Advanced Computational Methods for Monte Carlo Calculations

Advanced Computational Methods for Monte Carlo Calculations Prof. Forrest Brown This course is intended for graduate students who already have a basic understanding of Monte Carlo methods. It focuses on advanced topics that may be needed for thesis research, for developing new state-of-the-art methods, or for working with modern production Monte Carlo codes. Topics to be covered include: – Linear Boltzmann transport equation & integral form – Optimal random sampling from piecewise-linear PDFs – Parallel & vector Monte Carlo algorithms – Green's functions, the fission matrix, and linear integral operators – Adjoint-weighted integrals & sensitivity analysis – Precision & roundoff considerations, IEEE-floating point – Bit operations & random number generators – Detailed workings of delta-tracking & 3D CSG Thorough knowledge of some programming language is required (e.g., C++, Fortran-2003, perl, python). A previous course in transport theory is recommended. Students are assumed to be familiar with the material in UNM NE-462 / NE-562 (see F. Brown, "Monte Carlo Techniques for Nuclear Systems", LA-UR-16-29043, in the Reference Collection at the mcnp.lanl.gov website) Meet: 3 hours/week Advanced Computational Methods for Monte Carlo Calculations AMC-00 3 LA-UR-18-20247 Lecture Topics Transport Theory & Physics AMC-10 Linear Boltzmann Transport Equation & Integral Form AMC-11 Adjoints & Green's Functions AMC-12 Fission Matrix Method for MC Criticality Problems AMC-13 Continuously Varying Materials & Tallies Random Numbers & Sampling AMC-20 Random Number Generators & RNG Testing AMC-21 Random Sampling – Beyond the Basics AMC-22 Optimal Random Sampling from Piecewise-Linear PDFs AMC-23 Permutations, Sets of N-from-M, & Counting-sorts AMC-24 Some Ideas for a New Random Number Generator Code Development AMC-30 Monte Carlo Codes – Basic Algorithm & Structure AMC-31 Code Development – How to Time & Test AMC-32 Vector & Parallel Monte Carlo AMC-33 Optimizing Monte Carlo Calculations Advanced Computational Methods for Monte Carlo Calculations AMC-00 4 LA-UR-18-20247 References AMC-01 1 LA-UR-18-20247