Algorithm to Solve Dirichlet Problem for Laplace’s Equation

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Dr. Mohammad Miyan


The various researches and developments in the parallel computing Apache Spark framework allows to process petabyte-scale data and possesses properties such as scalability, fault tolerance, load balancing and mechanisms of in the memory computations across the nodes of the cluster. So, the features are much attractive for high performance of scientific computations. As the Hadoop platform is not much suitable for the iterative computing due to some typicality then Apache Spark with new distributed data structure (RDD) is much suitable. Here we are using the method and algorithm described by researchers from time to time for Hadoop-based algorithm to solve the Dirichlet problem for Laplace’s equation. The comparative figures are drawn with respect to time to verify the performance. By seeing graphs and other details, we can say that the Spark based implementation is much suitable for solving the Dirichlet problem for their improved performance as compared to Hadoop-based implementation.

Keywords:- Apache Spark; Dirichlets problem; Hadoop; Laplace’s equation; RDD.


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