A FINITE-ELEMENT ALGORITHM FOR ELLIPTIC-EQUATIONS OVER UNSTRUCTURED DOMAINS ON A DATA-PARALLEL COMPUTER

In the past, most finite element algorithms on data-parallel computers have been limited to structured problem domains. Here, we consider me thods to generalize the finite element method on data-parallel archite ctures to unstructured domains. A nodal assembly algorithm is describe d which effectively allows for both the generation of the sparse inter action matrix (coefficient matrix) and its solution via a precondition ed conjugate-gradient type routine utilizing several polynomial precon ditioners on the Connection Machine 200 (CM-200). Jacobi preconditioni ng along with Neumann series and least-squares polynomial precondition ers are presented and implemented. Only the Jacobi preconditioner prod uces an improvement in the convergence time for the problems examined. Several irregular interprocessor communication protocols available on the CM-200 are investigated in the solution portion of the algorithm, yielding differing performance characteristics. For one such protocol , sustained performance of over two-hundred MFlops/s. is demonstrated for a test problem on a 512 processing element CM-200 in slicewise mod e. The results are discussed and conclusions are drawn concerning this finite element algorithm.