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Last-passage Monte Carlo Algorithm for Charge Density on a Conducting Spherical Surface

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Abstract

For solving some elliptic boundary value problems, Monte Carlo diffusion algorithms are often the most efficient ones. Among them, last-passage algorithms are good for obtaining charge density at a specific point on a conducting surface. In our previous research, we developed the last-passage Monte Carlo algorithm for charge density on a flat conducting surface. In the research, we used the Laplace Green’s function only on a flat surface. In this paper, we further develop the last-passage algorithm on a spherical surface. We demonstrate the last-passage algorithm by obtaining charge density on a sphere held at unit potential. In addition, using the last-passage algorithm we compute the mutual capacitance and charge distribution of two conducting spheres. We compare them with the analytic results of J. Lekner to find an excellent agreement.

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Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant (No. 2017R1E1A1A03070543) funded by the Korea government (Ministry of Science and Information & Communication Technology (ICT)). In addition, this work was supported by the GIST Research Institute (GRI) grant funded by GIST in 2021.

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Correspondence to Chi-Ok Hwang.

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Yu, U., Lee, YM. & Hwang, CO. Last-passage Monte Carlo Algorithm for Charge Density on a Conducting Spherical Surface. J Sci Comput 88, 82 (2021). https://doi.org/10.1007/s10915-021-01594-w

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  • DOI: https://doi.org/10.1007/s10915-021-01594-w

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