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
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
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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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. ⟨inria-00442773⟩

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