Simulation of diffusion using quasi-random walk methods

Mathematics and Computers in Simulation

Volumn 47, Issue 2-5, 1998, Pages 153-163

  Coulibaly, Ibrahim ^a   Lécot, Christian ^a  

^a UNIVERSITÉ DE SAVOIE   (France)

Author keywords

Diffusion; Discrepancy; Error bounds; Monte Carlo methods; Random walk

Indexed keywords

EID: 0001159109     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-4754(98)00100-1     Document Type: Article

References (17)

1. R.E. Caflisch, B. Moskowitz, Modified Monte Carlo methods using quasi-random sequences, in: H. Niederreiter, P.J.-S. Shiue (Eds.), Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Springer, New York, 1995, pp. 1-16.
2. C.S. Chen, The method of fundamental solutions and the quasi-Monte Carlo method for Poisson's equation, in: H. Niederreiter, P.J.-S. Shiue (Eds.), Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Springer, New York, 1995, pp. 158-167.
3. R. Dautray, Méthodes probabilistes pour les équations de la physique, Eyrolles, Paris, 1989.
4. H. Faure, Discrépance de suites associées à un système de numération (en dimension s), Acta Arith. 41 (1982) 337-351.
5. J.H. Halton, On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals, Numer. Math. 2 (1960) 84-90; Berichtigung, Numer. Math. 2 (1960) p. 196.
6. J.H. Halton, On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals, Numer. Math. 2 (1960) 84-90; Berichtigung, Numer. Math. 2 (1960) p. 196.
7. A. Keller, A quasi-Monte Carlo algorithm for the global illumination problem in the radiosity setting, in: H. Niederreiter, P.J.-S. Shiue (Eds.), Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Springer, New Yok, 1995, pp. 239-251.
8. L. Kuipers, H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974.
9. C. Lécot, A quasi-Monte Carlo method for the Boltzmann equation, Math. Comput. 56 (1991) 621-644.
10. C. Lécot, I. Coulibaly, A quasi-Monte Carlo scheme using nets for a linear Boltzmann equation, SIAM J. Numer. Anal. 35 (1998) 51-70.
11. W.J. Morokoff, R.E. Caflisch, A quasi-Monte Carlo approach to particle simulation of the heat equation, SIAM J. Numer. Anal. 30 (1993) 1558-1573.
12. B. Moskowitz, Quasirandom diffusion Monte Carlo, in: H. Niederreiter, P.J.-S. Shiue (Eds.), Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Springer, New York, 1995, pp. 278-298.
13. H. Niederreiter, Quasi-Monte Carlo methods and pseudo-random numbers, Bull. Amer. Math. Soc. 84 (1978) 957-1041.
14. H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987) 273-337.
15. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992.
16. I.M. Sobol, On the distribution of points in a cube and the approximate evaluation of integrals, USSR Comput. Math. Math. Phys. 7 (1967) 86-112.
17. J. Spanier, Quasi-Monte Carlo methods for particle transport problems, in: H. Niederreiter, P.J.-S. Shiue (Eds.), Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Springer, New York, 1995, pp. 121-148.