Acknowledgment and Disclaimer: This material is based upon work supported by the National Science Foundation under Grant No. 0134424. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

ENBE 643: Homework #1 (Fall 2004) -- The File to download is: silicium.mat. -- The KEY is: PDF KEY #1.
ENBE 643: Homework #2 (Fall 2004) -- The KEY is: PDF KEY #2.
ENBE 643: Homework #3 (Fall 2004) -- The KEY is: PDF KEY #3.
ENBE 643: Homework #4 (Fall 2004) -- The KEY is: DOC KEY #4.
ENBE 643: Example of FDM using MATLAB (from class notes): FDM Example
ENBE 643: Example of FEM using MATLAB (from class notes): FEM Example

ENBE 643: A More Flexible FEM System
USE THE CODE AND DOCUMENTATION BELOW (after the News) FOR YOUR PROJECT #2

********************************************************************
**** NEWS as of Tuesday Evening: 11:54pm; Updated Thursday, 4:20pm
********************************************************************

If your PDEs contain advective terms that include gradients of a second species (common in animal transport or when solving flow and solute transport equations simultaneously) then, please use the updated advection file which works very well with monotonic gradients. It requires the following utility: elegradient.m and also, it requires that you use fem_nsY as FEM Solver -- i.e. modify the line at the bottom of your driver so that it calls fem_nsY instead of fem_nsX.

**********Thank you for your attention******************************

ENBE 643: FEM CODE FOR YOUR PROJECT #2 (and for the examples below)

When saving these M-files files to your directory, be sure to include the extension: ".m".

Driver Solver Display

Set BC Set IC Set Capacitance Set Sources Set Reactions Set Advection Set Diffusion

Util 1 Util 2 Util 3 Util 4 Util 5 Util 6 Util 7 Util 8 Util 9 Util 10 Util 11

ENBE 643: DOCUMENTATION TO HELP YOU WITH YOUR PROJECT #2

Here is the Users' Guide for Example 1: Click Here (doc) . M-files for Example 1 .

Example 2 explains nonlinear systems of PDEs Click Here (doc) . M-files for Example 2 .

Example 3 has a Cell and a kind of Soil Click Here (doc). M-files for Example 3.1 and for Example 3.2 .

Example 4 has non-rectangular 3-D domains and plotting Click Here (doc). M-files for Example 4.

The files below are the GNU Octave version of the above FEM code.

They have been developed on SUN Solaris 10 using the pre-packaged GNU Octave from www.blastwave.org. The version is "beta" -- It can solve multidimensional problems but is slow because Octave does not support sparse matrices. Additionally, Octave does not have the trisurf function for plotting 2-D results.

Driver Solver Display

Set BC Set IC Set Capacitance Set Sources Set Reactions Set Advection Set Diffusion

Util 1 Util 2 Util 3 Util 4 Util 5 Util 6 Util 7 Util 8 Util 9 Util 10 Util 11

Meshing 1 Meshing 2 Meshing 3 Meshing 4

Water Resources Research:

The solution is written in Matlab M-files. Sixteen files are needed in order to compute it. It uses the Newton-Cotes 8-panel rule for integration. The driver (file that specifies the time at which the solution is computed) is "anasol3.m". After downloading all files, type "anasol3" inside MATLAB to execute the program.

anasol3.m convolve.m Gaussian1d.m C1a21.m C1a32.m C2a21.m C2a32.m C3a21.m

C3a32.m C1a.m C2a.m C3a.m I3.m K3.m dI3.m dK3.m

Bioremediation:

Driver Reactions Advection Initial Conditions Boundary Conditions Display Solution Updated FEM_nsX Needed Function (new)

Some Recent Presentations (e.g. for BSCI 105 students, H&D):

From Towson University GIS Conference (2002): tugis2002poster.ppt

From the Institute of Biological Engineering Conference (IBE) (2003): Quantized.ppt

From the University of Maryland at College Park, Bioscience Day (2003): Bioscience_Day_2003.ppt

ABET Material:

ABET Course Assessment Form