Abstract
A multi-element group, domain decomposition algorithm is presented for solving linear nonsymmetric systems arising in finite element analysis. The iterative strategy employed is based on the generalized minimum residual (GMRES) procedure originally proposed by Saad and Shultz. Two levels of preconditioning are investigated. Applications to problems of high-speed compressible flow illustrate the effectiveness of the scheme.
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References
J.E. Carter [1972], “Numerical Solutions of the Navier-Stokes Equations for the Supersonic Laminar Flow over a Two-dimensional Compression Corner”,NASA Technical Report,NASA TR R-385.
R.M. Ferencz [ 1988 ], “Element-by-element Preconditioning Techniques for Large-scale, Vectorized Finite Element Analysis in Nonlinear Solid and Structural Mechanics”,Ph.D. Thesis, Division of Applied Mechanics, Stanford University, in preparation.
G.H. Golub, C.F. Van Loan [ 1983 ],Matrix Computations, The Johns Hopkins University Press, Baltimore.
T.J.R. Hughes [ 1987 ],The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, New Jersey.
T.J.R. Hughes, R.M. Ferencz [ 1987 ], “Implicit Solution of Large-scale Contact and Impact Problems Employing an EBE Preconditioned Iterative Solver”, Preprint of contribution toIMPACT 87 International Conference on Effects of Fast Transient Loading in the Context of Structural Mechanics, Lausanne, Switzerland, August 26 – 27.
T.J.R. Hughes, R.M. Ferencz, J.O. Hallquist [ 1987 ], “Large-scale Vectorized Implicit Calculations in Solid Mechanics on a Cray X-MP/48 Utilizing EBE Preconditioned Conjugate Gradients”,Computer Methods in Applied Mechanics and Engineering, 61, 215 – 248.
M. Mallet, J. Periaux, B. Stoufflet [1987], “Convergence Acceleration of Finite Element Methods for the Solution of the Euler and Navier-Stokes Equations of Compressible Flow”,Proceedings of the 7th GAMM Conference on Numerical Methods in Fluid Dynamics,to appear.
B. Nour-Omid, B.N. Parlett, A. Raefsky [ 1988 ], “Comparison of Lanczos with Conjugate Gradient Using Element Preconditioning”, pp. 250–260 inProceedings of the First International Symposium on Domain Decomposition Methods for Partial Differential Equations, (eds. R. Glowinski, G.H. Golub, G.A. Meurant, J. Periaux), SIAM, Philadelphia.
Y. Saad, M.H. Schultz [ 1983 ], “GMRES: a Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems”,Research Report YALEU/DCS/RR-254, Department of Computer Science, Yale University.
F. Shakib [ 1988 ], “Finite Element Analysis of the Compressible Euler and NavierStokes Equations”,Ph.D. Thesis, Division of Applied Mechanics, Stanford University.
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© 1989 Plenum Press, New York
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Shakib, F., Hughes, T.J.R., Johan, Z. (1989). Element-By-Element Algorithms for Nonsymmetric Matrix Problems Arising in Fluids. In: Kane, J.H., Carlson, A.D., Cox, D.L. (eds) Solution of Superlarge Problems in Computational Mechanics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0535-4_1
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DOI: https://doi.org/10.1007/978-1-4613-0535-4_1
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