Computing the first eigenelements of some linear operators using a branching Monte Carlo method

Antoine Lejay 1, 2 Sylvain Maire 3
1 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 : In earlier works, we have developed a Monte Carlo method to compute the first eigenvalue of linear operators, which is based on the simulation of exit times. In this paper, we show how to use a branching method to handle in a better way the simulation of large exit times. We show furthermore that this new method provides naturally an estimation of the first eigenfunction of the adjoint operator. Numerical examples are given on the Laplace operator and on homogeneous neutron transport operators.
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Antoine Lejay, Sylvain Maire. Computing the first eigenelements of some linear operators using a branching Monte Carlo method. Journal of Computational Physics, Elsevier, 2008, 227 (23), pp.9794-9806. ⟨10.1016/j.jcp.2008.07.018⟩. ⟨inria-00151884v2⟩

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