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Problem

This problem involves using the Monte Carlo method to find the volume of a unit sphere embedded in d-dimensional Euclidean space. My algorithm takes advantage of the symmetry, and finds the volume in a part of the domain, and gets the final answer by multiplying by . This is accomplished by randomly sprinkling points in the region , and looking at the frequency of occurance that the points fell in the unit sphere. The volume for that portion of the unit sphere is normalized against the volume of the domain, which is just 1. The parallelism is obtained by allowing the processor to do this task, and then sending the results to the controlling processor (0), where the results (both volume and standard deviation of sampling) are averaged.



Mark Miller
Wed Nov 15 00:01:31 EST 1995