Monte Carlo methods for computing the capacitance of the unit cube
It is well known that there is no analytic expression for the electrical capacitance of the unit cube However. there ate several Monte Carlo methods that have, been used to numerically estimate this capacitance to high accuracy These include a Brownian dynamics algorithm [H -X Zhou. A. Szabo. J.F. Douglas. J B Hubbard. A Brownian dynamics algorithm for calculating the hydrodynamic friction and the electrostatic capacitance of an arbitarily shaped object. J Chem Phys 100 (5) (1994) 3821-3826] coupled to the "walk on spheres" (WOS) method [M E Mullet, Some continuous Monte Carlo methods for the Dirichlet problem, Ann Math Slat 27 (1956) 569-589]. the Green's function fist-passage (GFFP) algorithm [J A. Given. J B Hubbard. J.F Douglas. A first-passage algorithm for the hydrodynamic friction and diffusion-limited reaction rate of macromolecules. J Chem Phys 106 (9) (1997) 3721-3771], an error-controlling Brownian dynamics algorithm [C -O Hwang. M Mascagni. Capacitance of the unit cube. J. Korean Phys Soc 42 (2003) L1-L4], an extrapolation technique coupled to the WOS method [C -O Hwang. Extrapolation technique in the "walk on spheres" method for the capacitance of the unit cube. J Korean Phys Soc 44 (2) (2004) 469-470], the "walk on planes" (WOB) method [M L. Mansfield. J.F Douglas. E J Garboczi. Intrinsic viscosity and the electrical of arbitiarily shaped objects. Phys Rev E 64 (6) (2001) 061401 1-061401 16: C -O Hwang. M Mascagni. Electrical capacitance of the unit cube. J Appl Phys. 95 (7) (2004) 3798-3802], and the random "walk on the boundary" (WOB) method [M Mascagni. N A Simonov, The random walk on the boundary method for calculating capacitance. J Comp Phys 195 (2004) 465-473] Monte Carlo methods are convenient and efficient for problems whose solution includes singularities In the calculation of the Linn cube capacitance. there are edge and cornet singularities in the charge density distribution In this paper. we review the above Monte Carlo methods for computing the electrical capacitance of a cube and compare their effectiveness We also provide a new result. We will focus our attention particularly on two Monte Carlo methods WOP [M.L Mansfield. J F Douglas, E J Garboczi. Intrinsic viscosity and the electrical polarizability of arbitiarily shaped objects. Phys Rev E 64 (6) (2001) 061401 1-061401 16: C -O Hwang, M Mascagni. Electrical capacitance oh the unit cube. J Appl Phys 95 (7) (2004) 3798-3802. C -O Hwang. T Won. Edge charge singularity of conductors. J Korean Phys. Soc 45 (2004) S551-S553] and the random WOB [M Mascagni. N A Simonov. The random walk on the boundary method for calculating capacitance. J. Comp Phys 195 (2004) 465-473] methods (C) 2008 IMACS Published by Elsevier B V All rights reserved
monte carlo random walk cube capacitance walk on boundary (wob)