Abstract
Abstract In this paper we present a high-efficiency medium-grained parallel spectral element method for numerical solution of the Stokes problem in general domains. The method is based upon: naturally concurrent Uzawa and Jacobi-preconditioned conjugate gradient iterative methods; geometry-based data-parallel distribution of work amongst processors; nearest-neighbor sparsity and high-order substructuring for minimum communication; general locally-structured/globally-unstructured parallel constructs; and efficient embedding of vector reduction operations for inner product and norm calculation. An analysis is given for the computational complexity of the algorithm on a “native” medium-grained parallel processor, and the potential communication superiority of high-order discretizations is described. Lastly, the method is implemented on the (fast) Intel vector hypercube, and the performance of this algorithm-architecture coupling is evaluated in a technical and economic framework that reflects the true advantages of parallel solution of partial differential equations.
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