Abstract
We develop a last-passage Monte Carlo algorithm on a conducting surface at non-constant potentials. In the previous researches, last-passage Monte Carlo algorithms on conducting surfaces with a constant potential have been developed for charge density at a specific point or on a finite region and a hybrid BIE-WOS algorithm for charge density on a conducting surface at non-constant potentials. In the hybrid BIE-WOS algorithm, they used a deterministic method for the contribution from the lower non-constant potential surface. In this paper, we modify the hybrid BIE-WOS algorithm to a last-passage Monte Carlo algorithm on a conducting surface at non-constant potentials, where we can avoid the singularities on the non-constant potential surface very naturally. We demonstrate the last-passage Monte Carlo algorithm for charge densities on a circular disk and the four rectangle plates with a simple voltage distribution, and update the corner singularities on the unit square plate and cube.
Funding source: National Research Foundation of Korea
Award Identifier / Grant number: 2017R1E1A1A03070543
Funding statement: This research was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Science, ICT and Future Planning (2017R1E1A1A03070543). Also, this work was supported by the GIST Research Institute (GRI) in 2020.
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