A spectral Monte Carlo method for the Poisson equation

Gobet Emmanuel and Maire Sylvain
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Gobet Emmanuel: CMAP, Ecole Polytechnique, 91128 Palaiseau cedex, France. Email: emmanuel.gobet@polytechnique.fr
Maire Sylvain: ISITV, Université de Toulon et du Var, avenue G. Pompidou, BP56, 83262 La Valette du Var cedex, France. Email: maire@univ-tln.fr

Monte Carlo Methods and Applications, 2004, vol. 10, issue 3-4, 275-285

Abstract: 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.

Keywords: Spectral method; Sequential Monte Carlo; Poisson equation; Variance reduction; Modified walk on spheres; Feyman-Kac formula (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1515/mcma.2004.10.3-4.275

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