Parallel network programming for numerical problems
Supervisor: Tony Roberts
Description: Numerical Partial Differential Equations: finite difference operators and their stability, Laplace's equation, heat flow problems, the Poisson equation, boundary conditions, parabolic and hyperbolic systems, iterative methods, applications. Advanced Numerical Methods: multigrid methods for PDE's, finite element methods, weighted residuals. Parallel programming: network topologies, C-Linda extensions and Tuplescope, domain decomposition, load balancing, tree codes, profiling with ParaGraph, message passing, robust programming, performance limitations. Algorithms from: matrix arithmetic, solving tridiagonal equations, Gauss-Jordan elimination, summation, recurrence relations, adaptive integration, multigrid Poisson solver, golden section optimisation, genetic algorithms, stochastic optimisation, the Mandelbrot set and other fractals, Monte Carlo simulation, sorting, binary searches, wavelets, or graphics.
Prerequisites: High performance numerical computing, Harmony of PDEs
Main text: TBA
Some potential study topics
| What is Maths? Ron Addie | Attitude and belief Patricia Cretchley | Computer Algebra Ed Patricia Cretchley | Assessment issues Patricia Cretchley |
| Education research? Patricia Cretchley | Bridge gaps Patricia Cretchley | Gender equity Patricia Cretchley | Teaching geometry Patricia Cretchley |
| Math history Patricia Cretchley | Gen Lin Models Peter Dunn | Bayesian stats Paul Fahey | Survey sampling Ashley Plank |
| Maths Methods Tony Roberts | Quantum Computing Tony Roberts | Water waves Tony Roberts | Games theory Tony Roberts |
| Parallel numerics Tony Roberts | Hydro stability Sergey Suslov | Math Biology Sergey Suslov | Banach spaces Oleksiy Yevdokimov |
| Fundamental Maths Education Oleksiy Yevdokimov | Number history Oleksiy Yevdokimov |