Computing the principal eigenvalue of the Laplace operator by a stochastic method

Antoine Lejay 1, 2 Sylvain Maire 3
1 OMEGA - Probabilistic numerical methods
CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : We describe a Monte Carlo method for the numerical computation of the principal eigenvalue of the Laplace operator in a bounded domain with Dirichlet conditions. It is based on the estimation of the speed of absorption of the Brownian motion by the boundary of the domain. Various tools of statistical estimation and different simulation schemes are developed to optimize the method. Numerical examples are studied to check the accuracy and the robustness of our approach.
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Submitted on : Saturday, September 9, 2006 - 7:23:59 PM
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Antoine Lejay, Sylvain Maire. Computing the principal eigenvalue of the Laplace operator by a stochastic method. Mathematics and Computers in Simulation, Elsevier, 2007, 73 (3), pp.351-363. ⟨10.1016/j.matcom.2006.06.011⟩. ⟨inria-00092408⟩

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