Math 610
Section 600, Spring 2008
- Instructor:
Dr. Raytcho Lazarov
-
TA:
Dimitar Trenev
-
E-mail - trenev@math.tamu.edu
- Office - Blocker 505E
- Office Hours - by appointment
(although feel free to come to my office any time)
- Phone - 845-7652
- Place and Time:
| Day |
Time |
Room |
| Wednesday |
4:10-5:00pm |
BLOC 126 |
- Helpful Links:
- Math610 Lab FAQ :
- How to write your reports?
-
You will need to turn in a report for each programming assignment.
Your report should be a PDF file looking like this : report.pdf.
Here is the LaTeX source used to create this PDF file :
report.tex, graph.eps
- To produce a .DVI file from your .TEX file, use the command:
latex [name_of_file].tex
You can view the .DVI file using the program 'xdvi'.
-
To convert your .DVI file to a .PS/.PDF file use the commands 'dvips' or 'dvipdf'.
- Past Labs (this section will be updated each week):
- Lab 1 (01/16) : General discussion about the course. Template for the programming reports (see above).
- Lab 2 (01/23) : Discussing of your first
homework and
programming assignments.
- Reminder of how we handle linear recurrence sequences
(useful for Problem 1).
- Discussion of the 1D finite element method.
- A three line Matlab code that you might find useful
when you want to plot some data that your program generates.
- Lab 3 (01/30) : Solutions of your first Homework and Programming assignments (see links above).
- Relationship (inequalities) between the H^1 norm and semi-norm depending on boundary conditions.
- A VERY simplified MATLAB code for a 1D FEM that can be used to solve PA#1.
- Lab 4 (02/06) : Further discussion.
- Condition number of the FEM discretisation of a second order problem.
- The LinearFEM.m file was updated with code that computes (approximately)
the L^2 and H^1 norms of the error. Discussed the rate of convergence.
- Lab 5 (02/13) : Solution of your
second (and third) Programming Assignments .
Following the basic structure of the previous example, a MatLab code for
arbitrary order Lagrange finite elements was written. (Although to really support high order elements, you'll
need to modify the code to calculate an accurate quadrature at run time instead of hardcoding weights and nodes
- you can find efficient algorithms (and freely distributed code) on the web.)
- Lab 6 (02/20) : 2D finite elements. Generating the mesh.
- Final comments on the 1D code from last time.
- 2D finite elements.
- A good mesh generator : Triangle
- Lab 7 (02/27) : Further discussion to help you with your
2D programming assignment.
- Boundary markers - imposing Dirichlet and Neumann boundary conditions on different parts of the boundary.
- Example MatLab code that reads the files generated from Triangle.
- Lab 8 (03/05) : Even further ( :-) ) discussion to help you with your
2D programming assignment.
- Integrating a function over a triangle : quad_2d.m.
We examined the performance of this very simple quadrature, by computing the integral of sin(x*y) over
triangulations of the unit square.
- Creating a good-looking 3D surface plot from our mesh/solution data : plot_surf.m.
You can use the code from last time (readmesh.m) to read Triangle data
for a given domain and use this file to plot some fancy functions over the domain.
- Spring Break (03/12)
- Lab 9 (03/19) : Discussing the problems from your 6th homework assignment.
- Trace inequality.
- Seminorm scaling.
- Lab 10 (03/26) : Preparing for your second midterm exam.
- Lab 11 (04/02) : Answering last minute questions on your programing assgnment. No more extensions, it's due before next lab!
- Lab 12 (04/09) : Discussing your programing assignment.
- A MatLab code that can be used to solve your 2D FEM programing assignment.
- An example of how we can handle sparse matrices. In particular, modification
of the above code not to assemble a global matrix is straight-forward.
- Lab 13 (04/16) : Von Neumann stability analysis
(Fourier mode analysis).
- Discussing the basic idea. Example of an unstable scheme (Leap-Frog).
- An unconditionally stable modification of the above shceme -
DuFort-Frankel scheme. The linked PDF (found with searching "DuFort-Frankel" on Google) does exactly what we did in class.