| We consider three classes of methods for solving large, sparse, positive definite finite element problems in parallel: global matrix methods, Schur complement methods, and partitioned matrix methods. Global matrix methods apply parallel preconditioned conjugate gradient (PCG) to the global system. We investigate the use of damped Jacobi for the preconditioning step. Schur complement methods use domain decomposition and apply parallel PCG to the Schur complement system. Damped Jacobi is also considered as a preconditioner for the Schur complement system. In addition, we introduce a new low-cost preconditioner for the Schur complement system. Partitioned matrix methods apply PCG to the global system, but use domain decomposition with approximate subdomain solves in the preconditioning step. We present an analysis of the computational, communication, and storage costs of the three classes of methods. We also report results obtained on an Intel iPSC/2 for two-dimensional and three-dimensional test problems. |
