Monte Carlo Algorithms for the Extracting of Electrical Capacitance

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...

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Autores principales:	Andrei Kuznetsov, Alexander Sipin
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	capacitance dirichlet boundary value problem monte carlo method unbiased estimator von-neumann-ulam scheme Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/2067a348e30846d282f3578e08b52ad8
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spelling	oai:doaj.org-article:2067a348e30846d282f3578e08b52ad82021-11-25T18:17:13ZMonte Carlo Algorithms for the Extracting of Electrical Capacitance10.3390/math92229222227-7390https://doaj.org/article/2067a348e30846d282f3578e08b52ad82021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2922https://doaj.org/toc/2227-7390We 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.Andrei KuznetsovAlexander SipinMDPI AGarticlecapacitancedirichlet boundary value problemmonte carlo methodunbiased estimatorvon-neumann-ulam schemeMathematicsQA1-939ENMathematics, Vol 9, Iss 2922, p 2922 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	capacitance dirichlet boundary value problem monte carlo method unbiased estimator von-neumann-ulam scheme Mathematics QA1-939
spellingShingle	capacitance dirichlet boundary value problem monte carlo method unbiased estimator von-neumann-ulam scheme Mathematics QA1-939 Andrei Kuznetsov Alexander Sipin Monte Carlo Algorithms for the Extracting of Electrical Capacitance
description	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.
format	article
author	Andrei Kuznetsov Alexander Sipin
author_facet	Andrei Kuznetsov Alexander Sipin
author_sort	Andrei Kuznetsov
title	Monte Carlo Algorithms for the Extracting of Electrical Capacitance
title_short	Monte Carlo Algorithms for the Extracting of Electrical Capacitance
title_full	Monte Carlo Algorithms for the Extracting of Electrical Capacitance
title_fullStr	Monte Carlo Algorithms for the Extracting of Electrical Capacitance
title_full_unstemmed	Monte Carlo Algorithms for the Extracting of Electrical Capacitance
title_sort	monte carlo algorithms for the extracting of electrical capacitance
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/2067a348e30846d282f3578e08b52ad8
work_keys_str_mv	AT andreikuznetsov montecarloalgorithmsfortheextractingofelectricalcapacitance AT alexandersipin montecarloalgorithmsfortheextractingofelectricalcapacitance
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Monte Carlo Algorithms for the Extracting of Electrical Capacitance

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