Introduction

COMP4187: Parallel Scientific Computing II #

This is the course webpage for COMP4187. It collects the exercises, syllabus, and notes. The source repository is hosted on GitHub.

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.

Syllabus #

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.

Lecturers #

Reading #

Recommended:

LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM (2007).

Optional:

Iserles, A first course in the numerical analysis of differential equations, Cambridge Texts in Applied Mathematics (2009).