White, David and Stuart, A. M. (2009) Green's functions by Monte Carlo. In: 8th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 08), Univ Montreal, Montreal, CANADA, JUL 06-11, 2008. Published in: Monte Carlo and Quasi-Monte Carlo Methods 2008 pp. 627-636. ISBN 978-3-642-04106-8. doi:10.1007/978-3-642-04107-5-41

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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.

Item Type:	Conference Item (Paper)
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Journal or Publication Title:	Monte Carlo and Quasi-Monte Carlo Methods 2008
Publisher:	Springer
ISBN:	978-3-642-04106-8
Editor:	LEcuyer, P and Owen, AB
Official Date:	2009
Dates:	Date Event 2009 Published
Number of Pages:	10
Page Range:	pp. 627-636
DOI:	10.1007/978-3-642-04107-5-41
Status:	Peer Reviewed
Publication Status:	Published
Conference Paper Type:	Paper
Title of Event:	8th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 08)
Type of Event:	Conference
Location of Event:	Univ Montreal, Montreal, CANADA
Date(s) of Event:	JUL 06-11, 2008

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