Preconditioning techniques for the Newton-Krylov solution of compressible flows

Journal of Computational Physics

Volumn 132, Issue 1, 1997, Pages 51-61

  Tidriri, M D ^a  

^a IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DEFECTS;

CORRECTION PROCEDURE; DEFECT CORRECTION; EFFICIENT STRATEGY; HIGH-ORDER; KRYLOV MATRICES; MATRIX; MATRIX-FREE METHODS; NEWTON-KRYLOV; PRECONDITIONERS; PRECONDITIONING TECHNIQUES;

ITERATIVE METHODS;

EID: 0040060100     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1996.5605     Document Type: Article

References (25)

1. T. J. Barth, Jan. 1987, Analysis of Implicit Local Linearization Techniques for Upwind and TVD Algorithms.
2. T. J. Barth, S. W. Linton, Jan. 1995, An Unstructured Mesh Newton Solver for Compressible Fluid Flow and Its Parallel Implementation.
3. Beam R. M., Warming R. F. An Implicit Factored Scheme for the Compressible Navier-Stokes Equations. AIAA J. 16:April 1978;393-402.
4. Brown P. N., Saad Y. Hybrid Krylov methods for nonlinear systems of equations. SIAM J. Sci. Statist. Comp. 11:1990;450-481.
5. X.-C. Cai, W. D. Gropp, D. E. Keyes, M. D. Tidriri, 1994, Parallel implicit methods for aerodynamics, Proceedings of the Seventh International Conference on Domain Decomposition Methods for Partial Differential Equations, American Math. Society, Providence, RI.
6. X.-C. Cai, W. D. Gropp, D. E. Keyes, M. D. Tidriri, 1994, Newton-Krylov-Schwarz Methods in CFD, Proceedings of the International Workshop on the Navier-Stokes Equations, R. Rannacher, Notes in Numerical Fluid Mechanics, Vieweg Verlag, Braunschweig.
7. Dembo R. S., Eisenstat S. C., Steihaug T. Inexact Newton methods. SIAM J. Numer. Anal. 19:April 1982;400-408.
8. Dennis J. E. Jr., Schnabel R. B. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. 1983;Prentice-Hall, Englewood Cliffs.
9. Johan Z., Hugues T. J. R., Mathur K. K., Johnsson S. L. A Data Parallel Finite Element Method for Computational Fluid Dynamics on the Connection Machine System. Computer Methods in Applied Mechanics and Engineering. 1992;. p. 113-124.
10. M.-S. Liou, B. Van Leer, 1988, Choice of Implicit and Explicit Operators for the Upwind Differencing Method, AIAA.
11. P. R. McHugh, D. A. Knoll, 1993, Inexact Newton's Method Solutions to the Incompressible Navier-Stokes and Energy Equations Using Standard and Matrix-Free Implementations, AIAA.
12. Mounts J. S., Belk D. M., Whitfield D. L. Multiblock Implicit, Steady-State Euler Code. Program EAGLE User's Manual. Sep. 1988;Air Force Armament Laboratory TR-88-117.
13. S. Osher, S. R. Chakravarthy, Sep. 1984, Very High Order Accurate TVD Schemes, ICASE.
14. Roe P. L. Approximate Riemann solvers, parameter vector, and difference schemes. J. Comp. Phys. 43:1981;357-372.
15. Saad Y., Schultz M. H. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comp. 7:1986;865-869.
16. E. Scholl, H.-H. Fruhauf, 1994, An accurate and efficient implicit upwind solver for the Navier-Stokes equations, Proceedings of the International Workshop on the Navier-Stokes Equations, R. Rannacher, Notes in Numerical Fluid Mechanics, Vieweg Verlag, Braunschweig.
17. Steger J. L., Warming R. F. Flux vector splitting of the inviscid gas dynamics equations with applications to finite-difference methods. J. Comp. Phys. 40:1981;263-293.
18. Thomkins W. T. Jr., Bush R. H. Boundary treatments for implicit solutions to Euler and Navier-Stokes equations. J. Comp. Phys. 48:1982;302-311.
19. M. D. Tidriri, May 1992, Couplage d'approximations et de modèles de types différent dans le calcul d'écoulements externes, Univ. of Paris XI.
20. Tidriri M. D. Domain decompositions for compressible Navier-Stokes equations. J. Comp. Phys. 119:1995;271-282.
21. M. D. Tidriri, June 1995, Krylov Methods for Compressible Flows.
22. M. D. Tidriri, Jan. 1996, Schwarz-Based Algorithms for Compressible Flows.
23. V. Venkatakrishnan, D. J. Mavriplis, May 1991, Implicit Solvers for Unstructured Meshes.
24. Yee H. C., Beam R. M., Warming R. F. Boundary approximations for implicit schemes for one-dimensional inviscid equations of gas dynamics. AIAA J. 20:Sep. 1982.
25. D. P. Young, C. C. Ashcraft, R. G. Melvin, M. B. Bieterman, W. P. Huffman, F. T. Johnson, C. L. Hilmes, J. E. Bussoletti, Aug. 1993, Ordering and Incomplete Factorization Issues for Matrices Arising from the TRANAIR CFD Code.