# 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 2 the course will run on Wednesdays at 12pm in **E245**. Links to
live code, the recording, a small amount of commentary, and the
blackboard notes appear in the notes section after the fact.

In the first week of term 2 (week beginning 10th January 2022), the lecture isonline only

You can attend remotely over zoom, and will need to be authenticated with your Durham account,

Meeting ID: 978 5235 0575

Passcode: 646264

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.

Measurement and modelling. Analysis of achieved performance, performance models, including the Roofline model.

Use of the PETSc library for parallel computing.

Irregular data distribution and load-balancing.

### 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 #

- Anne Reinarz (Term 1)
- Lawrence Mitchell (Term 2)

## 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).