Aims & Learning Objectives: The aim of this unit is to provide students with experience in the application of some of the techniques widely used in the simulation of physical systems, and to develop their ability at using computers in physical modelling. Topics will be chosen for study which encourage a greater understanding of both the model and the underlying physics. The emphasis will be on the application and interpretation of the techniques, not on programming.
After taking this unit the student should be able to:
* identify issues which influence the choice of language and architecture;
* interface C programs to a 2d graphics package;
* outline the physics and computational issues illustrated by the Ising model;
* develop finite difference and finite element simulations of given systems;
* discuss issues involved in the use of basis set methods;
* explain the methodology and output of the simulations performed.
Content: Overview of computer languages for scientific work; computer architecture and code optimisation. Revision of C programming in the UNIX environment. Simulation of systems with many degrees of freedom: The Ising model. Finite size effects, fluctuations, correlations, phase transition, thermal equilibrium state, evaluation of observables.
Numerical solution of partial differential equations. Application and exploration of finite difference and finite element programs. Visualisation of solutions. Application to contemporary problems.
Basis set methods. Illustration and comparison of computational schemes.
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