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A Well-Conditioned Hypersingular Boundary Element Method for Electrostatic Potentials in the Presence of Inhomogeneities within Layered Media

Part of: Higher-dimensional theory Physiological, cellular and medical topics

Published online by Cambridge University Press:  12 April 2016

Brian Zinser  and
Wei Cai
Brian Zinser
Affiliation:
Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
Wei Cai*
Affiliation:
Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA INS, Shanghai Jiaotong University, Shanghai 200240, P.R. China
*
*Corresponding author. Email addresses:bzinser@uncc.edu (B. Zinser), wcai@uncc.edu (W. Cai)
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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 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.

Keywords

Poisson Boltzmann equationLayered electrolytes and dielectricsJanus particlesion channelsexplicit/implicit hybrid solvation model

MSC classification

Secondary: 31B05: Harmonic, subharmonic, superharmonic functions 92C05: Biophysics 65Z05: Applications to physics
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 4 , April 2016 , pp. 970 - 997
Copyright
Copyright © Global-Science Press 2016 

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