A Scalable Parallel Multigrid Solver for Three Dimensional Adaptive Mesh Structural Analysis

Abstract

A parallel multigrid algorithm for solution of adaptive structural analysis meshes (ParMASA) is described. The user inputs a coarse mesh. The coarse mesh is successively solved, error estimated, and refined. The refinement simultaneously reduces discretization error and creates a hierarchy of meshes for use by the multigrid solver. The mesh may be refined in an arbitrarily irregular anisotropic manner. A block data structure is implemented to facilitate the parallelization of this complex refinement algorithm. For parallel runs an efficient algorithm must have balanced load in all algorithm steps. In addition communication must be minimized. A variety of procedures to optimize parallel performance by modifying the structure of multigrid cycle, smoothers, and communication patterns are discussed. Benefits of the advanced refinement and efficient parallelization are discussed. Good speedups to hundreds of processors are obtained on an SGI Origin 2000. ParMASA shows excellent performance a 256 processor SGI Origin 2000. ParMASA can perform all required IO, refinement, error estimation, and solution steps of an over 10 million degree-of-freedom system of equations in only 142 seconds.