COMP4187: Parallel Scientific Computing II #
This submodule builds on Numerical Algorithms I (Parallel Scientific Computing I) and introduces advanced topics in ODE integration schemes, and spatial discretisation.
Time and Place #
In term 1 lectures take place at 12:00 on Wednesdays in CM107. Recordings of each lecture will be uploaded on encore, but you are encouraged to attend synchronously in person or via zoom.
Numerical Methods (Term 1) #
- Topic 1: Spatial discretisation. Finite difference methods for partial differential equations (PDEs), stability, convergence, and consistency;
- Topic 2: Time dependent PDEs. Stability constraints for time-dependent PDEs, connection to eigenvalue analysis;
- Topic 3: Implicit ordinary differential equation (ODE) methods, and matrix representations of PDE operators;
- Topic 4: Advanced algorithms for PDEs. Fast methods of solving PDEs, high order discretisation schemes.
Parallel Computing (Term 2) #
Distributed memory programming models: MPI.
Parallel algorithms and data structures for finite difference codes.
Irregular data distribution and load-balancing.
Measurement and modelling. Analysis of achieved performance, performance models, including the Roofline model.
Discussion forum #
We have set up a discussion forum where you can ask, and answer, questions. You’ll need a GitHub account to use it, but you’ve all got one of those already, right? Note that this repository and forum is publically visible.
Office hours #
We’re happy to answer any questions in office hours, email to arrange a time.
LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM (2007).
Iserles, A first course in the numerical analysis of differential equations, Cambridge Texts in Applied Mathematics (2009).