CPS615 Homework 9

- Ho-Yen Chang


Assignment 9, Due Wednesday, Nov. 29

Write an HPF program that solves a Laplace equation over a rectangle by the red/black SOR technique. Run the program on at least 4 nodes of the SP2, using array grid sizes on the order of 100 by 100. Investigate the optimum value of the over-relaxation parameter w by making at least 10 runs for values of w between 1 and 2. Describe your results.

There is an example program in your class directory: examples/pgi/laplace.hpf which solves this problem by Jacobi iteration. You may extend this program to a red/black SOR solver. (Compiler note: some of us have had difficulty with spreads and modules - try to avoid these constructs for now.)


Reference:

Program using point-Jacobi method laplace.hpf

The result output laplace-jaco.out

Solution :

Program lpsor.hpf

The result output lpsor.out

The reference result of output, lpsor.out2

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By comparing the numbers of iteration, using red/black SOR technique is better than just using point-Jacobi method and it just take almost as half amount of iteration and less CPU time as using point-Jacobi method.

By observing the result, we know that the optimum value of parameter w for this problem is between 1.0 to 1.5, and then by comparing the converge behavior of eps value, we can estimate the optimum value of the over-relaxation parameter w probably equal to 1.3.


Ho-Yen Chang
B17-8 Slocum Heights, Syracuse, NY 13210
Tel (315) 442-7239
hchang03@top.cis.syr.edu