, a prototype 8-way, bus-based, shared-memory multiprocessor are discussed in detail. © 1991.