Efficient parallel algorithms for parabolic problems

SIAM Journal on Numerical Analysis

Volumn 39, Issue 5, 2001, Pages 1469-1487

  Du, Q ^a   Mu, M ^a   Wu, Z N ^b  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^b TSINGHUA UNIVERSITY   (China)

Author keywords

Approximation accuracy; Finite difference; Parabolic equations; Parallel efficiency; Stability

Indexed keywords

EID: 0036410156     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142900381710     Document Type: Article

References (14)

1. X. CAI, Additive Schwarz algorithms for parabolic convection-diffusion equations, Numer. Math, 50 (1991), pp. 41-52.
2. T. F. CHAN AND T. MATHEW, Domain Decomposition Algorithms, CAM report CAM 94-2, UCLA, 1994.
3. C. N. DAWSON, Q. DU, AND T. F. DUPONT, A finite difference domain decomposition algorithm for numerical solution of the heat equation, Math. Comp., 57 (1991), pp. 63-71.
4. B. GUSTAFSSON, The convergence rate for difference approximations to general mixed initial boundary value problems, SIAM J. Numer. Anal., 18 (1981), pp. 179-190.
5. B. GUSTAFSSON, H.-O. KREISS, AND A. SUNDSTRÖM, Stability theory of difference approximations for mixed initial boundary value problems. II, Math. Comp., 26 (1972), pp. 649-686.
6. D. E. KEYES, Domain Decomposition: A Bridge between Nature and Parallel Computers, ICASE report 92-44, Langley, VA, 1992.
7. Y. KUZNETSOV, New algorithms for approximate realization of implicit difference scheme, Soviet J. Numer. Anal. Math. Modelling, 3 (1988), pp. 99-114.
8. D. MICHELSON, Stability theory of difference approximations for multidimensional initial-boundary value problems, Math. Comp., 40 (1983), pp. 1-45.
9. D. MICHELSON, Convergence theorem for difference approximations of hyperbolic quasilinear initial-boundary value problems, Math. Comp. 49, (1987), pp. 445-459.
10. K. W. MORTON AND D. F. MAYERS, Numerical Solution of Partial Differential Equations, Cambridge University Press, Cambridge, UK, 1994.
11. S. OSHER, Stability of parabolic difference approximations to certain mixed initial boundary value problems, Math. Comp., 26 (1972), pp. 13-39.
12. Z. N. WU AND H. ZOU, Grid overlapping for implicit parallel computations of compressible flows, J. Comput. Phys., 157 (2000), pp. 2-43.
13. G. YUAN, L. SHEN, AND Y. ZHOU, Unconditional stability of alternating difference schemes with intrinsic parallelism for two-dimensional parabolic systems, Numer. Methods Partial Differential Equations, 15 (1999), pp. 625-636.
14. Y. ZHOU AND G. YUAN, General difference schemes with intrinsic parallelism for semilinear parabolic systems of divergence type, J. Comput. Math., 17 (1999), pp. 337-352.