Math 610
Section 600, Spring 2007
- 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 0 (01/17) : No lab the first week - university closed.
- Lab 1 (01/24) : General discussion about the course. Report templates.
- Lab 2 (01/31) :
Programming Assignment #1.
- Lab 3 (02/07) : Discussion on the implementation of the Finite Element Method.
- A more general program for solving second order elliptic equations in 1D, broken in several parts:
- Discussion on what (minor) changes are needed to make the above program work with quadratic elements
and how to modify it if we want to use (for example) the Conjugate Gradient solver
(implemented here for the Math609 class).
- Lab 4 (02/14) : Further discussion on the implementation of the Finite Element Method.
- A continuation on the program from Lab 3:
- Lab 5 (02/21) : A question from Lab4. 2D Finite Elements. Creating the mesh.
- All norms on a finite-dimensional vector space are equivalent. A short proof is given
here
.
- Triangulating a 2D domain:
- A good mesh generator: Triangle.
- An example of how we can read the mesh data from the files that Triangle generates:
2d_FE.h (<- declaring data structures),
readmesh.cc (<- the IO procedures),
readmesh.cpp (<- an example of how we use the above 2).
- Gnuplot - a useful tool for our course.
- Lab 6 (02/28) : Continuation of various discussions/questions from Lab 5.
- Lab 7 (03/07) : Last lab before Spring Break. Answering questions:
- A short proof of the Bell-Holland formula (induction on the dimension).
- Imposing the boundary conditions in a FEM implementation.
- Lab 8 (03/21) : Discussions. How to impose the essential boundary conditions
when we do not assemble the global matrix (ex. when we use
a Conjugate Gradient solver and only implement the action of
the matrix).
- LABS IN APRIL : Since we have been mostly discussing questions concerning problems from
your homeworks/exams, I have not been updating this site.
- Example of a working 2D FE code (it follows the same structural guidelines as our 1D examples).
- 2d_linear.cc - an implementation of 2D linear finite elements.
- second_order_2d.cpp - a program solving the problem
from your
Programming Assignment #4.
Actually this implementation solves the problem with Dirichlet boundary conditions instead of
Neumann boundary conditions. Comment out the part of code imposing the boundary conditions to
have an implementation of homogeneous Neumann boundary condition ;-).
Compare this program to our 1D version from Lab 4. Apart from differences dealing with the
mesh - the code is almost the same!
- second_order_2d_v2.cpp - second version of the above
program, that does not assemble the global matrix and uses a CG sovler instead of direct one.
- You'll need cg.cc and quadrature_2d.cc
to compile and run the above examples.