Intel Cluster Poisson Solver Library

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Information about Intel Cluster Poisson Solver Library

Published on December 7, 2013

Author: IlyaKryukov


Intel®Cluster Poisson Solver Library, a research project for heterogeneous clusters Alexander Kalinkin, Ilya Krjukov, Intel Corporation Introduction • • • This research explores Intel®Cluster Poisson Solver Library that implements a direct method to solve a grid Laplace problem in 3D parallelepiped domain on a cluster of Intel® Xeon® processors. This method is based on a novel approach of data decomposition and transportation, which leads to performance improvement on largescale clusters. Elliptic boundary value problems with separable variables can be solved in a fast and direct manner. This type of problems usually presume a single computational domain (rectangle or circle) and constant coefficients [1], [2]. They can be used to generate preconditioners for iterative solvers that solve far more complex problems. For example, high-accuracy models for atmospheric and oceanic flow simulation, such as those used in the Numerical Weather Simulations, can be solved iteratively using a Helmholtz solver with constant coefficients as a preconditioner. Because the preconditioner is used in every iteration step, the Helmholtz solver performance is critical to the overall computation time of the iterative solver. On a cluster, the size of the initial grid and data distribution determine the number of data transfers among computing processes, as well as the amount of computations needed for the Helmholtz solver. These can significantly affect its performance. This work studies the implementation of a Helmholtz solver on clusters using 2D memory decomposition with the objective of minimizing data transfer and synchronization overhead. This work is a continuation of a series of works on Helmholtz solver for shared and distributed memory machines. Paper [3] compared the performance of a Poisson solver from Intel®Math Kernel Library (Intel®MKL) [6] with the NETLIB* Fishpack solver. It also presented an implementation of Intel®Cluster Poisson Solver Library. Paper [4] demonstrated the performance of Intel® MKL Poisson Solvers with the support of periodic boundary conditions. Algorithm Experiments The 3D Helmholtz problem is to find an approximate solution of the Helmholtz equation: All experiments have been performed on a cluster with Infiniband* interconnect, consisting of 128 computational nodes where each node contains two Intel®Xeon® E5-2670 processors and 64G of RAM. We used Intel®MKL version 11.0.1 [6] and Intel®MPI version 4.1. −

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