PH5618: Introduction to Computational Physics

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Course Information

L-T-P-C2-0-2-3
Prerequisites None

Syllabus

Module 1: Introduction to computational physics

Lecture hours: 2 · Tutorial hours: 0 · Lab hours: 2

Structured programming, Approximations, Statistics, Round-off and truncation errors, Debugging, profiling and optimization, Open source libraries (GSL, LAPACK, BLAS) .

Module 2: Numerical Methods

Lecture hours: 10 · Tutorial hours: 0 · Lab hours: 8

Recap of root finding methods, numerical integration and differentiation, Ordinary differential equations: Euler, predictor-corrector, Runge-Kutta methods, boundary-value and eigenvalue problems, Partial differential equations: solution technique, boundary conditions, control-volume approach, Crank-Nicolson method, introduction to finite-element method, Optimization: golden-section search, parabolic interpolation, direct methods, gradient methods, simulated annealing, curve fitting .

Module 3: Simulation Methods

Lecture hours: 7 · Tutorial hours: 0 · Lab hours: 5

Statistical mechanics: basic concepts, Monte Carlo simulations: MC integration, importance sampling, principle of detailed balance and equilibrium sampling, MC simulation of lattice and off-lattice systems, acceptance criteria for various ensembles, Molecular dynamics simulations: basic principles, MD simulation in various ensembles, calculation of various observables and their averages, space and time correlation functions, introduction of Langevin dynamics and faster equilibrium simulation methods .

Study Materials

Textbooks

  1. Numerical Methods for Engineers, Steven Chapra and Raymond Canale, 6th Edition, ISBN: 978-0-07-340106-5
  2. Understanding Molecular Simulation: From Algorithms to Applications, Daan Frenkel and Berend Smit, , ISBN: 0122673514

References

  1. Numerical Methods for Scientific and Engineering Computation, M. K. Jain, S. R. K. Iyengar, R. K. Jain, New Age International (2003), ISBN: 9788122414615
  2. An Introduction to Computational Physics, Tao Pang, 2nd Edition, ISBN: 9780521532761
  3. A Guide to Monte Carlo Simulations in Statistical Physics, David P. Landau and Kurt Binder, 4th Edition, ISBN: 1107074029
  4. Computer Simulation of Liquids, Michael P. Allen and Dominic J. Tildesley, 2nd Edition, ISBN: 0198803206