Accession Number : ADA290458

Title :   Parallel Partitioning Strategies for the Adaptive Solution of Conservation Laws.

Descriptive Note : Technical rept.,

Corporate Author : RENSSELAER POLYTECHNIC INST TROY NY

Personal Author(s) : Devine, Karen D. ; Flaherty, Joseph E. ; Loy, Raymond M. ; Wheat, Stephen R.

PDF Url : ADA290458

Report Date : JAN 1994

Pagination or Media Count : 31

Abstract : We describe and examine the performance of adaptive methods for solving hyperbolic systems of conservation laws on massively parallel computers. The differential system is approximated by a discontinuous Galerkin finite element method with a hierarchical Legendre piecewise polynomial basis for the spatial discretization. Fluxes at element boundaries are computed by solving an approximate Riemann problem; a projection limiter is applied to keep the average solution monotone; time discretization is performed by Runge Kutta integration; and a p-refinement-based error estimate is used as an enrichment indicator. Adaptive order (p-) and mesh (h-) refinement algorithms are presented and demonstrated. Using an element-based dynamic load balancing algorithm called tiling and adaptive prefinement, parallel efficiencies of over 60% are achieved on a 1024-processor nCUBE/2 hypercube. We also demonstrate a fast, tree-based parallel partitioning strategy for three-dimensional octree-structured meshes. This method produces partition quality comparable to recursive spectral bisection at a greatly reduced cost.

Descriptors :   *FINITE ELEMENT ANALYSIS, *PARALLEL PROCESSORS, *PARTIAL DIFFERENTIAL EQUATIONS, *CONSERVATION, ALGORITHMS, EFFICIENCY, PARALLEL PROCESSING, COSTS, FINITE DIFFERENCE THEORY, SOLUTIONS(GENERAL), POLYNOMIALS, ADAPTIVE SYSTEMS, INDICATORS, RUNGE KUTTA METHOD, MONOTONE FUNCTIONS.

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE