FEM reading assignment

Please read through the lecture note on "Finite Element Methods for Elliptic Problems Variational Formulation: The Poisson Problem," at the link Lectures 13 & 14 (March 17 & 29) on Stellar prior to our first FEM class on 17 March. Note that the Notes marked Optional are truly optional: these will not be covered in class, are not needed to understanding the material, and will not be required to
do the homework.

Announced on 09 March 2005  1:00  p.m. by Debra Blanchard

Added matlab script

I've added a matlab script for integrating the ODE:

du/dt = lambda*u

using different numerical integration shemes. It is in the general section of the materials page.

:-D

Announced on 04 March 2005  3:23  p.m. by David Willis

Recitation on Stability for ODE solution techniques

PDE Course,

During this Friday (1:00pm-3:00pm) office hours and Wednesday (11:30am-1:30pm) office hours I will be spending 45 minutes on a recitation session covering Absolute Stability of Numerical ODE Techniques (Recitations are held in room 36-888). This material is in the last few pages of the current set of lecture notes. Professor Peraire will only briefly cover the material in class, hence, it is recommended you attend one of these recitation times for deeper coverage of the material.

I will be available to answer course related questions after presenting the material.

Cheers,
:-Dave

Announced on 03 March 2005  2:28  p.m. by David Willis

16.920j/2.097j/6.339j: Small Correction to PSet 1 : Question 2 part # 3b

PDE Course,

Question # 2, part # 3b currently asks you to use the multigrid with parameters 1,4,1,4,1... & 1,8,1,8,1,8... for a 2 grid multigrid cycle. There is a small correction which should not affect you significantly in terms of time or overall effort. The correction is:

Try the multigrid for 1,4,1,1,4,1,1,4... where the numbers here refer to : 1 pre-smoothing iter fine grid, 4 coarse grid iters, 1 post-smoothing iter fine grid, 1 pre-smoothing iter fine grid, 4 coarse grid iters, 1 post-smoothing iter fine grid... etc. In light of this, since your code should already have this versitility, it should not be difficult to run the following cases: a 2 cycle multigrid with 1,2,1...(pre, coarse, post iters), also, 2,2,2...(pre, coarse, post iters), as well as 1,4,1...(pre, coarse, post iters), also try 2,4,2...(pre, coarse, post iters) also 1,8,1...(pre, coarse, post iters) and 2,8,2(pre, coarse, post iters) The aim of this question is to see how the different options you have for the various parameters in the 2-step multigrid can affect the convergence. Feel free to investigate beyond these options if you feel inclined. Furthermore, we should remember when looking at this question, that in actuality, a multiple grid multigrid will be much more ideal due to the ability to reduce the previous "low-mode" error more effectively at each coarser level.

Sorry for any confusion for those who reached this question already. Hopefully this correction makes the question a little clearer. If you have any questions or concerns about this update, please email me (djwillis at mit.edu).

:-D

Announced on 23 February 2005  10:33  a.m. by David Willis

First Assignment Online

The first assignment for the PDE course is online. It will be due March 8th 2005, before class. It comprises 2 questions. Students need not type their solutions, but should attempt to present their material as neatly as possible. In addition, any matlab code wich is used should be attached to the back of the assignment hand-in.

Office hours will be held in 36-888 on Wed. 11:30am-1:30pm and Fri. 1:00pm-3:00pm. They are *not* mandatory.

For more information, consult the assignment and the assignment presentation slides.

Announced on 08 February 2005  11:49  a.m. by David Willis