Selected Topics in Numerical Analysis, fall 1999 term

Advanced scientific computing, many-body problems

Instructor: B. J. Braams (braams@courant.nyu.edu)

Cross-listed as G22.2945.002 and G63.2011.002.

Class meets Wednesdays 9:55-11:45, room 1013, Warren Weaver Hall.

Prerequisites: basic scientific computing or numerical analysis; undergraduate physics including quantum mechanics.

The course will cover computational methods for many-body problems in physics and chemistry. The focus will be on the mathematical problem formulations rather than on code implementation issues. Topics will include: (1) Statistical physics. Monte Carlo approach for finding the lowest energy state and for evacuating thermodynamic properties of liquids and solids. Metropolis algorithm. Importance sampling. Critical slowing down and methods to overcome it; (2) Electronic structure. Born-Oppenheimer approximation. Hartree-Fock method, configuration interaction expansion, perturbation theories, density functional approach, density matrices; (3) Particle simulation and molecular dynamics. Fast Poisson methods. Methods for multiple timescales, especially Car-Parrinello.

Texts: K. Binder and D. W. Heermann, Monte Carlo Simulation in Statistical Physics, 3rd Edition, Springer-Verlag, 1998; A. Szabo and N. S. Ostlund, Modern Quantum Chemistry, revised edition, Dover, 1996; D. Frenkel and B. Smit, Understanding Molecular Simulation, Academic Press, 1996.


Notes to the class

Sep 8. Reading advice for the coming week: Binder and Heermann, Ch. 2, esp. Secs. 2.1 and 2.2. Frenkel and Smit, Part I, esp. Ch. 3.


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