An approximate block Newton method for coupled iterations of nonlinear solvers: Theory and conjugate heat transfer applications

Journal of Computational Physics

Volumn 228, Issue 23, 2009, Pages 8566-8588

  Yeckel, Andrew ^a   Lun, Lisa ^a   Derby, Jeffrey J ^a  

^a University of Minnesota   (United States)

Author keywords

Approximate Newton methods; Block Gauss Seidel methods; Crystal growth; Modular iterations; Multiphysics coupling; Multiscale coupling

Indexed keywords

CRYSTAL GROWTH; HEAT TRANSFER;

APPROXIMATE NEWTON METHOD; BLOCK GAUSS-SEIDEL METHOD; CONJUGATE HEAT TRANSFER; GAUSS SEIDEL METHOD.; MODULAR ITERATION; MODULARS; MULTI-PHYSICS COUPLINGS; MULTISCALE COUPLING; NEWTON'S METHODS; NON-LINEAR SOLVER;

NEWTON-RAPHSON METHOD;

EID: 70349753460     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.08.003     Document Type: Article

References (25)

1. Dubini G., Pietrabissi R., and Montevecchi F.M. Fluid-structure interaction in bio-fluid mechanics. Med. Eng. Phys. 17 (1995) 609-617
2. Piperno S., Farhat C., and Larrouturou B. Partitioned procedures for the transient solution of coupled aeroelastic problems - Part I: Model problem, theory, and two-dimensional application. Comput. Method Appl. Mech. Eng. 124 (1995) 79-112
3. Piperno S., and Farhat C. Partitioned procedures for the transient solution of coupled aeroelastic problems - Part II: Energy transfer analysis and three-dimensional applications. Comput. Method Appl. Mech. Eng. 190 (2001) 3147-3170
4. Farhat C., Lesoinne M., and LeTallec P. Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation, optimal discretization and application to aeroelasticity. Comput. Method Appl. Mech. Eng. 157 (1998) 95-114
5. A. Pandy, Global Modeling of Bulk Crystal Growth of Cadmium Zinc Telluride in Industrial VB/VGF Systems, Ph.D. Thesis, University of Minnesota, 2004.
6. Pandy A., Yeckel A., Reed M., Szeles C., Hainke M., Müller G., and Derby J.J. Analysis of the growth of cadmium zinc telluride in an electrodynamic gradient freeze furnace via a self-consistent, multi-scale numerical model. J. Cryst. Growth 276 (2005) 133-147
7. Yeckel A., Pandy A., and Derby J.J. Fixed-point convergence of modular steady-state heat transfer models coupling multiple scales and phenomena for melt-crystal growth. Int. J. Numer. Method Eng. 67 (2006) 1768-1789
8. Derby J.J., Lun L., and Yeckel A. Strategies for the coupling of global and local crystal growth models. J. Cryst. Growth 303 (2007) 114-123
9. R.W. Hooper, M.H. Hopkins, R.P. Pawlowski, Enabling Newton-based coupling within a multi-physics environment using NOX - an object-oriented nonlinear solver library, in: M. Papadrakakis, E. Oñate, B. Schrefler (Eds.), International Conference on Computational Methods for Coupled Problems in Science and Engineering, CIMNE, Barcelona, 2005.
10. R.W. Hooper, M.H. Hopkins, R.P. Pawlowski, B. Carnes, H.K. Moffat, Final Report on LDRD Project: Coupling Strategies for Multi-physics Applications, Tech. Rep. SAND2007-7146, Sandia National Laboratories, 2008.
11. T.G. Kolda, R.P. Pawlowski, NOX Home Page. .
12. Chan T.F. An approximate Newton method for coupled nonlinear systems. SIAM J. Numer. Anal. 22 5 (1985) 904-913
13. Artlich S., and Mackens W. Newton-coupling of fixed point iterations. In: Hackbusch W., and Wittum G. (Eds). Numerical Treatment of Coupled Systems (1995), Vieweg-Verlag, Braunschweig, Wiesbaden 1-10
14. Menck J. An approximate Newton-like coupling of subsystems. Z. Angew. Math. Mech. 82 2 (2002) 101-114
15. Matthies H.G., and Steindorf J. Partitioned but strongly coupled iteration schemes for nonlinear fluid-structure interaction. Comput. Struct. 80 (2002) 1991-1999
16. Knoll D.A., and Keyes D.E. Jacobian-free Newton-Krylov methods: a survey of approaches and applications. J. Comput. Phys. 193 (2004) 357-397
17. Saad Y. Iterative Methods for Sparse Linear Systems (1996), PWS Pub. Co., Boston
18. Yeckel A., and Derby J.J. Computer modelling of bulk crystal growth. In: Capper P. (Ed). Bulk Crystal Growth of Electronic, Optical and Optoelectronic Materials (2005), Springer, Berlin 73-119
19. A. Yeckel, R.T. Goodwin, Cats2D (Crystallization and Transport Simulator), User Manual, 2003. .
20. Kurz M., Pusztai A., and Müller G. Development of a new powerful computer code CrysVUN++ especially designed for fast simulation of bulk crystal growth processes. J. Cryst. Growth 198/199 (1999) 101-106
21. Kurz M., and Müller G. Control of thermal conditions during crystal growth by inverse modeling. J. Cryst. Growth 208 (2000) 341-349
22. Fainberg J., Vizman D., Friedrich J., and Müller G. A new hybrid method for the global modeling of convection in CZ crystal growth configurations. J. Cryst. Growth 303 (2007) 124-134
23. CrysMAS. .
24. Saad Y., and Schultz M.H. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7 (1986) 856-869
25. Lee R.L., Gresho P.M., and Sani R.L. Smoothing techniques for certain primitive variable solutions of the Navier-Stokes equations. Int. J. Num. Method Eng. 14 (1979) 1785-1804