Further it is wise to mention that the above

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ors to discourage assessing the results in the context of quality of the random events derived from the random number generator. Further, it is wise to mention that the above observations are speci c to using random real numbers, and not random integers. In particular, there may exist a resonance between the physical problem and random integers such as the successive odd/even pairs obtained when using a modulus of a power of two in a linear, congruential generator. As the complexity of the problem decreases, the potential for problems with the random number generator increases. We note that FORTRAN 90 will obviate many of the impediments to a portable implementation of random number generators, as: (1) it allows arbitrary precision in numbers, which can be made large enough to eliminate over ow and problems with a sign bit, and (2) it has embedded in the language functions to return the date and time, which now are system calls and vary from system to system. Moreover, a random number generator intrinsic function exists as part of the language, and it may be quite good (although it will have to be tested thoroughly by the Monte Carlo community before gaining universal acceptance). 8 References N. S. Altman. \Bitwise Behavior of Random Number Generators," SIAM J. Sci. Stat. Comput., 9(5), September, pps. 941-949, 1988. 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. S. L. Anderson. \Random Number Generators on Vector Supercomputers and Other 42 Advanced Architectures," SIAM Review, 32 (2), pps. 221-251, 1990. E. F. Beckenback (ed.) Modern Mathematics for the Engineer, McGraw Hill, New York, NY, 1956. K. Binder. Applications of the Monte Carlo Method in Statistical Physics, SpringerVerlag, Berlin, 1984. 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. T. B. Brown. Vectorized Monte Carlo, Ph.D. Dissertation, Department of Nuclear Engineering, University of Michigan, 1981. 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. 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. 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. P. J. Burns and D. V. Pryor. \Vector and parallel Monte Carlo radiative heat transfer," Numerical Heat Transfer, Part B: Fundamentals 16(101), 1989. R. D. Chandler, J. N. Panaia, R. B. Stevens and G. E. Zinmeister. \The solution of steady-state convection problems by the xed random walk method," Journal of Heat Transfer 90(3), 361-363, 1968. Cray Research, Inc. UNICOS Libraries, Macros and Opdefs Reference Manual, Publication SR-2013, Cray Research, Inc., Mendota Heights, MN, 1987. D. Crockett, J. D. Maltby and P. J. Burns, \MONT3V user's manual," Internal Publication, Department of Mechanical Engineering, Colorado State University, 1989. J. H. Curtis. \Sampling Methods Applied to Di erential and Di erence Equations," Proceedings IBM Seminar on Scienti c Computation, Nov. 1949, IBM Corp., New York, 87-109, 1950. L. Dagum. \Implementation of a hypersonic rare ed ow particle simulation on the connection machine," Proceedings, Supercomputing '89, ACM Press, Baltimore, MD, 42-50, Nov. 13-17, 1989. R. Eckhard. \Stan Ulam, John von Neumann and the Monte Carlo method," Los Alamos Science, 15, 1987. Remarks 43 L. W. Ehrlich. \Monte Carlo 2Solutions of Boundary Value problems Involving the [email protected] ference Analogue of @xu + @2v + @ w ," Journal of the Association of Computing Machinery, 2 @y2 @z2 6,204-218, 1959. A. F. Emery and W. W. Carson. \A modi cation to the Monte Carlo method - the exodus method," Journal of Heat Transfer 90(3), 328-332, 1968. 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. S. W. Golomb, Shift Register Sequences, (Revised Ed.), Aegean Park Press, 1982. A. Haji-Sheikh, \Monte Carlo Methods," Ch. 16 in Handbook of Numerical Heat Transfer, 673-722, 1988. 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. J. M. Hammersly and D. C. Handscomb. Monte Carlo Methods, Methuen, London, 1964. D. B. Heifetz. \Vectorizing and macrotasking Mont...
View Full Document

This document was uploaded on 01/28/2014.

Ask a homework question - tutors are online