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.
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Abide, S., Chesneau, X., Zeghmati, B. (2013). A Fourth-Order Iterative Solver for the Singular Poisson Equation. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_13
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DOI: https://doi.org/10.1007/978-3-642-41515-9_13
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