Fundamentals of Monte Carlo Particle Transport

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 />