Numerical Methods for Differential Equations I, DN2225
                  Applied Numerical Methods III, DN2251
 Numerical Methods for Physicists II at SU (project not compulsary for these students)
 
                        Project, autumn 2008



    In the project 1-5 persons collaborate on a problem concerned with
    a mathematical model from some application. The problems are 
    taken from Comsol Multiphysics model library and the task is to run 
    the problem in Comsol using the graphical user interface (GUI) and 
    also to treat a corresponding 1D problem (chosen by yourselves) in 
    Matlab with one of the methods taugth in this course.

    The results of your investigations are to be presented in an oral
    seminar of 15-20 minutes. 
    All participants of the group have to participate with one part of
    the presentation. The presentation should be done with overhead (or PP)
    pictures describing (the separation below is suitable for a group of
    five persons)

        * the scientific/engineering background of the specific problem
          explained so that the audience gets a clear introduction

        * the 2D mathematical model with BC and IC.

        * the results obtained with Comsol, visualizations

        * the 1D mathematical model (ODE-problem or 1D PDE)
          the numerical method used for the 1D problem

        * results for the 1D problem, graphs, problem, etc

    Neither details of the input to FEMLAB nor details of the Matlab
    program should be presented at the oral seminar. Observe that the
    1D problem should be investigated with respect to the NUMERICAL 
    properties (e.g. structure of tha jacobian, stability and accuracy 
    of the method, etc). It is not always possible to give a simple 
    physical interpretation of the 1D problem, hence that problem need
    not have any physical background. Also the parameter values
    of the 1D problem must not correspond to the parameters of the 
    2D problem. Choose yourself!
    Copies of the overhead presentation is to be given to me on the
    DAY BEFORE the presentation, so that I can make copies for the 
    other groups in the audience. If you want color copies of some
    pictures (on paper or on overhead) go down to Delfi on their
    opening hours and use the computers and the printers of their
    resourse room.

    The project is to be chosen from one of the following:

      1) Heat Transfer Model
      2) Steady Incompressible Flow
      3) Flow Past a Cylinder
      4) Structural Mechanics Problem
      5) The Korteweg-de-Vries Equation and Solitons
      6) A Transport Problem (1st order hyperbolic 2D-problem)
      7) Skin Effect in Circular Wire
      8) The Convection and Diffusion Application Mode
      9) Tubular Reactor

    Times for presentations will be the last scheduled classes of the
    course, i.e.

           Tuesday    Dec 2nd, 15-17 in D41
           Wednesday  Dec 3rd, 15-17 in D31
           Thursday   Dec 4th, 13-15 in M35
           Friday     Dec 5th,  8-10 in D31
      
    It is expected that all groups giving a presentation on one of
    these days listen to all presentations given that day!


                                                  / Lennart Edsberg