Browse > Article
http://dx.doi.org/10.3795/KSME-B.2003.27.6.753

Parallel Preconditioner for the Domain Decomposition Method of the Discretized Navier-Stokes Equation  

Choi, Hyoung-Gwon (서울산업대학교 기계공학과)
Yoo, Jung-Yul (서울대학교 기계항공공학부)
Kang, Sung-Woo (서울대학교 대학원 기계항공공학부)
Publication Information
Transactions of the Korean Society of Mechanical Engineers B / v.27, no.6, 2003 , pp. 753-765 More about this Journal
Abstract
A finite element code for the numerical solution of the Navier-Stokes equation is parallelized by vertex-oriented domain decomposition. To accelerate the convergence of iterative solvers like conjugate gradient method, parallel block ILU, iterative block ILU, and distributed ILU methods are tested as parallel preconditioners. The effectiveness of the algorithms has been investigated when P1P1 finite element discretization is used for the parallel solution of the Navier-Stokes equation. Two-dimensional and three-dimensional Laplace equations are calculated to estimate the speedup of the preconditioners. Calculation domain is partitioned by one- and multi-dimensional partitioning methods in structured grid and by METIS library in unstructured grid. For the domain-decomposed parallel computation of the Navier-Stokes equation, we have solved three-dimensional lid-driven cavity and natural convection problems in a cube as benchmark problems using a parallelized fractional 4-step finite element method. The speedup for each parallel preconditioning method is to be compared using upto 64 processors.
Keywords
Domain Decomposition Method; Parallel Preconditioner; Navier-Stokes Equation;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Fusegi, T., Hyun, J. M., Kuwahara, K. and Farouk, B., 1991, 'A Numerical Study of Three-dimensional Natural Convection in a Differentially Heated Cubical Enclosure,' Int. J. Heat Mass Transfer, Vol. 34, No.6, pp. 1543-1557   DOI   ScienceOn
2 Kershaw, D. S., 1978, 'The Incomplete Cholesky-Conjugate Gradient Method for the Iterative Solution of Systems of Linear Equations,' J. Comput. Phys., Vol. 26, pp. 43-65   DOI   ScienceOn
3 Jiang, B. N, Lin, T. L. and Povinelli, L. A., 1994, 'Large-scale Computation of Incompressible Viscous Flow by Least-squares Finite Element Method,' Comput. Methods Appl. Mech. Eng., Vol. 114, pp. 213-231   DOI   ScienceOn
4 Snir, M., Otto, S., Huss-Lederman, S., Walker, D., Dongarra, J., 1996, MPI: The complete reference, The MIT Press, London
5 http://www-users.cs.umn.edu/~karypis/metis
6 Carey, G. F., Shen, Y. and McLay, R. T., 1998, 'Parallel Conjuate Gradient Performance for Least-Squares Finite Elements and Transport Problems,' Int. J. Numer. Meth. Fluids, Vol. 28, pp. 1421-1440   DOI   ScienceOn
7 Van der Vorst, H. A., 1992, 'Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Non-symmetric Linear Systems,' SIAM J. Sci. Statist. Comput., Vol. 12, pp. 631-634   DOI
8 Radicati di Brozolo, G. and Robert, Y., 1989, 'Parallel Conjugate Gradient-like Algorithms for Solving Sparse Nonsymmetric Linear Systems on a Vector Multiprocessor ,' Parallel Computing, Vol. 11, pp. 223-239   DOI   ScienceOn
9 Saad, Y., 1996, Iterative Methods for Sparse Linear Systems, PWS Publishing Company, Boston, pp. 374-376
10 Saad, Y. and Sosonkina, M., 1999, 'Distributed Schur Complement Techniques for General Sparse Linear Systems,' SIAM J. Sci. Comput., Vol. 21, pp. 1337-1356   DOI   ScienceOn
11 Choi, H. G., Choi, H. and Yoo, J. Y., 1997, 'A Fractional Four-step Finite Element Formulation of the Unsteady Incompressible Navier-Stokes Equations Using SUPG and Linear Equal-order Element Methods,' Comput. Methods Appl. Mech. Eng., Vol. 143, pp. 333-348   DOI   ScienceOn
12 Magolu monga Made, M. and van der Vorst, H. A., 2001, 'A Generalized Domain Decomposition Paradigm for Parallel Incomplete LU Factorization Preconditionings,' Future Generation Comput. Syst. Vol. 17, pp. 925-932   DOI   ScienceOn
13 Magolu monga Made, M. and van der Vorst, H. A., 2001,'Parallel Incomplete Factorizations with Pseudo-overlapped Subdomains,' Parallel Computing, Vol. 27, pp. 989-1008   DOI   ScienceOn
14 Wissink, A. M., Lyrintzis, A. S. and Chronopoulos, A. T., 1996, 'Efficient Iterative Methods Applied to the Solution of Transonic Flows,' J. Comput. Phys., Vol. 123, pp. 379-393   DOI   ScienceOn
15 Chronopoulos, A. T. and Wang, G., 1997, 'Parallel Solution of a Traffic Flow Simulation Problem,' Parallel Computing, Vol. 22, pp. 1965-1983   DOI   ScienceOn
16 Issman, E. and Degrez, G., 1997, 'Non-overlapping Preconditioners for a Parallel Implicit Navier-Stokes Solver,' Future Generation Comput. Syst., Vol. 13, pp. 303-313   DOI   ScienceOn
17 Basermann, A., Reichel, B. and Schelthoff, C., 1997, 'Preconditioned CG methods for Sparse Matrices on Massively Parallel Machines,' Parallel Computing, Vol. 23, pp. 381-398   DOI   ScienceOn