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

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. © 2006 IMACS. Published by Elsevier B.V. All rights reserved. MSC: 65C05; 60F15

• Type: Journal
• Year: 2007
• Where: MCS
• Authors: Antoine Lejay, Sylvain Maire
• Keywords: MCS 2007, Monte Carlo Method, Numerical Computation, Pattern Recognition, Principal Eigenvalue