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<p>Random walks are widely applicable in statistical and scientific computations. Inparticular, they are used in the Monte Carlo method to solve elliptic and parabolic partialdifferential equations (PDEs). This method holds several advantages over other methodsfor PDEs as it solves problems with irregular boundaries and/or discontinuities, givessolutions at individual points, and exhibits great parallelism. However, the generation ofeach random walk in the Monte Carlo method has been done sequentially because eachpoint in the walk is derived from the preceding point by moving one grid step along arandomly selected direction. A parallel algorithm for random walk generation in regular as well as irregular regions is presented. The algorithm is based on parallel prefixcomputations. The communication structure of the algorithm is shown to ideally fit on ahypercube of n nodes, where n is the number of processors.</p>
Index Termsparallel algorithm; random walk construction; Monte Carlo solution; partial differential equations; irregular boundaries; discontinuities; randomly selected direction; parallel prefix computations; communication structure; hypercube; hypercube networks; Monte Carlo methods; parallel algorithms; partial differential equations

A. Youssef, "A Parallel Algorithm for Random Walk Construction with Application to the Monte Carlo Solution of Partial Differential Equations," in IEEE Transactions on Parallel & Distributed Systems, vol. 4, no. , pp. 355-360, 1993.
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