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Walk On Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence

Author

Listed:
  • Xuxin Yang

    (Hunan First Normal University)

  • Antti Rasila

    (Aalto University)

  • Tommi Sottinen

    (University of Vaasa)

Abstract

We show that a constant-potential time-independent Schrödinger equation with Dirichlet boundary data can be reformulated as a Laplace equation with Dirichlet boundary data. With this reformulation, which we call the Duffin correspondence, we provide a classical Walk On Spheres (WOS) algorithm for Monte Carlo simulation of the solutions of the boundary value problem. We compare the obtained Duffin WOS algorithm with existing modified WOS algorithms.

Suggested Citation

  • Xuxin Yang & Antti Rasila & Tommi Sottinen, 2017. "Walk On Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 589-602, June.
    • Handle: RePEc:spr:metcap:v:19:y:2017:i:2:d:10.1007_s11009-016-9504-9
    DOI: 10.1007/s11009-016-9504-9
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    References listed on IDEAS

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    1. Hwang, Chi-Ok & Mascagni, Michael & Given, James A., 2003. "A Feynman–Kac path-integral implementation for Poisson’s equation using an h-conditioned Green’s function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(3), pages 347-355.
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    Cited by:

    1. Yang, Xuxin & Rasila, Antti & Sottinen, Tommi, 2019. "Efficient simulation of the Schrödinger equation with a piecewise constant positive potential," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 315-323.

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