Krylov subspace solvers in parallel numerical computations of partial differential equations modeling heat transfer applications

Numerical Heat Transfer; Part A: Applications

Volumn 45, Issue 5, 2004, Pages 479-503

  Rathish Kumar, B V ^a   Kumar, Bipin ^a   Shalini, ^a   Mehra, Mani ^a   Chandra, Peeyush ^a   Raghvendra, V ^a   Singh, R K ^b   Mahindra, A K ^b  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

^b BHABHA ATOMIC RESEARCH CENTRE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; ITERATIVE METHODS; LINEAR SYSTEMS; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; PERFORMANCE; PROBLEM SOLVING;

CONJUGATE GRADIENT SQUARED (CGS); QUASI MINIMAL RESIDUAL (QMR);

HEAT TRANSFER;

EID: 1842789458     PISSN: 10407782     EISSN: None     Source Type: Journal    
DOI: 10.1080/10407780490269094     Document Type: Article

References (19)

1. Y. Saad, Iterative Methods for Sparse Linear Systems, PWS, Boston, 1995.
2. C. Pommerell, Solution to Large Unsymmetric Systems of Linear Equations, Hartung-Goore Verlag, Konstanz, 1992.
3. A. Brandt, Multi-level Adaptive Solutions to Boundary Value Problems, Math. Comput., vol. 31, pp. 333-390, 1977.
4. Y. Saad, Krylov Subspace Methods on Super Computers, SIAM J. Sci. Stat. Comput., vol. 10, no. 6, pp. 1200-1232, 1989.
5. F. Shakib, T. J. R. Hughes, and Z. Johan, A Multi-element Group Preconditioned GMRES(K) Algorithm for Nonsymmetric Systems Arising in Finite Element Analysis, Comput. Meth. Appl. Mech. Eng., vol. 75, pp. 415-456, 1989.
6. T. J. R. Hughes, I. Levit, and J. Winget, Element-by-Element Solution Algorithm for Problems of Structural and Solid Mechanics, Comput. Meth. Appl. Mech. Eng., vol. 36, pp. 241-254, 1983.
7. Y. Eguchi and G. Yagawa, A Conjugate-Residual FEM for Incompressible Viscous Flow Analysis, Comput. Mech., vol. 3, pp. 59-72, 1988.
8. P. Carriere and D. Jeandel, A 3D Finite Element Method for the Simulation of Thermo Convective Flows and Its Performance on a Vector Parallel Computer, Int. J. Numer. Meth. Fluids, vol. 12, pp. 929-946, 1991.
9. A. Farcy and T. A. de Roquefort, Chebyshev Pseudospectral Solution of the Incompressible Navier-Stokes Equations in Curvilinear Domains, Comput. Fluids, vol. 16, no. 4, pp. 459-473, 1988.
10. G. B. Deng, J. Piquet, P. Queutey, and M. Visonneau, Three-Dimensional Full Navier-Stokes Solvers for Incompressible Flows past Arbitrary Geometries, Int. J. Numer. Meth. Eng., vol. 31, pp. 1427-1451, 1991.
11. K. Chen, Conjugate Gradient Methods for the Solution of Boundary Integral Equations on a Piecewise Smooth Boundary, J. Comput Phys., vol. 97, pp. 127-143, 1991.
12. H. W. Lin, Numerical Simulation of the Dynamics and Instability of Flame Flicker when Subject to Perturbed Boundary Conditions, Ph.D. dissertation, Department of Mechanical Engineering, University of Iowa, Iowa City, IA, 1993.
13. Hsiao-Wen Lin and Lea-Der Chen, Application of the Krylov Subspace Method to Numerical Heat Transfer, Numer. Heat Transfer A, vol. 30, pp. 249-270, 1996.
14. B. V. Rathish Kumar and Shalini, Natural Convection in a Thermally Stratified Wavy Porous Enclosure, Numer. Heat Transfer A, vol. 43, pp. 753-776, 2003.
15. D. Angirasa, G. P. Peterson, and I. Pop, Combined Heat and Mass Transfer by Natural Convection in a Saturated Thermally Stratified Porous Medium, Numer. Heat Transfer A, vol. 31, pp. 255-272, 1997.
16. F. C. Lai and F. A. Kulacki, Non-Darcy Convection from Horizontal Impermeable Surfaces in Saturated Porous Medium, Int. J. Heat Mass Transfer, vol. 30, no. 1, 2189-2192, 1987.
17. B. V. Rathish Kumar and Shalini, Natural Convection in a Thermally Stratified Non-Darcian Vertical Porous Enclosure, J. Porous Media (In press).
18. K. L. Walker and G. M. Homsy, Convection in a Porous Cavity, J. Fluid Mech., vol. 87, pp. 449-474, 1978.
19. O. V. Trevisan and A. Bejan, Natural Convection with Combined Heat and Mass Transfer Buoyance Effects in Porous Medium, Int. J. Heat Mass Transfer, vol. 28, pp. 1596-1611, 1985.