**[Cr:4, Lc:3, Tt:0, Lb:3]**

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

- 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):
- Many particle simulations with short range interactions.
- Many particle simulations with long range interactions.
- Computational Fluid Dynamics.
- Simulations of spin systems.
- Simulations of quantum mechanical scattering.
- Parameter estimation for unknown parameters from experimental/observational data.

- 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)*