Fundamentals of Monte Carlo Particle Transport

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Fundamentals of Monte Carlo Particle Transport

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Solving particle transport problems with the Monte Carlo method is simple - just simulate the particle behavior. The devil is in the details, however. This course provides a balanced approach to the theory and practice of Monte Carlo simulation codes, with lectures on transport, random number generation, random sampling, computational geometry, collision physics, tallies, statistics, eigenvalue calculations, variance reduction, and parallel algorithms.

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LA-UR-05-4983<br /> Approved for public release;<br /> distribution is unlimited.<br /> <br /> Title:<br /> <br /> Author(s):<br /> <br /> Submitted to:<br /> <br /> FUNDAMENTALS OF MONTE CARLO<br /> PARTICLE TRANSPORT<br /> <br /> FORREST B. BROWN<br /> <br /> Lecture notes for Monte Carlo course<br /> <br /> Los Alamos National Laboratory, an affirmative action/equal opportunity employer, is operated by the University of California for the U.S.<br /> Department of Energy under contract W-7405-ENG-36. By acceptance of this article, the publisher recognizes that the U.S. Government<br /> retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S.<br /> Government purposes. Los Alamos National Laboratory requests that the publisher identify this article as work performed under the<br /> auspices of the U.S. Department of Energy. Los Alamos National Laboratory strongly supports academic freedom and a researcher’s right to<br /> publish; as an institution, however, the Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness.<br /> Form 836 (8/00)<br /> <br /> Fundamentals of Monte Carlo Particle Transport<br /> Lecture 1<br /> <br /> Fundamentals<br /> of Monte Carlo<br /> Particle Transport<br /> <br /> Forrest B. Brown<br /> Monte Carlo Group (X-3)<br /> Los Alamos National Laboratory<br /> 1 -1<br /> <br /> LA-UR-04–8817<br /> <br /> Abstract<br /> Fundamentals of Monte Carlo Particle Transport<br /> Solving particle transport problems with the Monte Carlo method is simple just simulate the particle behavior. The devil is in the details, however. This<br /> course provides a balanced approach to the theory and practice of Monte<br /> Carlo simulation codes, with lectures on transport, random number<br /> generation, random sampling, computational geometry, collision physics,<br /> tallies, statistics, eigenvalue calculations, variance reduction, and parallel<br /> algorithms. This is not a course in how to use MCNP or any other code, but<br /> rather provides in-depth coverage of the fundamental methods used in all<br /> modern Monte Carlo particle transport codes. The course content is suitable<br /> for beginners and code users, and includes much advanced material of<br /> interest to code developers. (10 lectures, 2 hrs each)<br /> The instructor is Forrest B. Brown from the X-5 Monte Carlo team. He has 25 years experience in<br /> developing production Monte Carlo codes at DOE laboratories and over 200 technical publications on<br /> Monte Carlo methods and high-performance computing. He is the author of the RACER code used by the<br /> DOE Naval Reactors labs for reactor design, developed a modern parallel version of VIM at ANL, and is a<br /> lead developer for MCNP5, MCNP6, and other Monte Carlo codes at LANL.<br /> 1 -2<br /> <br /> LA-UR-04–8817<br /> <br /> Topics<br /> 1. Introduction<br /> – Monte Carlo & the Transport Equation<br /> – Monte Carlo & Simulation<br /> <br /> 2. Random Number Generation<br /> 3. Random Sampling<br /> 4. Computational Geometry<br /> 5. Collision Physics<br /> 6. Tallies & Statistics<br /> 7. Eigenvalue Calculations – Part I<br /> 8. Eigenvalue Calculations – Part II<br /> 9. Variance Reduction<br /> 10. Parallel Monte Carlo<br /> 11. References<br /> 1 -3<br /> <br /> LA-UR-04–8817<br /> <br /> Introduction<br /> <br /> •<br /> <br /> Von Neumann invented scientific computing in the 1940s<br /> –<br /> –<br /> –<br /> –<br /> <br /> •<br /> <br /> Stored programs, "software"<br /> Algorithms & flowcharts<br /> Assisted with hardware design as well<br /> "Ordinary" computers today are called "Von Neumann machines"<br /> <br /> Von Neumann invented Monte Carlo methods for particle transport in<br /> the 1940s (with Ulam, Fermi, Metropolis, & others at LANL)<br /> – Highly accurate – no essential approximations<br /> – Expensive – typically the "method of last resort"<br /> – Monte Carlo codes for particle transport have been proven to work<br /> effectively on all types of computer architectures:<br /> SIMD, MIMD, vector, parallel, supercomputers,<br /> workstations, PCs, Linux clusters, clusters of anything,…<br /> <br /> 1 -4<br /> <br /> LA-UR-04–8817<br /> <br />

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