Run-Time Load Balancing Techniques for a Parallel Unstructured Multi-Grid Euler Solver with Adaptive Grid Refinement

Abstract Multi-level methods use a hierarchy of successively finer grids. In an adaptive unstructured grid hierarchy each grid is obtained by solution-dependent refinement of the grid on the previous level. In this paper the load balancing issues involved in the parallel implementation of an unstructured multi-grid algorithm with run-time grid refinement for the steady Euler equations on a distributed memory computer are discussed. A number of techniques for data partitioning and mapping are proposed. The parallel performance of the code is evaluated on hypercube computers.

[1]  Wayne R. Cowell,et al.  On the parallelization of an adaptive multigrid algorithm for a class of flow problems , 1992, Parallel Comput..

[2]  A. Jameson,et al.  Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes , 1981 .

[3]  Johan De Keyser,et al.  Partitioning and mapping adaptive multigrid hierarchies on distributed memory computers , 1992 .

[4]  Roy David Williams,et al.  A dynamic solution-adaptive unstructured parallel solver , 1992 .

[5]  W. K. Anderson,et al.  Comparison of Finite Volume Flux Vector Splittings for the Euler Equations , 1985 .

[6]  Johan De Keyser,et al.  Load Balancing Data Parallel Programs on Distributed Memory Computers , 1993, Parallel Comput..

[7]  A. Jameson.  Solution of the Euler equations for two dimensional transonic flow by a multigrid method , 1983 .

[8]  Wolfgang Hackbusch,et al.  Multi-grid methods and applications , 1985, Springer series in computational mathematics.

[9]  Joel H. Saltz,et al.  ICASE Report No . 92-12 / iVG / / ff 3 J / ICASE THE DESIGN AND IMPLEMENTATION OF A PARALLEL UNSTRUCTURED EULER SOLVER USING SOFTWARE PRIMITIVES , 2022 .

[10]  Roy D. Williams,et al.  Performance of dynamic load balancing algorithms for unstructured mesh calculations , 1991, Concurr. Pract. Exp..

[11]  D. C. Jespersen.  Recent developments in multigrid methods for the steady Euler equations , 1984 .

[12]  Dirk Roose,et al.  Load Balancing Grid-Oriented Applications on Distributed Memory Parallel Computers , 1992 .

[13]  J. De Keyser,et al.  A Software Tool for Load Balanced Adaptive Multiple Grids on Distributed Memory Computers , 1991, The Sixth Distributed Memory Computing Conference, 1991. Proceedings.

[14]  Elias N. Houstis,et al.  Geometry based mapping strategies for PDE computations , 1991, ICS '91.

[15]  J. De Keyser,et al.  Incremental mapping for solution-adaptive multigrid hierarchies , 1992, Proceedings Scalable High Performance Computing Conference SHPCC-92..

[16]  S. P. Spekreijse,et al.  Multiple grid and Osher''s scheme for the efficient solution of the steady Euler equations Applied N , 1986 .

[17]  Daniel J. Quinlan,et al.  Asynchronous multilevel adaptive methods for solving partial differential equations on multiprocessors: performance results , 1989, Parallel Comput..

[18]  Erich Ortner,et al.  Solution of the Navier-Stokes equations on a massively parallel transputer system , 1992 .

[19]  Stefan Vandewalle,et al.  A comparison of parallel multigrid strategies , 1989 .