Last-passage Monte Carlo algorithm for mutual capacitance

Abstract

We develop and test the last-passage diffusion algorithm, a charge-based Monte Carlo algorithm, for the mutual capacitance of a system of conductors. The first-passage algorithm is highly efficient because it is charge based and incorporates importance sampling; it averages over the properties of Brownian paths that initiate outside the conductor and terminate on its surface. However, this algorithm does not seem to generalize to mutual capacitance problems. The last-passage algorithm, in a sense, is the time reversal of the first-passage algorithm; it involves averages over particles that initiate on an absorbing surface, leave that surface, and diffuse away to infinity. To validate this algorithm, we calculate the mutual capacitance matrix of the circular-disk parallel-plate capacitor and compare with the known numerical results. Good agreement is obtained.

Capacitance Evaluation on Parallel-Plate Capacitors by Means of Finite Element Analysis

“…Nowadays, owe to the calculation power of the computers, different iterative algorithms are used to solve the equations that govern the behaviour of this type of capacitors [5][6][7][8][9], these algorithms are designed to obtain the surface distributions of load, the values of the electric field and the total capacitance. The disadvantage of these algorithms is that they are designed for specific cases, so that, if geometry changes, the algorithm must almost be reconstructed entirely.…”

Spatial first-passage statistics ofAl∕Si(111)−(3×3)step fluctuations

“…Traditionally, these step edge fluctuations have been examined using correlation function approaches. However additional information is available in the form of first-passage analyses [6][7][8][9] , which may be pertinent to applications in self assembly and nanoscale device properties [10][11][12][13] .…”

A Parallel Method for Solving Laplace Equations with Dirichlet Data Using Local Boundary Integral Equations and Random Walks

“…A charge q is located at r s = (0, 0, −h). Then the potential in the upper space is given by 17) and u(r) satisfies the Laplace equation ∇ 2 u(r) = 0, z > 0 with a variable Dirichlet data on the boundary z = 0.…”

“…For example, QuickCap [20] [19] can calculate the potential or charge density at only one point locally without finding the solution elsewhere. Usually, random methods are based on the Feynman-Kac probabilistic formula and the potential (or charge density) is expressed as a weighted average of the boundary values [17]. The Feynman-Kac formula allows a local solution of the PDE, and fast sampling techniques of the diffusion paths with the walk on sphere (WOS) methods are available for simple PDEs such as Laplace or modified Helmholtz equations.…”