Green's Functions by Monte Carlo
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.
© 2009 Springer-Verlag. David White and Andrew Stuart are grateful to EPSRC for financial support. They are also very grateful to both the University of Warwick's High Performance Systems Group and the Centre for Scientific Computing for use of the Condor and IBM clusters.