Experiences with sparse matrix solvers in parallel ODE software

Computers and Mathematics with Applications

Volumn 31, Issue 9, 1996, Pages 43-55

  De Swart, J J B ^a   Blom, J G ^a  

^a CWI   (Netherlands)

Author keywords

Newton iteration; Numerical analysis; Parallelism; Runge Kutta methods; Sparse matrices

Indexed keywords

COMPUTER SOFTWARE; FUNCTIONS; ITERATIVE METHODS; LINEAR ALGEBRA; MATRIX ALGEBRA; NONLINEAR EQUATIONS; NUMERICAL METHODS;

DERIVATIVE FUNCTION; JACOBIAN; NEWTON TYPE PROCESS; PARALLEL ODE SOFTWARE; RUNGE KUTTA METHODS; SPARSE MATRIX SOLVERS; STIFF INITIAL VALUE PROBLEM;

DIFFERENTIAL EQUATIONS;

EID: 0030151235     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/0898-1221(96)00041-7     Document Type: Article

References (19)

1. I.S. Duff, MA28 - A set of Fortran subroutines for sparse unsymmetric linear equations, Technical Report AERE R8730, HMSO, London, (1977).
2. Z. Zlatev, J. Wasniewski and K. Schaumburg, Y12M, solution of large and sparse systems of linear algebraic equations, In Lecture Notes in Computer Science, No. 121, Springer-Verlag, Berlin, (1981).
3. B.P. Sommeijer, Parallelism in the numerical integration of initial value problems, Ph.D. Thesis, University of Amsterdam, (1992).
4. A. Bellen, Parallelism across the steps for difference and differential equations, In Lecture Notes in Mathematics, p. 1386, Springer-Verlag, (1987).
5. A. Bellen, R. Vermiglio and M. Zennaro, Parallel ODE-solvers with stepsize control, JCAM 31, 277-293 (1990).
6. K. Burrage, Parallel methods for initial value problems, Applied Numerical Mathematics 11, 5-26 (1993).
7. P. Chartier, Parallelism in the numerical solutions of initial value problems for ODEs and DAEs, Ph.D. Thesis, Université de Rennes I, France, (1993).
8. B. Orel, Parallel Runge-Kutta methods with real eigenvalues, Applied Numerical Mathematics 11, 241-250 (1993).
9. P.J. van der Houwen and B.P. Sommeijer, Iterated Runge-Kutta methods on parallel computers, SIAM J. Sci. Stat. Comput. 12, 1000-1028 (1991).
10. P.J. van der Houwen and B.P. Sommeijer, Analysis of parallel diagonally implicit iteration of Runge-Kutta methods, APNUM 11, 169-188 (1993).
11. H.M. Markowitz, The elimination form of the inverse and its application to linear programming, Management Sci. 3, 255-269 (1957).
12. I.S. Duff, A.M. Erisman and J.K. Reid, Direct Methods for Sparse Matrices, Monographs on Numerical Analysis, Oxford Science Publications, (1986).
13. J.J. Dongarra and E. Grosse, Distribution of software via electronic mail, Technical Report 30, Commun. ACM, 403-407 (1987).
14. M.Z. Jacobson and R.P. Turco, SMVGEAR: A sparse-matrix, vectorized gear code for atmospheric models, Atmospheric Environment 28, 273-284 (1994).
15. A.C. Hindmarsh, ODEPACK, a systemized collection of ODE solvers, In Scientific Computing, (Edited by R. Stepleman et al.), pp. 55-64, IMACS, North-Holland, Amsterdam, (1983).
16. J.G. Verwer, J.G. Blom, M. van Loon and E.J. Spee, A comparison of stiff ODE solvers for atmospheric chemistry problems, Atmospheric Environment 29 (1995).
17. B.W. Char, K.O. Geddes, G.H. Gonnet, B.L. Leong, M.B. Monagan and S.M. Watt, Maple V Language Reference Manual, Springer-Verlag, New York, (1991).
18. Cray Research, Inc., UNICOS Performance Utilities Reference Manual, SR-2040 8.0 edition, (1994).
19. Cray Research, Inc., CF77 Commands and Directives, SR-3771 6.0 edition, (1994).