In many areas of the science there is a need to evaluate a functional of the solution of a given problem directly without computing the solution itself. The problem here is a linear functional of the solution of an elliptic boundary value problem to be estimated. Such kind of problems are similar to the air pollution problems in environmental sciences, where a rough estimate of the solution is acceptable. For practical computations it means that the relative error is about 5% – 10%. To solve this problem a grid–free Monte Carlo (MC) algorithm is used. The algorithm makes use of a Monte Carlo procedure called “Walk on the balls”. Here we consider parallel realizations of the considered grid–free MC algorithm. Various numerical results are obtained by the implementation of the proposed parallel algorithms on several high performance machines: IBM +p690 Regata system and Sun Fire 15K server. One can see that the efficiency of the proposed parallel algorithm is close to 100%.
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