Program 2 FDM solution to Laplacian using Successive Over-Relaxation (SOR) method

Written for Course :-
Computational Electromagnetics, Fall 2011
Department of Electrical Engineering
Indian Institute of Technology Madras (IITM)
Chennai - 600036, India

Authors:-
Sathya Swaroop Ganta, B.Tech., M.Tech. Electrical Engg.
Kayatri, M.S. Engineering Design
Pankaj, M.S. Electrical Engg.
Sumantra Chaudhuri, M.S. Electrical Engg.
Projesh Basu, M.S. Electrical Engg.
Nikhil Kumar CS, M.S. Electrical Engg.

Instructor :-
Dr. Ananth Krishnan
Assistant Professor
Department of Electrical Engineering
Indian Institute of Technology Madras

Description:-

In the Successive Over-Relaxation (SOR) technique the matrix update after each iteration is done in a different way. Before, the next matrix was computed using the current matrix using the FDM update and and the difference between the two values was measured and if the difference was greater than tolerance, the next matrix was updated as the current matrix. This process was repeated until the difference between the two matrices was less than the tolerance. In the SOR method, the current matrix summed with alpha times the difference between the two matrices is updated as the current matrix. The process is repeated from alpha=1 to alpha=1.9. The imagesc movie for the converging solution is shown for alpha=1.8. The iterations are counted for each alpha and it is observed that the no of iterations are least for alpha=1.8.