Green’s Functions by Monte Carlo

David White () and Andrew Stuart
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David White: University of Warwick, Mathematics Institute

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2008, 2009, pp 627-636 from Springer

Abstract: Abstract We describe a new numerical technique to estimate Green’s functions of elliptic differential operators on bounded open sets. The algorithm utilizes SPDE based function space sampling techniques in conjunction with Metropolis-Hastings MCMC. The key idea is that neither the proposal nor the acceptance probability require the evaluation of a Dirac measure. The method allows Green’s functions to be estimated via ergodic averaging. Numerical examples in both 1D and 2D, with second and fourth order elliptic PDE’s, are presented to validate this methodology.

Keywords: Covariance Operator; Dirac Delta Function; Gaussian Measure; MCMC Method; Acceptance Probability (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04107-5_41

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DOI: 10.1007/978-3-642-04107-5_41

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