A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature

Mathematics of Computation

Volumn 69, Issue 229, 2000, Pages 177-195

  Sheen, Dongwoo ^a   Sloan, Ian H ^b   Thomée, Vidar ^c  

^a Seoul National University   (South Korea)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

^c CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034407089     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-99-01098-4     Document Type: Article

References (20)

1. P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York, 1975. MR 56:7119
2. P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York, 1975. MR 56:7119
3. J. Douglas, Jr., J. E. Santos, D. Sheen, and L. S. Bennethum, Frequency domain treatment of one-dimensional scalar waves, Math. Mod. Meth. Appl. Sci. 3 (1993), 171-194. MR 94g:65111
4. J. Douglas, Jr., J. E. Santos, D. Sheen, and L. S. Bennethum, Frequency domain treatment of one-dimensional scalar waves, Math. Mod. Meth. Appl. Sci. 3 (1993), 171-194. MR 94g:65111
5. J. Douglas, Jr., J. E. Santos, and D. Sheen, Approximation of scalar waves in the space-frequency domain, Math. Mod. Meth. Appl. Sci 4 (1994), 509-531. MR 95e:65089
6. J. Douglas, Jr., J. E. Santos, and D. Sheen, Approximation of scalar waves in the space-frequency domain, Math. Mod. Meth. Appl. Sci 4 (1994), 509-531. MR 95e:65089
7. S. C. Eisenstat, Jr., H. E. Elman, N. H. Schultz, and A. H. Sherman, The (new) Yale Sparse Matrix Package, Elliptic Problem Solvers II (A. L. Schoenstadt and G. Birkhoff, eds.), Academic Press, New York, 1983, pp. 45-52. MR 85g:65007
8. S. C. Eisenstat, Jr., H. E. Elman, N. H. Schultz, and A. H. Sherman, The (new) Yale Sparse Matrix Package, Elliptic Problem Solvers II (A. L. Schoenstadt and G. Birkhoff, eds.), Academic Press, New York, 1983, pp. 45-52. MR 85g:65007
9. E. Gallopoulos and Y. Saad, Efficient solution of parabolic equations by Krylov approximation methods, SIAM J. Sci. Statist. Comput. 13 (1992), 1236-1264. MR 93d:65085
10. E. Gallopoulos and Y. Saad, Efficient solution of parabolic equations by Krylov approximation methods, SIAM J. Sci. Statist. Comput. 13 (1992), 1236-1264. MR 93d:65085
11. M. Hochbruck and C. Lubich, On Krylov Subspace Approximations to the Matrix Exponential Operator, SIAM J. Numer. Anal. 34 (1997), 1911-1925. MR 98h:65018
12. M. Hochbruck and C. Lubich, On Krylov Subspace Approximations to the Matrix Exponential Operator, SIAM J. Numer. Anal. 34 (1997), 1911-1925. MR 98h:65018
13. C.-O. Lee, J. Lee, and D. Sheen, A frequency-domain method for finite element solutions of parabolic problems, RIM-GARC Preprint 97-41, Department of Mathematics, Seoul National University, 1997.
14. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983. MR 85g:47061
15. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983. MR 85g:47061
16. D. Sheen and Y. Yeom, A frequency-domain parallel method for the numerical approximation of parabolic problems, RIM-GARC Preprint 96-38, Department of Mathematics, Seoul National University, 1996.
17. V. Thomée, Galerkin Finite Element Methods for Parabolic Problems, Springer Series in Computational Mathematics, Vol. 25, Springer-Verlag, Berlin Heidelberg New York, 1997. MR 98m:65007
18. V. Thomée, Galerkin Finite Element Methods for Parabolic Problems, Springer Series in Computational Mathematics, Vol. 25, Springer-Verlag, Berlin Heidelberg New York, 1997. MR 98m:65007
19. R. S. Varga, Functional Analysis and Approximation Theory in Numerical Analysis, Conference Board of the Mathematical Sciences Regional Conferences Series in Applied Mathematics, No. 3, SIAM, Philadelphia, PA, 1971. MR 46:9602
20. R. S. Varga, Functional Analysis and Approximation Theory in Numerical Analysis, Conference Board of the Mathematical Sciences Regional Conferences Series in Applied Mathematics, No. 3, SIAM, Philadelphia, PA, 1971. MR 46:9602