Department of Physics, Unit Catalogue 2006/07 
PH30031 Simulation techniques 
Credits: 6 
Level: Honours 
Semester: 1 
Assessment: CW 20%, EX 80% 
Requisites: 
Before taking this unit you must take PH20020 
Aims & Learning Objectives: The aims of this unit are to identify some of the issues involved in constructing mathematical models of physical processes, and to introduce major techniques of computational science used to find approximate solutions to such models. After taking this unit the student should be able to: * dedimensionalise an equation representing a physical system; * discretise a differential equation using grid and basis set methods; * outline the essential features of each of the simulation techniques introduced; * give examples of the use of the techniques in contemporary science; * use the simulation schemes to solve simple examples by hand; * describe and compare algorithms used for key processes common to many computational schemes. Content: Construction of a mathematical model of a physical system; dedimensionalisation, order of magnitude estimate of relative sizes of terms. Importance of boundary conditions. The need for computed solutions. Discretisation using grids or basis sets. Discretisation errors. The finite difference method; review of ODE solutions. Construction of difference equations from PDEs. Boundary conditions. Applications. The finite element method; Illustration of global, variational approach to solution of PDEs. Segmentation. Boundary conditions. Applications. Molecular Dynamics and MonteCarlo Methods; examples of Nbody problems, ensembles and averaging. The basic MD strategy. The basic MC strategy; random number generation and importance sampling. Applications in statistical mechanics. Simulated annealing. Computer experiments. Solving finite difference problems via random walks. Other major algorithms of computational science; the Fast Fourier Transform, matrix methods, including diagonalisation, optimisation methods, including nonlinear least squares fitting. 
