Iterative and parallel performance of high-order compact systems

SIAM Journal on Scientific Computing

Volumn 19, Issue 1, 1998, Pages 1-14

  Spotz, W F ^a   Carey, G F ^b  

^a NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Compact stencils; Condition numbers; Eigenvalues; High order methods; Parallel performance

Indexed keywords

EID: 0001947326     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S106482759630379X     Document Type: Article

References (21)

1. S. ABARBANEL AND A. KUMAR, Compact higher-order schemes for the Euler equations, J. Sci. Comput., 3 (1988), pp. 275-288.
2. G. F. CAREY, W. JOUBERT, A. LORBER, R. MCLAY, Y. SHEN, AND W. SPOTZ, Development and application of a parallel portable system solver for PDEs, in Proc. High Performance Computing '96, 1996 SCS Simulation MultiConference, New Orleans, LA, 1996, pp. 272-277.
3. G. F. CAREY AND J. T. ODEN, Finite Elements: Fluid Mechanics, Vol. VI, Prentice-Hall, Englewood Cliffs, NJ, 1986.
4. M. H. CARPENTER, D. GOTTLIEB, AND S. ABARBANEL, The stability of numerical boundary treatments for compact high-order finite-difference schemes, J. Comput. Phys., 108 (1993), pp. 272-295.
5. A. DATTA GUPTA, L. W. LAKE, G. A. POPE, AND K. SEPEHRNOORI, High-resolution monotonic schemes for reservoir fluid flow simulation, In Situ, 15 (1991), pp. 289-317.
6. 4 finite difference approximations to operators of Navier-Stokes type, J. Comput. Phys., 85 (1989), pp. 390-416.
7. S. C. R. DENNIS AND Q. WING, Generalized finite differences for operators of Navier-Stokes type, in Proc. 10th International Conference on Numerical Methods in Fluid Dynamics, F. G. Zhuang and Y. L. Zhu, eds., Lecture Notes in Physics 264, Springer-Verlag, 1986, pp. 222-228.
8. M. M. GUPTA, R. P. MANOHAR, AND J. STEPHENSON, Single-cell high order difference method for steady state advection-diffusion equation, in Proc. Symposium -International Association for Hydraulic Research, Ecole Nationale des Ponts et Chaussees, Paris, France, 1982, pp. 101-108.
9. M. M. GUPTA, R. P. MANOHAR, AND J. W. STEPHENSON, A single cell high order scheme for the convection-diffusion equation with variable coefficients, Internat. J. Numer. Methods Fluids, 4 (1984), pp. 641-651.
10. W. D. JOUBERT, G. F. CAREY, R. T. MCLAY, N. A. BERNER, H. KOHLI, A. LORBER, AND Y. SHEN, PCG Reference Manual, Version 1.0α, Center for Numerical Analysis, University of Texas at Austin, Austin, TX, 1995.
11. B. P. LEONARD, A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Comput. Methods Appl. Mech. Engrg., 19 (1979), pp. 59-98.
12. M. LI, T. TANG, AND B. FORNBERG, A compact fourth-order finite difference scheme for the steady incompressible Navier-Stokes equations, Internat. J. Numer. Methods Fluids, 20 (1995), pp. 1137-1151.
13. R. J. MACKINNON AND G. F. CAREY, Analysis of material interface discontinuities and superconvergent fluxes in finite difference theory, J. Comput. Phys., 75 (1988), pp. 151-167.
14. R. J. MACKINNON AND G. F. CAREY, Superconvergent derivatives: A Taylor series analysis, Internat. J. Numer. Methods Engrg., 28 (1989), pp. 489-509.
15. R. J. MACKINNON AND G. F. CAREY, Nodal superconvergence and solution enhancement for a class of finite element and finite difference methods, SIAM J. Sci. Statist. Comput., 11 (1990), pp. 343-353.
16. R. J. MACKINNON AND R. W. JOHNSON, Differential equation based representation of truncation errors for accurate numerical simulation, Internat. J. Numer. Methods Fluids, 13 (1991), pp. 739-757.
17. R. T. MCLAY, S. L. SWIFT, AND G. F. CAREY, Maximizing sparse matrix-vector product performance on RISC-based MIMD computers, J. Parallel and Distrib. Comput., 37 (1996), pp. 146-158.
18. W. F. SPOTZ, High-Order Compact Finite Difference Schemes for Computational Mechanics, Ph.D. thesis, University of Texas at Austin, Austin, TX, 1995.
19. W. F. SPOTZ AND G. F. CAREY, High-order compact scheme for the stream-function vorticity equations, Internat. J. Numer, Methods Engrg., 38 (1995), pp. 3497-3512.
20. W. F. SPOTZ AND G. F. CAREY, A high-order compact formulation for the 3D Poisson equation, Numer. Methods Partial Differential Equations, 12 (1996), pp. 235-243.
21. J. WILKINSON, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965.