Department of Physics, Unit Catalogue 2007/08 |
PH30031 Simulation techniques |
| Credits: 6 |
| Level: Honours |
| Semester: 1 |
| Assessment: EX 100% |
| Requisites: |
| Before taking this unit you must take PH20019 and take PH20020 |
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Aims: 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.
Learning Outcomes: After taking this unit the student should be able to: * de-dimensionalise 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 and give examples of their use in contemporary science; * use the simulation schemes to solve simple examples by hand. Skills: Numeracy T/F A, Problem Solving T/F A. Content: Construction of a mathematical model of a physical system (4 hours): De-dimensionalisation, order of magnitude estimate of relative sizes of terms. Importance of boundary conditions. The need for computed solutions. Discretisation (2 hours): Grids and basis sets. Discretisation errors. The finite difference method (4 hours): Review of ODE solutions. Construction of difference equations from PDEs. Boundary conditions. Applications. The finite element method (3 hours): Illustration of global, variational approach to solution of PDEs. Segmentation. Boundary conditions. Applications. Introduction to computational methods for matrix problems (3 hours). Molecular Dynamics and Monte Carlo methods (6 hours): Examples of N-body 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. |