References

1

N. S. Altman. ``Bitwise Behavior of Random Number Generators,'' SIAM J. Sci. Stat. Comput., 9(5), September, pps. 941-949, 1988.

2

G. M. Amdahl. ``Validity of the single processor approach to achieving large-scale computing capabilities,'' Proceedings of the American Federation of Information Processing Societies, 30, Washington, DC, pps. 483-485, 1967.

3

S. L. Anderson. ``Random Number Generators on Vector Supercomputers and Other Advanced Architectures,'' SIAM Review, 32 (2), pps. 221-251, 1990.

4

E. F. Beckenback (ed.) Modern Mathematics for the Engineer, McGraw Hill, New York, NY, 1956.

5

K. Binder. Applications of the Monte Carlo Method in Statistical Physics, Springer-Verlag, Berlin, 1984.

6

J. Briesmeister, ed. ``MCNP: a general Monte Carlo code for neutron and photon transport,'' LA-7396-M, Rev 2, Los Alamos National Laboratory report, 1986.

7

T. B. Brown. Vectorized Monte Carlo, Ph.D. Dissertation, Department of Nuclear Engineering, University of Michigan, 1981.

8

C. E. Burghart and P. N. Stevens. ``A general method of importance sampling the angle of scattering in Monte Carlo calculations,'' Nuclear Science and Engineering 46(1), 12- 21, 1971.

9

P. Burns, M. Christon, R. Schweitzer, H. Wasserman, M. Simmons, O. Lubeck and D. Pryor. ``Vectorization of Monte Carlo particle transport - an architectural study using the LANL benchmark GAMTEB,'' Proceedings, Supercomputing '89, Reno, NV, 10 - 20, Nov. 13, 1988.

10

P. J. Burns and D. V. Pryor. ``Vector and parallel considerations for the Rayleigh problem in molecular gas dynamics,'' Proceedings, 7th International Conference on Finite Element Methods in Flow Problems, Huntsville, AL, April 3-7, 1989.

11

P. J. Burns and D. V. Pryor. ``Vector and parallel Monte Carlo radiative heat transfer,'' Numerical Heat Transfer, Part B: Fundamentals 16(101), 1989.

12

R. D. Chandler, J. N. Panaia, R. B. Stevens and G. E. Zinmeister. ``The solution of steady-state convection problems by the fixed random walk method,'' Journal of Heat Transfer 90(3), 361-363, 1968.

13

Cray Research, Inc. UNICOS Libraries, Macros and Opdefs Reference Manual, Publication SR-2013, Cray Research, Inc., Mendota Heights, MN, 1987.

14

D. Crockett, J. D. Maltby and P. J. Burns, ``MONT3V user's manual,'' Internal Publication, Department of Mechanical Engineering, Colorado State University, 1989.

15

J. H. Curtis. ``Sampling Methods Applied to Differential and Difference Equations,'' Proceedings IBM Seminar on Scientific Computation, Nov. 1949, IBM Corp., New York, 87-109, 1950.

16

L. Dagum. ``Implementation of a hypersonic rarefied flow particle simulation on the connection machine,'' Proceedings, Supercomputing '89, ACM Press, Baltimore, MD, 42-50, Nov. 13-17, 1989.

17

R. Eckhard. ``Stan Ulam, John von Neumann and the Monte Carlo method,'' Los Alamos Science, 15, 1987.

18

L. W. Ehrlich. ``Monte Carlo Solutions of Boundary Value problems Involving the Difference Analogue of ,'' Journal of the Association of Computing Machinery, 6,204-218, 1959.

19

A. F. Emery and W. W. Carson. ``A modification to the Monte Carlo method - the exodus method,'' Journal of Heat Transfer 90(3), 328-332, 1968.

20

P. Frederickson, R. Hiromoto, T. L. Jordan, B. Smith, T. Warnock, ``Pseudo-random trees in Monte Carlo,'' Parallel Computing, 1(3), December, 175-180, 1984.

21

S. W. Golomb, Shift Register Sequences, (Revised Ed.), Aegean Park Press, 1982.

22

A. Haji-Sheikh, ``Monte Carlo Methods,'' Ch. 16 in Handbook of Numerical Heat Transfer, 673-722, 1988.

23

A. Haji-Sheikh and E. M. Sparrow. ``The Floating Random Walk and its Application to Monte Carlo Solutions of Heat Equations,'' Journal of Heat Transfer 89(2), 121-131, 1967.

24

J. M. Hammersly and D. C. Handscomb. Monte Carlo Methods, Methuen, London, 1964.

25

D. B. Heifetz. ``Vectorizing and macrotasking Monte Carlo neutral particle algorithms,'' Princeton Plasma Physics Laboratory Report PPPL-2427, April 1987.

26

J. R. Howell. Application of Monte Carlo to Heat Transfer Problems, Advances in Heat Transfer, 5, 1-54, 1968.

27

C. C. Hurd, ed., Proceedings of the Seminar on Scientific Computation, International Business Machines Corporation, New York, NY, Nov. 1949.

28

H. Kahn and A. W. Marshall. ``Methods of reducing sample size in Monte Carlo computations,'' Journal of Operations Research Society of America, 1, 263-278, 1953.

29

M. H. Kalos. ``Monte Carlo methods and the computers of the future,'' Ultracomputer Note #83, April 1985.

30

M. A. Kalos and P. A. Whitlock, Monte Carlo Methods, Volume I: Basics, Wiley Interscience, New York, 1986.

31

J. P. C. Kleinjnen. Statistical Techniques in Simulation, Part 1, Marcel Dekker, New York, NY, 1974.

32

D. E. Knuth. Seminumerical Algorithms, 2nd Ed., Vol. 2 of The Art of Computer Programming, Addison-Wesley, Reading PA, 1981.

33

J. M. Lanore. ``Weighting and biasing of a Monte Carlo calculation for very deep penetration of radiation,'' Nuclear Science Engineering 45(1), 66-72, 1971.

34

M. E. Larsen and J. R. Howell. ``Least-squares smoothing of direct-exchange areas in zonal analysis,'' Journal of Heat Transfer, 108, 239-242, 1986.

35

J. D. Maltby. Three-dimensional Simulation of Radiative Heat Transfer by the Monte Carlo Method, Master's Thesis, Department of Mechanical Engineering, Colorado State University, 1987.

36

J. D. Maltby. Analysis of Electron Heat Transfer via Monte Carlo Simulation, Ph.D. Dissertation, Department of Mechanical Engineering, Colorado State University, 1987.

37

J. D. Maltby and P. J. Burns, ``MONT2D and MONT3D user's manual,'' Internal Publication, Department of Mechanical Engineering, Colorado State University, 1988.

38

J. D. Maltby and P. J. Burns, ``MONT3E user's manual,'' Internal Publication, Department of Mechanical Engineering, Colorado State University, 1989.

39

G. Marsaglia, A Current View of Random Number Generators, Computer Science and Statistics, The Interface, Elsevier Science Publishers B. V. (North Holland) L. Billard (ed.), 1985.

40

W. R. Martin, P. F. Nowak and J. A. Rathkopf. ``Monte Carlo photon tracing on a vector supercomputer,'' IBM Journal of Research and Development 30(2), 1986.

41

M. Mascagni, S. Cuccaro, D. Pryor, and M. Robinson, ``A fast, high quality, reproducible, parallel, lagged-Fibonacci pseudorandom number generator,'' SRC-TR-94-115, Supercomputing Research Center, 17100 Science Drive, Bowie, MD 20715, 1994.

42

J. D. McDonald and D. Baganoff. ``Vectorization of a particle simulation method for hypersonic rarefied flow,'' AIAA-88-2735, AIAA Thermophysics, Plasmadynamics and Lasers Conference, San Antonio, June 27-29, 1988.

43

N. Metropolis, ``The beginning of the Monte Carlo method,'' Los Alamos Science, 15, 1987.

44

N. Metropolis. ``Monte Carlo - in the beginning and some great expectations,'' Monte Carlo Methods and Applications in Neutronics, Photonics and Statistical Physics, Cadarache Castle, France, 1985.

45

M. F. Modest. ``Monte Carlo method in analysis of three-dimensional radiative exchange factors for non-gray non-diffuse surfaces,'' Numerical Heat Transfer, 1, 403, 1978.

46

M. E. Mueller. ``Some continuous Monte Carlo methods for the Dirichlet problem,'' Annals of Mathematical Statistics, 27, 569-589, 1956.

47

S. K. Park and K. W. Miller, ``Random Number Generators: Good Ones are Hard to Find,'' Transactions of the ACM, Nov. 1988.

48

L. C. Polgar and J. R. Howell. ``Directional thermal-radiative properties of conical cavities,'' NASA TN D-2904, 1965

49

W. H. Press et al. Numerical Recipes (FORTRAN), pps. 191-225, 1988.

50

D. V. Pryor and P. J. Burns. ``A parallel Monte Carlo model for radiative heat transfer,'' Presented at the 1986 SIAM Meeting, Boston, MA, July 21-25,1986.

51

D. V. Pryor and P. J. Burns. ``Vectorized molecular aerodynamics simulation of the Rayleigh problem,'' Proceedings, Supercomputing '88, Orlando, FL, Nov. 14, 1988.

52

D. Pryor, S. Cuccaro, M. Mascagni, and M. Robinson. ``Implementation and usage of a portable and reproducible parallel pseudorandom number generator,'' SRC-TR-94-116, Supercomputing Research Center, 17100 Science Drive, Bowie, MD 20715, 1994.

53

Lord Rayleigh, ``On James Bernoulli's Theorem in Probabilities,'' Philosophical Magazine, 47, 1899, pp. 246-251.

54

S. M. Ross. A First Course in Probability, 2nd Ed., Macmillan, New York, NY (1976).

55

R. Y. Rubenstein. Simulation and the Monte Carlo Method, Wiley, New York, NY, 1981.

56

Y. A. Schreider. Methods of Statistical Testing, Elsevier, New York, NY, 1964.

57

Sequent Computer Systems. ``Parallel ray tracing study,'' TN-85-09(rvp), Rev. 1.0, 1985.

58

N. Shamsunder, E. M. Sparrow and R. P. Heinisch. ``Monte Carlo radiative solutions - effect of energy partitioning and number of rays,'' International Journal of Heat and Mass Transfer 16(3), 690-694, 1973.

59

S. Ulam and N. Metropolis. ``The Monte Carlo method,'' Journal of American Statistical Association, 44, 335, 1949.

60

S. Ulam, R. D. Richtmeyer and J. von Neumann. ``Statistical methods in neutron diffusion,'' LAMS-551, Los Alamos National Laboratory, 1947.

61

Y. Q. Zhong and M. H. Kalos. ``Monte Carlo transport calculations on an Ultracomputer,'' Ultracomputer Note #46, March 1983.

62

G. E. Zinsmeister and J. A. Sawyer. ``A method for improving the efficiency of Monte Carlo calculation for Dirichlet problems,'' Journal of Heat Transfer 96(2), 1057-1064, 1976.