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Monte Carlo Algorithms for the Extracting of Electrical Capacitance

Author

Listed:
  • Andrei Kuznetsov

    (Department of Applied Mathematics, Vologda State University, Lenina 15, 160000 Vologda, Russia)

  • Alexander Sipin

    (Department of Applied Mathematics, Vologda State University, Lenina 15, 160000 Vologda, Russia)

Abstract

We present new Monte Carlo algorithms for extracting mutual capacitances for a system of conductors embedded in inhomogeneous isotropic dielectrics. We represent capacitances as functionals of the solution of the external Dirichlet problem for the Laplace equation. Unbiased and low-biased estimators for the capacitances are constructed on the trajectories of the Random Walk on Spheres or the Random Walk on Hemispheres. The calculation results show that the accuracy of these new algorithms does not exceed the statistical error of estimators, which is easily determined in the course of calculations. The algorithms are based on mean value formulas for harmonic functions in different domains and do not involve a transition to a difference problem. Hence, they do not need a lot of storage space.

Suggested Citation

  • Andrei Kuznetsov & Alexander Sipin, 2021. "Monte Carlo Algorithms for the Extracting of Electrical Capacitance," Mathematics, MDPI, vol. 9(22), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2922-:d:680816
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    References listed on IDEAS

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    1. Iverson, Ralph B. & Le Coz, Yannick L., 2001. "A floating random-walk algorithm for extracting electrical capacitance," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(1), pages 59-66.
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    Cited by:

    1. Ioannis S. Triantafyllou, 2022. "Signature-Based Analysis of the Weighted- r -within-Consecutive- k -out-of- n : F Systems," Mathematics, MDPI, vol. 10(15), pages 1-13, July.

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