Monte Carlo Algorithms for the Extracting of Electrical Capacitance

Andrei Kuznetsov and Alexander Sipin
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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

Mathematics, 2021, vol. 9, issue 22, 1-19

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.

Keywords: capacitance; dirichlet boundary value problem; monte carlo method; unbiased estimator; von-neumann-ulam scheme (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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