This project aims at developing experience in implementing and experimenting finite difference discretizations of PDEs. This is a very important goal of this course.

The students can work in groups with maximum three persons per group.

You can look at the list of PDEs from which you will choose your favorite (allowing for no more than few groups per PDE). Your task is to find out as much as you can about the problem, to propose a finite difference discretization of the equation (motivated by an analysis), and to implement the discretization method as efficiently as possible using MATLAB (or OCTAVE).

The official starting week for the project is week 11. This means that all the groups must have choosen a PDE from the list and sent a message to Elena or Håkon before the 15.03.2009.

However you are welcome to choose your test problem and work on the project before week 11. The deadline for handing in the project is april 30th. (this means you have to send your code to Håkon and your project description in pdf format to Elena - maximum of four pages per group-member -.)

Tentatively on week 18 we will arrange a poster presentation of your projects in the lunchroom 1329 in the 13. floor. All the members of the department will be invited, your projets and your presentation will be evaluated and we will select the three best posters/projects. All the participants in a group for a project will have the opportunity to present their work and your individual mark might depend on your performance in this presentation.

How to make posters. Check this out (in Norwegian).

How to print posters. The institute for Architecture can print A0-size for a small fee (I beileve). The link above describes how to split an A0-file, but there are some errors. You need to change the brukposter script (it should read "./poster" instead of "poster"), and you need to give yourself execution rights for the brukposter script by running "chmod +x brukposter". Then you can run the script using ./brukposter input.ps output.ps (note the ./). It runs for a while and generates a lot of output. See also this page and in particular this quote:

I had a lot of trouble with included EPS graphics, which largely went away when I normalised the EPS files with the eps2eps utility which is part of the Ghostscript distribution.

You are welcome to use Google and other sources for understanding more about the PDE problem you are going to solve. Use for example the databasis: MathSciNet, and Zentralblatt Math.

Evaluation Total 30 points.

• Correctness. The main goal of the project is to gain ability in using finite difference methods in practice. You should show your ability of producing a correct simulation of the problem. Evidence that the code is correct must be given in the report. Max score for this task is 15 points.
• Analysis. You should provide an analysis of the problem motivating the choice of the finite difference discretization and the convergence of the numerical scheme. Max score for this part is 8 points.
• Efficiency. Finally the last 7 points will be concerned with the efficiency of the implementation. We hope you will be able to exploit the facilities offered by MATLAB and to produce a code which requires as little as possible storage and runs fast. The codes will be handed in and tested, so please make a minimum of documentation for your code.

The poster presentation will be an important step in the evaluation process: you will be asked to present your project in general and to explain how you handled these three different tasks (correctness, analysis, and efficiency).