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PARALLEL PARTITIONING STRATEGIES FOR THE ADAPTIVE SOLUTION OF
CONSERVATION LAWS

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
*p*-refinement, 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.