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A Fourth-Order Iterative Solver for the Singular Poisson Equation

  • Stéphane Abide
  • Xavier Chesneau
  • Belkacem Zeghmati
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)

Abstract

A compact fourth-order finite difference scheme solver devoted to the singular-Poisson equation is proposed and verified. The solver is based on a mixed formulation: the Poisson equation is splitted into a system of partial differential equations of the first order. This system is then discretized using a fourth-order compact scheme. This leads to a sparse linear system but introduces new variables related to the gradient of an unknow function. The Schur factorization allows us to work on a linear sub-problem for which a conjugated-gradient preconditioned by an algebraic multigrid method is proposed.Numerical results show that the new proposed Poisson solver is efficient while retaining the fourth-order compact accuracy.

Keywords

Large Eddy Simulation Poisson Equation Mixed Formulation Stagger Grid Compact Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Stéphane Abide
    • 1
  • Xavier Chesneau
    • 1
  • Belkacem Zeghmati
    • 1
  1. 1.LAboratoire de Mathématiques et PhySique, EA 4217Univ. Perpignan via DomitiaPerpignanFrance

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