Efficient solution of liquid state integral equations using the Newton-GMRES algorithm

Computer Physics Communications

Volumn 119, Issue 2, 1999, Pages 122-134

  Booth, Michael J ^a,e   Schlijper, A G ^b   Scales, L E ^c   Haymet, A D J ^d  

^a UNIVERSITY OF SYDNEY   (Australia)

^b UNILEVER RESEARCH   (United Kingdom)

^c SHELL RESEARCH AND TECHNOLOGY CENTRE   (Netherlands)

^d University of Houston   (United States)

^e WESTPAC BANKING CORPORATION   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; EXTRAPOLATION; INTEGRAL EQUATIONS; ITERATIVE METHODS; NONLINEAR EQUATIONS; VECTORS;

NEWTON-RAPHSON METHOD; ORNSTEIN-ZERNIKE INTEGRAL EQUATIONS; PICARD ITERATIVE METHODS;

EQUATIONS OF STATE OF LIQUIDS;

EID: 0033516241     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0010-4655(99)00186-1     Document Type: Article

References (49)

1. M.R. Bush, M.J. Booth, A.G. Schlijper, A.D.J. Haymet, Molec. Phys. 95 (1998) 601.
2. J. Boronat, A. Polls, A. Fabrocini, Phys. Rev. B 56 (1997) 11854.
3. J. Chihara, G. Kahl, Structure Factor for Electronic Structure of Compressed Liquid Rubidium, available from the Condensed Matter preprint server, cond-mat/980116 (1998).
4. D. Henderson, L. Blum, J. Electroanal. Chem. 93 (1978) 151.
5. S. Li, R.M. Mazo, J. Chem. Phys. 86 (1987) 5757.
6. M. Ikeguchi, J. Doi, J. Chem. Phys. 103 (1995) 5011.
7. M. Kinoshita, M. Harada, Mol. Phys. 81 (1994) 1473.
8. S. Labík, A. Malijevský, A class of efficient algorithms for the numerical solution of the Ornstein-Zernike equation (1996), this work was presented at the CECAM Workshop, Integral Equations for the Pair Structure of Classical and Quantum Fluids: State of the Art and Recent Applications, Lyon, France, 26-29 June (1996).
9. S. Labík, A. Malijevský, P. Vonka, Molec. Phys. 56 (1985) 709.
10. G. Zerah, J. Comput. Phys. 61 (1985) 280.
11. L. Mier Y Terán, E. Díaz-Herrera, M. Lozada-Cassou, J. Comput. Phys. 84 (1989) 326.
12. P.T. Cummings, P.A. Monson, Int. J. Thermophys. 11 (1990) 97.
13. A. Malijevský, R. Pospíšil, W.R. Smith, S. Labík, Molec. Phys. 72 (1991) 199.
14. A. Busigin, C.R. Phillips, Molec. Phys. 76 (1992) 89.
15. M. Kinoshita, M. Harada, Mol. Phys. 79 (1993) 145.
16. S. Labík, R. Pospíšil, A. Malijevský, W.R. Smith, J. Comput. Phys. 115 (1994) 12.
17. G. Pastore, F. Matthews, O. Akinlade, Z. Badirkhan, Molec. Phys. 84 (1995) 653.
18. J.A. Anta, E. Lomba, C. Martín, M. Lombardero, Molec. Phys. 84 (1995) 743.
19. H.H.H. Homeier, S. Rast, H. Krienke, Comput. Phys. Commun. 92 (1995) 188.
20. M. Rovere, J.P. Hansen, G. Pastore, Integral Equations for the Pair Structure of Classical and Quantum Fluids: State of the Art and Recent Applications, 26-29 June (1996), this report is available from http://www.cecam.fr/reports/reports96/rovere.ps.gz.
21. P.N. Brown, Y. Saad, SIAM J. Sci. Stat. Comput. 11 (1990) 450.
22. C.T. Kelley, Iterative methods for linear and nonlinear equations, Frontiers in Applied Mathematics, Vol. 16 (SIAM, Philadelphia, PA, 1995).
23. M. Pernice, H.F. Walker, SIAM J. Sci. Comput. 19 (1998) 302.
24. T. Ichiye, A.D.J. Haymet, J. Chem. Phys. 89 (1988) 4315.
25. M.J. Booth, D. Duh-M., A.D.J. Haymet, J. Chem. Phys. 101 (1994) 7925.
26. Y. Saad, M.H. Schultz, SIAM J. Sci. Stat. Comput. 7 (1986) 856.
27. P. Pulay, Chem. Phys. Lett. 73 (1980) 393.
28. P. Pulay, J. Comput. Chem. 3 (1982) 556.
29. S. Maw, H. Sato, S. Tenno, F. Hirata, Chem. Phys. Lett. 276 (1997) 20.
30. M. Kawata, C.M. Cortis, R.A. Friesner, J. Chem. Phys. 108 (1998) 4426.
31. K.E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind (Cambridge Univ. Press, Cambridge, 1997).
32. K.E. Atkinson, J. Int. Eqs. Appl. 4 (1992) 15.
33. M.J. Gillan, Molec. Phys. 38 (1979) 1781.
34. G.M. Abernethy, M.J. Gillan, Molec. Phys. 39 (1980) 839.
35. L.L. Lee, H.D. Cochran, Integral equations for the microstructures of supercritical fluids, in: Supercritical Fluids Fundamentals for Application, E. Kiran, J.M.H. Levelt Sengers, eds. (Kluwer Academic, Dordrecht, 1994) pp. 365-383.
36. M. Kinoshita, D.R. Bérard, J. Comput. Phys. 124 (1996) 230.
37. Z. Chen-M., B.M. Pettitt, Comput. Phys. Commun. 85 (1995) 239.
38. S.C. Eisenstat, H.F. Walker, SIAM J. Sci. Comput. 17 (1996) 16.
39. The NITSOL distribution may be obtained as a compressed tar archive from http://www.chpc.utah.edu/~usimap/nitsol/nitsol.tar.gz.
40. The FLOPS V2.0 (18 Dec 1992) benchmark for this machine returned values of MFLOPS(1) = 40.3, MFLOPS(2) = 26.3, MFLOPS(3) = 37.1 and MFLOPS(4) = 45.7. For information on the FLOPS benchmark we refer the interested reader to http://performance.netlib.org/benchweb/ or ftp://ftp.nosc.mil/pub/aburto/flops/.
41. M.J. Booth, A. Eaton, A.D.J. Haymet, Molec. Phys. (1999), in preparation.
42. D. Duh-M., A.D.J. Haymet, J. Chem. Phys. 97 (1992) 7716.
43. A.R. Allnatt, Molec. Phys. 8 (1964) 533.
44. P.J. Rossky, H.L. Friedman, J. Chem. Phys. 72 (1980) 5694.
45. D. Henderson, F.F. Abraham, J.A. Barker, Mol. Phys. 31 (1976) 1291.
46. D. Henderson, Integral equation theories for inhomogeneous fluids, in: Fundamentals of Inhomogeneous Fluids, D. Henderson, ed. (Marcel Dekker, New York, 1992).
47. A. Malijevský, R. Pospíšil, W.R. Smith, S. Labík, Molec. Phys. 75 (1992) 981.
48. D. Feng, T.H. Pulliam, SIAM J. Opt. 7 (1997) 757.
49. Further information may be obtained from http://www.hem.usyd.edu.au/~boothm/NITSOL/NITSOL.html.