Project Course in Scientific Computing (projsc08) 7.5c

Overview

The goal of this course is to give insight into an active research area in scientific computing (for example the finite element method) with focus on an aspect of the method or an application in wave propagation, solid mechanics, fluid mechanics with turbulence, chemical engineering or similar areas. In the course you will:

• Study relevant literature, i.e. relevant course books or scientific articles.
• Derive and implement a method by using components of an existing software system for computational modeling and execute numerical experiments.
• Present your work in the form of a short seminar (compulsory, but not graded) and write a project report (compulsory and graded).

News

081105: Reschedule weekly meeting at Nov 7 to 13:15 in 1537. Updated literature list.

Course components

You will perform primarily individual work with regular supervision/consultation and support by researchers at KTH. The course consists of the following main components:

• Project plan (choose a suggested project or come up with your own).
• Two mandatory progress reports (oral, with your supervisor).
• Software implementation in a computational modeling environment (for example FEniCS in Python or C++).
• Written project report.
• Oral project presentation.

Projects

Projects are done in groups of 2 students (or possibly 3 students if you can provide a motivation). You may also choose to work on your own. A preliminary list of suggestions for projects is available as a pdf file. A project plan template is given.

Suggested Literature

"K. Eriksson, D. Estep, P. Hansbo, C. Johnson: Computational Differential Equations",

P. Hansbo, Beyond the elements of finite elements. (Solid mechanics, general algorithms for non-linear problems)

S.C. Brenner and L.R. Scott, "The mathematical theory of Finite Element Methods", Springer Verlag, 1994. (Mathematical; elliptic problems, mixed methods,..)

A. Logg, Automating the finite element method.

D. Estep, A short course on duality, adjoint operators, Green's functions, and a posteriori error analysis.

Body and soul books (computational mathematics, FEM, turbulent flow).

Navier-Stokes: Quick and Easy

Compressible Flow (p. 37- for compressible Euler in 2d/3d)

Laplacian models

Teachers

Coordinator is Johan Jansson; email: jjan@csc.kth.se

Examination

The examination consists of a written project report and a compulsory oral presentation.

Schedule

The first meeting for the course takes place wednesday 2008-10-29 at 10:15 in room 4523, Lindstedtsvägen 3, floor 5.

Deadline for project plan is November 7.

Weekly meetings at fridays 10:15 in room 4523, Lindstedtsvägen 3, floor 5. First weekly meeting 7 November in 1537 at 13:15.

Software

Unicorn on kd0

First you need a matching version of DOLFIN for Unicorn. Perform the following steps:

• Log into kd0
• bash
• cd /NOBACKUP/jjan/fenics/dolfin-kth
• source dolfin.conf
• Go to your own directory
• Follow the steps in "Sample session" in the local Unicorn page.

Mesh conversion

xmlmesh.m Matlab script for converting Comsol meshes to DOLFIN XML.

Usage:

In Comsol do "File->Export to FEM", then you can access your mesh in a Matlab-style language. Then you can use the xmlmesh function:

xmlmesh('filename.xml', fem.mesh.p, fem.mesh.t)