MA 625: Assignment 6

The assignment is due Thursday, April 30 in class. This assignment should be done without any teamwork, i.e., only dead sources and the advice of the instructor.

Please download the software package labeled Fortuna from the free software area of MGNet. The code is the file mgsor.tgz. The file extension .tgz means that it is a gzipped tar file. You may unpack it with

followed by the command You can do both steps at once with the GNU tar program using Make certain that you unpack the file in its own directory.

The code is written in Fortran-77. You are do not need to modify it to do the assignment. Thus, you should not need to know any Fortran in order to use this package. You might find it worthwhile to look at the code, however. If you modify the code in order to simplify some of the parts below, do not use your modified code when reporting times.

Please compile and run the program on a UNIX workstation. You can compile and link the code with the command make. If your Fortran compiler objects to the -O3 option, try deleting the 3 (look in the file called Makefile).

Experiment with choices of the parameters. Determine the fastest choice of methods and parameters to solve Laplace's equation according to this software package. Pleae do all of the following:

  1. What is the size of the solution grid?
  2. Roughly what is the cost of 1 iteration of point or line SOR in terms of the number of unknowns on a grid with N total points?
  3. How many iterations do line and point SOR take for an acceleration parameter of 1?
  4. For just one of point or line SOR, is there a better choice of the acceleration parameter? (Do not spend a lot of time on this part.)
  5. What is the cost of a V cycle (in terms of N, the number of unknowns on the finest grid)?
  6. What is the cost of a W cycle (in terms of N, the number of unknowns on the finest grid)?
  7. For 2-7 levels, how many iterations of a V and W cycle does it take to converge?
  8. For 2-7 levels, how many iterations of a full multigrid with a V or W cycle does it take to converge?
  9. For 2-7 levels, what is the cost of one full multigrid V cycle (in terms of N, the number of unknowns on the finest grid)?
  10. What is the fastest method?

Write a report on what you found and provide details. Please provide tables and make a solid recommendation (no wiggling) backed up by your analysis.

Cheers,
Craig C. Douglas