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. © 2013 Springer-Verlag.
CITATION STYLE
Abide, S., Chesneau, X., & Zeghmati, B. (2013). A fourth-order iterative solver for the singular poisson equation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8236 LNCS, pp. 143–150). https://doi.org/10.1007/978-3-642-41515-9_13
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