PHY425: Computational methods in physics II

        [Cr:4, Lc:3, Tt:0, Lb:3]

Knowledge of the content of PHY422 is essential to follow this course.

Course Outline

• Solution of Ordinary Differential Equations, Euler's method, Runge-Kutta methods, Initial and Boundary Value Problems.
• Fast Fourier Transforms, relation with Fourier series and Fourier transforms.
• Partial differential equations: Diffusion equation, Wave equation, Poisson equation. Finite element and relaxation methods.
• Parallel computing: Decomposition of problems, functional, data and domain decomposition. Shared memory and distributed memory parallelization. Optimization with co-processors and GP-GPUs.
• Topics in Numerical Simulations (At least two topics to be covered):
  1. Many particle simulations with short range interactions.
  2. Many particle simulations with long range interactions.
  3. Computational Fluid Dynamics.
  4. Simulations of spin systems.
  5. Simulations of quantum mechanical scattering.
  6. Parameter estimation for $n>3$ unknown parameters from experimental/observational data.

Recommended Reading

• H. M. Antia, Numerical Methods For Scientists And Engineers, 02nd edition, Birkhauser Basel (2002).
• Numerical Recipes in C: The Art of Scientific Computing, W. H. Press, S. A. Teukolsky, W. T. Vellerling and B. P. Flannery, Cambridge University Press (1992).
• Programming Massively Parallel Processors: A Hands-on Approach, by David B. Kirk, Wen-mei W. Hwu, Publisher: Morgan Kaufmann; 3rd edition (2016)
• Computational Physics, J. M. Thijssen, Cambridge University Press (1999)