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      High performance parallel algorithm for solving elliptic equations with non-separable variables

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          Abstract

          A parallel algorithm for computing the finite difference solution to the elliptic equations with non-separable variables is presented. The resultant matrix is symmetric positive definite, thus the preconditioning conjugate gradient or the chebyshev method can be applied. A differential analog to the Laplace operator is used as preconditioner. For inversion of the Laplace operator we implement a parallel version of the separation variable method, which includes the sequential FFT algorithm and the parallel solver for tridiagonal matrix equations (dichotomy algorithm). On an example of solving acoustic equations by the integral Laguerre transformation method, we show that the algorithm proposed is highly efficient for a large number of processors.

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          Author and article information

          Journal
          2010-02-16
          2010-11-27
          Article
          1002.3094
          f035cc1a-a413-41de-8a29-90e1d8eda1d5

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          65F05, 65Y05, 68W10, 35J05
          In Russian; Formula 27 has been corrected
          math.NA

          Numerical & Computational mathematics
          Numerical & Computational mathematics

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