A Well-Conditioned Hypersingular Boundary Element Method for Electrostatic Potentials in the Presence of Inhomogeneities within Layered Media. (12th April 2016)

• Record Type: Journal Article
• Authors: Zinser, Brian; Cai, Wei
• Is Part Of: Communications in computational physics. Volume 19:Number 4(2016:Apr.)
• Page Start: 970
• Page End: 997
• Publication Date: 2016-04-12
• Subjects: 31B05, -- 92C05, -- 65Z05; Poisson Boltzmann equation, -- Layered electrolytes and dielectrics, -- Janus particles, -- ion channels, -- explicit/implicit hybrid solvation model; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.090415.170815a
• Languages: English
• ISSNs: 1815-2406

Abstract

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.