An Investigation of Numerical Methods for Obtaining Green's Functions.

The study was devoted to obtaining an optimal numerical method for computing discrete Greens functions for the Laplacian operator. Two competitive numerical methods were employed successive over-relaxation and a modified Monte Carlo methodd, the Exodus method. Greens functions were computed for square and cubic grids. Comparisons were made on the basis of accuracy and required computation time. Accuracy was determined by comparing numerical Greens functions with analytical solutions. Both methods, iterative and statistical, gave comparable accuracy results. Required computation times for the successive overrelaxation method were consistently less than the Exodus method. For all regions considered, both planar and volumetric, the successive overrelaxation method was found to be the optimal numerical method for determining Greens functions accurately and rapidly. Author