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A fourth-order Hermitian box-scheme with fast solver for the Poisson problem in a cube

Authors

  • Ali Abbas

    Corresponding author
    1. Department of Mathematics, Faculty of Sciences, Lebanese International University, Bekaa-Rayak, Lebanon
    • Correspondence to: Ali Abbas, Department of Mathematics, Faculty of Sciences, Lebanese International University, Bekaa-Rayak, Lebanon (e-mail: ali.abbas@liu.edu.lb)

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Abstract

We present a fourth-order Hermitian box-scheme (HB-scheme) for the Poisson problem in a cube. A single-nonstaggered regular grid is used supporting the discrete unknowns u and math formula. The scheme is fourth-order accurate for u and math formula in math formula norm. The fast numerical resolution uses a matrix capacitance method, resulting in a computational complexity of math formula. Numerical results are reported on several examples including nonseparable problems. The present scheme is the extension to the three-dimensional case of the HB-scheme presented in Abbas and Croisille [J Sci Comp 49 (2011), 239–267]. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 609–629, 2015

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