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Article Dans Une Revue Journal of Scientific Computing Année : 2011

A Fourth Order Hermitian Box-Scheme with Fast Solver for the Poisson Problem in a Square

Résumé

A new fourth order box-scheme for the Poisson problem in a square with Dirichlet boundary conditions is introduced, extending the approach in [17]. The design is based on a " hermitian box " approach, combining the approximation of the gradient by the fourth order hermitian derivative, with a conservative discrete formulation on boxes of length 2h. The goal is twofold: first to show that fourth order accuracy is obtained both for the unknown and its gradient; second, to describe a fast direct algorithm, based on the Sherman-Morrison formula and the Fast Sine Transform. Several numerical results in a square are given, indicating an asymptotic O(N 2 log 2 (N)) computing complexity.
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hal-01283639 , version 1 (05-03-2016)

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Ali Abbas, Jean-Pierre Croisille. A Fourth Order Hermitian Box-Scheme with Fast Solver for the Poisson Problem in a Square. Journal of Scientific Computing, 2011, 49, pp.239--267. ⟨10.1007/s10915-010-9458-y⟩. ⟨hal-01283639⟩
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