A Well-Conditioned Hypersingular Boundary Element Method for Electrostatic Potentials in the Presence of Inhomogeneities within Layered Media (Communications in Computational Physics, 2018)
In this paper, we will present a high-order, well-conditioned boundary elementmethod (BEM) based on Müller's hypersingular second kind integral equationformulation to accurately compute electrostatic potentials in the presence of inhomogeneityembedded 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 cylindricalcavity embedded in a layered electrolytes/membrane environment, and the secondone 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 fastconvergence of iterative solvers compared to previous work using first kind of integralequations. We also show that the second order basis converges faster and is moreaccurate than the first order basis for the BEM.