Monte Carlo Methods in Scientific Computing

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Presentation transcript:

Monte Carlo Methods in Scientific Computing 3-7 November 2003 Beijing International Center for Computational Physics This set of powerpoint slides MC-0 to MC-15 is copyright J.-S. Wang. I thank Dr Yu Xijun for his kind invitation to organize this workshop. I also thank the other lectures Profs Bo Zheng, Junni Zhang and Pei Lucheng for their contributions to this workshop. A soft copy of the slides is available at http://staff.science.nus.edu.sg/~phywjs/BeijingWorkshop.html. The background Monte Carlo carpet is from http://valuecarpetonline.com/montecarlo_bg.jpg.

Outline (Monday) What is Monte Carlo Introduction to probability Random number generator Numerical integration Quasi-Monte Carlo method Markov chain

Outline (Tuesday) Metropolis and other algorithms Selected applications Convergence and Monte Carlo error Quantum Monte Carlo methods Variational, diffusion Monte Carlo Trotter-Suzuki formula

Outline (Wednesday) Cluster algorithms Re-weighting methods Extended ensemble methods (Multi-canonical, simulated tempering, replica MC, replica exchange) Transition matrix MC, flat-histogram and Wang-Landau

Thursday Morning: Non-equilibrium dynamics in statistical mechanics and other applications (by Bo Zheng) Afternoon: Markov chain Monte Carlo in statistics (by Junni Zhang)

Friday Whole day: Monte Carlo method and its characteristics (by Pei Lucheng)

Reference Books M H Kalos and P A Whitlock, “Monte Carlo Methods”, John Wiley & Sons, 2nd ed, 2008. D P Landau and K Binder, “A Guide to Monte Carlo Simulations in Statistical Physics”, 4th ed, Cambridge, 2015. J S Liu, “Monte Carlo Strategies in Scientific Computing”, Springer,2002. Other books and references will be introduced at the bottom notes with the slides later.