Globalization strategies for Newton-Krylov methods for stabilized FEM discretization of Navier-Stokes equations

Journal of Computational Physics

Volumn 226, Issue 2, 2007, Pages 2317-2340

  Bellavia, Stefania ^a   Berrone, Stefano ^b  

^a UNIVERSITY OF FLORENCE   (Italy)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

Finite element methods; Globalization strategy; Inexact Newton methods; Numerical Navier Stokes equation

Indexed keywords

FINITE ELEMENT METHOD; NEWTON-RAPHSON METHOD; NONLINEAR EQUATIONS; NUMERICAL METHODS; VISCOUS FLOW;

DISCRETIZATIONS; ELLIPTICALS; GLOBALISATION; GLOBALIZATION STRATEGY; INEXACT NEWTON METHOD; NAVIER-STOKES EQUATION; NEWTON KRYLOV METHOD; NUMERICAL NAVI-STOKE EQUATION; STABILIZED FEM; TRUST REGION;

NAVIER STOKES EQUATIONS;

EID: 34548671187     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.07.021     Document Type: Article

References (30)

1. An H.B., and Bai Z.Z. A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations. Appl. Numer. Math. 57 (2007) 235-252
2. S. Balay, K Buschelman, V Eijkhout, W.D. Gropp, D. Kaushik, M.G. Knepley, L. Curfman McInnes, B.F. Smith, H. Zhang, PETSc Users Manual, ANL-95/11 - Revision 2.1.5, Argonne National Laboratory, http://www-unix.mcs.anl.gov/petsc, 2004.
3. Bellavia S., and Morini B. Newton-GMRES subspace method for systems of nonlinear equations. SIAM J. Sci. Comput. 23 (2003) 940-960
4. Bellavia S., and Morini B. Subspace trust-region methods for large bound constrained nonlinear equations. SIAM J. Numer. Anal. 44 (2006) 1535-1555
5. Branch M.A., Coleman T.F., and Li Y. A subspace, interior, and conjugate gradient method for large scale bound-constrained minimization problems. SIAM J. Sci. Comput. 21 (1999) 1-23
6. Brezzi F., and Fortin M. Mixed and Hybrid Finite Element Methods (1991), Springer-Verlag, New York/Berlin
7. Brown P.N., and Saad Y. Hybrid Krylov methods for nonlinear systems of equations. SIAM J. Sci. Stat. Comput. 11 (1990) 450-481
8. Byrd R.H., Schnabel R.B., and Shultz M.H. Approximate solution of the trust-region problem by minimization over two-dimensional subspaces. Math. Program. 40 (1988) 247-263
9. Ciarlet P.G. The Finite Element Method for Elliptic Problems (1978), North-Holland Publishing Company, Amsterdam
10. A.R. Conn, N.I.M. Gould, P.L. Toint, Trust Region Methods, Springer Series in Optimization, 2000.
11. Dembo R.S., Eisenstat S.C., and Steihaug T. Inexact Newton methods. SIAM J. Numer. Anal. 19 (1982) 400-408
12. Dennis J.E., Gay D.M., and Welsh R.E. An adaptive nonlinear least squares algorithm. ACM Trans. Math. Soft. 7 (1981) 348-368
13. Dolan E.D., and Moré J.J. Benchmarking optimization software with performance profiles. Math. Program. 91 2 Ser. A (2002) 201-213
14. Elias R.N., Coutinho A.L.G.A., and Martins M.A.D. Inexact-Newton-Type methods for non-linear problems arising from the SUPG/PSPG solution of steady incompressible Navier-Stokes Equations. J. Braz. Soc. Mech. Sci. & Eng. 26 (2004) 330-339
15. Eisenstat S.C., and Walker H.F. Globally convergent inexact Newton methods. SIAM J. Optim. 4 (1994) 393-422
16. Eisenstat S.C., and Walker H.F. Choosing the forcing term in an inexact Newton method. SIAM J. Sci. Comput. 17 (1996) 16-32
17. Franca L.P., and Frey S.L. Stabilized finite element methods: II. The incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. 99 (1992) 209-233
18. Ghia U., Ghia K.N., and Shin C.T. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. J. Comput. Phys. 48 (1982) 387-411
19. Girault V., and Raviart P.A. Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms (1986), Springer-Verlag, Berlin/Heidelberg
20. Harari I., and Hughes T.J.R. What are C and h?: Inequalities for the analysis and design of finite element methods. Comput. Methods Appl. Mech. Eng. 97 (1992) 157-192
21. Hughes T.J.R., Franca L.P., and Balestra M. A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput. Methods Appl. Mech. Eng. 59 (1986) 85-99
22. Kelley C.T. Iterative Methods for Linear and Nonlinear Equations (1995), SIAM, Philadelphia
23. A GAMM workshop, in: K. Morgan, J. Periaux, F. Thomasset (Eds.), Analysis of Laminar Flow over a Backward Facing Step, Friedr. Vieweg & Sohn, Braunschweig, 1984.
24. J. Nocedal, S.J. Wright, Numerical Optimization, Springer Series in Operations Research, 1999.
25. Pawlowski P., Shadid J.N., Simonis J.P., and Walker H.F. Globalization techniques for Newton-Krylov methods and applications to the fully-coupled solution of the Navier-Stokes equations. SIAM Rev. 48 (2006) 700-721
26. P. Pawlowski, J.P. Simonis, H.F. Walker, J.N. Shadid, Inexact Newton Dogleg methods, WPI Math. Sciences Dept. Tech. Rep. MS-5-05-36, SIAM J. Numer. Anal., submitted for publication.
27. Pernice M., and Walker H.F. NITSOL: a new iterative solver for nonlinear systems. SIAM J. Sci. Comput. 19 (1998) 302-318
28. Saad Y., and Schultz M.H. GMRES: a generalized minimal residual method for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 6 (1985) 856-869
29. Shadid J.N., Tuminaro R.S., and Walker H.F. An inexact newton method for fully coupled solution of the Navier-Stokes equations with heat and mass transport. J. Comput. Phys. 137 (1997) 155-185
30. Tuminaro R.S., Walker H.F., and Shadid J.N. On backtracking failure in Newton-GMRES methods. J. Comput. Phys. 180 (2002) 549-558