A Fourth-Order Iterative Solver for the Singular Poisson Equation

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


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.


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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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