A Well-Conditioned Hypersingular Boundary Element Method for Electrostatic Potentials in the Presence of Inhomogeneities within Layered Media
Year: 2016
Communications in Computational Physics, Vol. 19 (2016), Iss. 4 : pp. 970–997
Abstract
In this paper, we will present a high-order, well-conditioned boundary element method (BEM) based on Müller's hypersingular second kind integral equation formulation to accurately compute electrostatic potentials in the presence of inhomogeneity embedded within layered media. We consider two types of inhomogeneities: the first one is a simple model of an ion channel which consists of a finite height cylindrical cavity embedded in a layered electrolytes/membrane environment, and the second one is a Janus particle made of two different semi-spherical dielectric materials. Both types of inhomogeneities have relevant applications in biology and colloidal material, respectively. The proposed BEM gives $\mathcal{O}$(1) condition numbers, allowing fast convergence of iterative solvers compared to previous work using first kind of integral equations. We also show that the second order basis converges faster and is more accurate than the first order basis for the BEM.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.090415.170815a
Communications in Computational Physics, Vol. 19 (2016), Iss. 4 : pp. 970–997
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
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Reference Module in Life Sciences
A Review of Mathematical Modeling, Simulation and Analysis of Membrane Channel Charge Transport ☆
Chen, Duan
Wei, Guo-Wei
2017
https://doi.org/10.1016/B978-0-12-809633-8.12044-8 [Citations: 3]