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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 30, 1996 - Issue 3
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Original Articles

APPLICATION OF THE KRYLOV SUBSPACE METHOD TO NUMERICAL HEAT TRANSFER

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Pages 249-270 | Received 28 Nov 1995, Accepted 16 Feb 1996, Published online: 03 Apr 2007

References

  • A. Brandt , Multi-Level Adaptive Solutions to Boundary Value Problems , Math. , vol. 31 , pp. 333 – 390 , 1977 .
  • M. R. Hestenes and E. Stiefel , Method of Conjugate Gradients for Solving Linear Systems , Natl. Bur. Standards J. Res. , vol. 49 , pp. 409 – 436 , 1952 .
  • Y. Saad , Krylov Subspace Methods on Supercomputers , SIAM J. Sci. Stat. Comput. , vol. 10 , no. 6 , pp. 1200 – 1232 , 1989 .
  • F. Shakib , T. J. R. Hughes , and Z. Johan , A Multi-Element Group Preconditioned GMRES Algorithm for Nonsymmetric Systems Arising in Finite Element Analysis , Comput. Methods Appl. Mech. Eng. , vol. 75 , pp. 415 – 456 , 1989 .
  • T. J. R. Hughes , I. Levit , and J. Winget , Element-by-Element Solution Algorithm for Problems of Structural and Solid Mechanics , Comput. Methods Appl. Mech. Eng. , vol. 36 , pp. 241 – 254 , 1983 .
  • E. Barragy and G. F. Carey , A Parallel Element-by-Element Solution Scheme , Int. J. Numer. Methods Eng. , vol. 26 , pp. 2367 – 2382 , 1988 .
  • G. F. Carey , E. Barragy , R. Mclay , and M. Sharma , Element-by-Element Vector and Parallel Computations , Commun. Appl. Numer. Methods , vol. 4 , pp. 299 – 307 , 1988
  • Y. Eguchi and G. Yagawa , A Conjugate-Residual-FEM for Incompressible Viscous Flow Analysis , Comput. Mech. , vol. 3 , pp. 59 – 72 , 1988 .
  • L. Yu. Kolotilina and A. Yu. Yeremin , Block SSOR Preconditionings for High Order 3D FE Systems , BIT , vol. 29 , pp. 805 – 823 , 1989 .
  • P. Carriere and D. Jeandel , A 3D Finite Element Method for the Simulation of Thermoconvective Flows and Its Performances on a Vector-Parallel Computer , Int. J. Numer. Methods Fluids , vol. 12 , pp. 929 – 946 , 1991 .
  • A. Farcy , 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 .
  • 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. Methods Eng. , vol. 31 , pp. 1427 – 1451 , 1991 .
  • 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 .
  • 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 , Iowa , 1993 .
  • Z. Mikic and E. C. Morse , The Use of a Preconditioned Bi-conjugate Gradient Method for Hybrid Plasma Stability Analysis , J. Comput. Phys. , vol. 61 , pp. 154 – 185 , 1985 .
  • S. Bette , J. C. Diaz , W. R. Jines , and T. Steihaug , A Block Preconditioned Conjugate Gradient-Type Iterative Solver for Linear Systems in Thermal Reservoir Simulation , J. Comput. Phys. , vol. 67 , pp. 37 – 58 , 1986 .
  • P. Sonneveld , CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear Systems , Report 84–16 , Department of Mathematics and Informatics, Delft University of Technology , 1984 .
  • P. Sonneveld , P. Wesseling , P. M. de Zeeuw , Multigrid and Conjugate Gradient Methods as Convergence Acceleration Techniques , in D. J. Paddon and H. Holstein (eds.), Multigrid Methods for Integral and Differential Equations , pp. 117 – 167 , Clarendon Press , Oxford , 1985 .
  • P. Sonneveld , CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear Systems , SIAM J. Sci. Stat. Comput. , vol. 10 , pp. 36 – 52 , 1989 .
  • Y. Saad and M. H. Schultz , GMRES A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems , Research Report YALEU/DCS/RR-254, August 24 , 1983 .
  • P. N. Brown , A Theoretical Comparison of the Arnoldi and GMRES Algorithms , SIAM J. Sci. Stat. Comput. , vol. 12 , no. 1 , pp. 58 – 78 , 1991 .
  • Y. Saad and M. H. Schultz , GMRES A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems , SIAM J. Sci. Stat. Comput. , vol. 7 , pp. 856 – 869 , 1986 .
  • Y. Saad , Practical Use of Polynomial Preconditionings for the Conjugate Gradient Method , SIAM J. Sci. Stat. Comput. , vol. 6 , pp. 865 – 881 , 1985 .
  • H.-W. Lin , A Control-Volume Finite-Element Method for Navier-Stokes Equations , M. S. thesis , Department of Mechanical Engineering, The University of Iowa , Iowa City , Iowa , 1989 .
  • R. I. Issa , Solution of the Implicitly Discretised Fluid Row Equations by Operator-Splitting , J. Comput. Phys. , vol. 62 , pp. 40 – 65 , 1985 .
  • R. I. Issa , A. D. Gosman , and A. P. Watkins , The Computation of Compressible and Incompressible Recirculating Flows by a Non-Iterative Implicit Scheme ,” J. Comput. Phys. , vol. 62 , pp. 62 – 82 , 1986 .
  • Address correspondence to Professor Lea-Der Chen, Department of Mechanical Engineering, The University of Iowa, 2129 Engineering Building, Iowa City, Iowa, IA 52242-1527, USA, E-mail: [email protected].

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