A parallel algorithm for Algebraic MultiGrid

The major portion of computing time in a computational fluid dynamic (CFD) flow solver is consumed by the solution of the linear equations, the use of an efficient matrix solver is critical to obtain high performance flow solver. Currently, Algebraic Multi-Grid (AMG) is recognized in CFD community as one of the best choices to achieve high efficiency for solving linear algebraic equations. As AMG is increasingly used for large problems, its parallelization is highly demanded. In this paper, a parallel algorithm for AMG is proposed with regard to unique characteristics of partial differential equations governing fluid flows. An implicit block coupling method was developed and implemented into AMG. The parallelized AMG has demonstrated excellent performance on many test cases.

[1]  David Anthony Venditti,et al.  Grid adaptation for functional outputs of compressible flow simulations , 2000 .

[2]  Alain Dervieux,et al.  Unstructured multigridding by volume agglomeration: Current status , 1992 .

[3]  Sijun Zhang,et al.  A PARALLELIZED, ADAPTIVE, MULTI-GRID HYBRID UNSTRUCTURED SOLVER FOR ALL-SPEED FLOWS , 2002 .

[4]  Dimitri J. Mavriplis,et al.  A 3D AGGLOMERATION MULTIGRID SOLVER FOR THE REYNOLDS-AVERAGED NAVIER-STOKES EQUATIONS ON UNSTRUCTURED MESHES , 1995 .

[5]  Alain Dervieux,et al.  Unstructured volume‐agglomeration MG: Solution of the Poisson equation , 1994 .

[6]  Dimitri J. Mavriplis,et al.  Three-dimensional multigrid Reynolds-averaged Navier-Stokes solver for unstructured meshes , 1995 .

[7]  David C. Slack,et al.  Time integration algorithms for the two-dimensional Euler equations on unstructured meshes , 1994 .

[8]  John C. Lin,et al.  Optimization of an Advanced Design Three-Element Airfoil at High Reynolds Numbers , 1995 .

[9]  D. Mavriplis.  Three dimensional unstructured multigrid for the Euler equations , 1991 .

[10]  J. Peraire,et al.  A 3D finite element multigrid solver for the Euler equations , 1992 .

[11]  Jiwen Liu,et al.  Parallelized, Solution Adaptive, Multi-Grid Hybrid Unstructured Methods for the Navier-Stokes Equations on Complex Configurations , 2003 .

[12]  V. Venkatakrishnan,et al.  IMPLICIT SCHEMES AND PARALLEL COMPUTING IN UNSTRUCTURED GRID CFD , 1995 .

[13]  V. Venkatakrishnan,et al.  A 3D AGGLOMERATION MULTIGRID SOLVER FOR THE REYNOLDS-AVERAGED NAVIER-STOKES EQUATIONS ON UNSTRUCTURED MESHES , 1995 .

[14]  Joel H. Saltz,et al.  Implementation of a parallel unstructured Euler solver on shared- and distributed-memory architectures , 1992, Supercomputing '92.

[15]  P. Zulli,et al.  Preconditioned Multigrid Method for Fluid Flow in Porous Media , 1999 .

[16]  Sijun Zhang,et al.  A Parallel Implementation of General Purpose Unstructured Flow Solver , 2002 .

[17]  Stuart Connell,et al.  A 3D unstructured adaptive multigrid scheme for the Euler equations , 1993 .

[18]  Dimitri J. Mavriplis,et al.  AGGLOMERATION MULTIGRID FOR THE THREE-DIMENSIONAL EULER EQUATIONS , 1994 .

[19]  Y. Kallinderis,et al.  New multigrid approach for three-dimensional unstructured, adaptive grids , 1994 .

[20]  Dimitri J. Mavriplis,et al.  Agglomeration multigrid for two-dimensional viscous flows , 1995 .