Using a sequential Monte Carlo algorithm, we compute a spectral approximation of the solution of the Poisson equation in dimension 1 and 2. The Feyman-Kac computation of the pointwise solution is achieved using either an integral representation or a modified walk on spheres method. The variances decrease geometrically with the number of steps. A global solution is obtained, accurate up to the interpolation error. Surprisingly, the accuracy depends very little on the absorption layer thickness of the walk on spheres.
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A spectral Monte Carlo method for the Poisson equation
* CMAP, Ecole Polytechnique, 91128 Palaiseau cedex, France. Email: emmanuel.gobet@polytechnique.fr
† ISITV, Université de Toulon et du Var, avenue G. Pompidou, BP56, 83262 La Valette du Var cedex, France. Email: maire@univ-tln.fr
Citation Information: Monte Carlo Methods and Applications mcma. Volume 10, Issue 3-4, Pages 275–285, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: 10.1515/mcma.2004.10.3-4.275, May 2008
Publication History:
- Published Online:
- 2008-05-09
Keywords: Spectral method; Sequential Monte Carlo; Poisson equation; Variance reduction; Modified walk on spheres; Feyman-Kac formula
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