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Numerical solution of the Poisson equation over hypercubes using reduced Chebyshev polynomial bases

Christophe de Luigi 1 Sylvain Maire 2, 3 Serge Dumont 4
2 TOSCA
CNRS - Centre National de la Recherche Scientifique : UMR7502, INPL - Institut National Polytechnique de Lorraine, Université Nancy 2, UHP - Université Henri Poincaré - Nancy 1, CRISAM - Inria Sophia Antipolis - Méditerranée , INRIA Lorraine
Abstract : We describe how to use new reduced size polynomial approximations for the numerical solution of the Poisson equation over hypercubes. Our method is based on a non-standard Galerkin method which allows test functions which do not verify the boundary conditions. Numerical examples are given in dimensions up to 8.
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Submitted on : Wednesday, December 23, 2009 - 1:24:03 PM
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Christophe de Luigi, Sylvain Maire, Serge Dumont. Numerical solution of the Poisson equation over hypercubes using reduced Chebyshev polynomial bases. Journal of Computational and Applied Mathematics, Elsevier, 2010, 234 (1), pp.181-191. ⟨10.1016/j.cam.2009.12.014⟩. ⟨inria-00442773⟩

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