Monte Carlo Algorithms for the Extracting of Electrical Capacitance

Кузнецов, А. В.; Сипин, А. С.

doi:10.3390/math9222922

Cited by 5 publications

(3 citation statements)

References 15 publications

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“…For a finite flat boundary or in two-plate between boundaries, WOP algorithm can not be used and WOH one is very plausible. In the previous works 4 , 12 , 13 , WOH algorithm was implemented via Von Neumann’s accecptance-rejection method 14 . In this paper, via a conformal map 15 , 16 combined with an accecptance-rejection method 14 we implement and demonstrate the WOH algorithm for the induced charge density distribution on parallel infinite conducting plates when a unit charge is between the plates and apply it to the mutual capacitance of two circular parallel plates.…”

Section: Discussionmentioning

confidence: 99%

“…Diffusion Monte Carlo algorithms have been mainly applied for extracting mutual capacitances for a system of conductors, 12 , 13 , 31 , 32 . In semiconductor industry, a powerful commercial 3D CAD tool, QuickCap has been used 33 .…”

Section: Discussionmentioning

confidence: 99%

“…In this paper, we implement a new diffusion algorithm called “Walk-on-Hemispheres” (WOH) for a finite flat boundary, which can be also used for the (parallel) finite or infinite planes boundary. In the previous researches of Ermakov 4 , 12 , he gave mathematical proofs for the transition probabilities regarding the hemisphere geometry based on image charge method and later 4 , 12 , 13 the WOH algorithm was implemented via Von Neumann’s acceptance-rejection method 14 . Here, we implement WOH algorithm by applying a conformal map 15 , 16 combined with an acceptance rejection method 14 .…”

Section: Introductionmentioning

confidence: 99%

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Walk-on-Hemispheres first-passage algorithm

Son¹,

Shin

Hwang

2023

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Due to the isomorphism between an electrostatic problem and the corresponding Brownian diffusion one, the induced charge density on a conducting surface by a charge is isomorphic to the first-passage probability of the diffusion initiated at the location of the charge. Based on the isomorphism, many diffusion algorithms such as “Walk-on-Spheres” (WOS), “Walk-on-Planes” and so on have been developed. Among them, for fast diffusion simulations WOS algorithm is generally applied with an $$\varepsilon $$ ε -layer, which is used for diffusion convergence on the boundary but induces another error from the $$\varepsilon $$ ε -layer in addition to the intrinsic Monte Carlo error. However, for a finite flat boundary it is possible to terminate a diffusion process via “Walk-on-Hemispheres” (WOH) algorithm without the $$\varepsilon $$ ε -layer. In this paper, we implement and demonstrate this algorithm for the induced charge density distribution on parallel infinite planes when a unit charge is between the plates. In addition, we apply it to the mutual capacitance of two circular parallel plates. In both simulations, WOH algorithm shows much better performance than the previous WOS algorithm.

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