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A spectral Monte Carlo method for the Poisson equation

Author

Listed:
  • 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)

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.

Suggested Citation

  • Gobet Emmanuel & Maire Sylvain, 2004. "A spectral Monte Carlo method for the Poisson equation," Monte Carlo Methods and Applications, De Gruyter, vol. 10(3-4), pages 275-285, December.
    • Handle: RePEc:bpj:mcmeap:v:10:y:2004:i:3-4:p:275-285:n:10
    DOI: 10.1515/mcma.2004.10.3-4.275
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