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Quasi-Monte Carlo Simulation of Diffusion in a Spatially Nonhomogeneous Medium

In: Monte Carlo and Quasi-Monte Carlo Methods 2008

Author

Listed:
  • Rami El Haddad

    (Université Saint-Joseph, Département de Mathématiques, Faculté des Sciences)

  • Christian Lécot

  • Gopalakrishnan Venkiteswaran

Abstract

We propose and test a quasi-Monte Carlo (QMC) method for solving the diffusion equation in the spatially nonhomogeneous case. For a constant diffusion coefficient, the Monte Carlo (MC) method is a valuable tool for simulating the equation: the solution is approximated by using particles and in every time step the displacement of each particle is drawn from a Gaussian distribution with constant variance. But for a spatially dependent diffusion coefficient, the straightforward extension using a spatially variable variance leads to biased results. A correction to the Gaussian steplength was recently proposed and provides satisfactory results. In the present work, we devise a QMC variant of this corrected MC scheme. We present the results of some numerical experiments showing that our QMC algorithm converges better than the corresponding MC method for the same number of particles.

Suggested Citation

  • Rami El Haddad & Christian Lécot & Gopalakrishnan Venkiteswaran, 2009. "Quasi-Monte Carlo Simulation of Diffusion in a Spatially Nonhomogeneous Medium," Springer Books, in: Pierre L' Ecuyer & Art B. Owen (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2008, pages 339-354, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-04107-5_21
    DOI: 10.1007/978-3-642-04107-5_21
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