A Linear Scaling in Accuracy Numerical Method for Computing the Electrostatic Forces in the $N$-Body Dielectric Spheres Problem

Abstract

This article deals with the efficient and accurate computation of the electrostatic forces between charged, spherical dielectric particles undergoing mutual polarisation. We use the spectral Galerkin boundary integral equation framework developed by Lindgren et al. (J. Comput. Phys. 371 (2018): 712-731) and subsequently analysed in two earlier contributions of the authors to propose a linear scaling in cost algorithm for the computation of the approximate forces. We establish exponential convergence of the method and derive error estimates for the approximate forces that do not explicitly depend on the number of dielectric particles $N$. Consequently, the proposed method requires only $\mathcal{O}(N)$ operations to compute the electrostatic forces acting on $N$ dielectric particles up to any given and fixed relative error.

arXiv comment41 pages including Appendix and References; 10 figures

References in corpus (8)

• Three-dimensional Binary Superlattices of Oppositely-charged Colloids
• Dielectric effects in the self-assembly of binary colloidal aggregates
• Three-body Interactions Improve the Prediction of Rate and Mechanism in Protein Folding Models
• Many-Body Electrostatic Forces Between Colloidal Particles at Vanishing Ionic Strength
• Electrostatic interaction in the presence of dielectric interfaces and polarization-induced like-charge attraction
• Boundary integral equation analysis for suspension of spheres in Stokes flow
• Optimized M2L Kernels for the Chebyshev Interpolation based Fast Multipole Method
• An Integral Equation Formulation of the $N$-body Dielectric Spheres Problem. Part II: Complexity Analysis