An Integral Equation Formulation of the N-body Dielectric Spheres Problem. Part II: Complexity Analysis

11/17/2019
by   Berenger Bramas, et al.
0

This article is the second in a series of two papers concerning the mathematical study of a boundary integral equation of the second kind that describes the interaction of N dielectric spherical particles undergoing mutual polarisation. The first article presented the numerical analysis of the Galerkin method used to solve this boundary integral equation and derived N-independent convergence rates for the induced surface charges and total electrostatic energy. The current article will focus on the computational aspects of the algorithm. We provide a convergence analysis of the iterative method used to solve the underlying linear system and show that the number of liner solver iterations required to obtain a solution is independent of N. Additionally, we present two linear scaling solution strategies for the computation of the approximate induced surface charges. Finally, we consider a series of numerical experiments designed to validate our theoretical results and explore the dependence of the numerical errors and computational cost of solving the underlying linear system on different system parameters.

READ FULL TEXT
research
02/04/2020

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

This article deals with the efficient and accurate computation of the el...
research
01/15/2020

Fast large-scale boundary element algorithms

Boundary element methods (BEM) reduce a partial differential equation in...
research
01/27/2022

An analysis of least-squares oversampled collocation methods for compactly perturbed boundary integral equations in two dimensions

In recent work (Maierhofer Huybrechs, 2022, Adv. Comput. Math.), the...
research
11/10/2020

Fast Galerkin Method for Solving Helmholtz Boundary Integral Equations on Screens

We solve first-kind Fredholm boundary integral equations arising from He...
research
07/08/2023

Multi-Level Power Series Solution for Large Surface and Volume Electric Field Integral Equation

In this paper, we propose a new multilevel power series solution method ...
research
02/13/2022

On a Boundary Updating Method for the Scalar Stefan Problem

We report on a general purpose method for the scalar Stefan problem insp...
research
07/17/2019

Corrections on A numerical method for solving nonlinear Volterra--Fredholm integral equations

Some corrections are made in our article, which was published in Appl. A...

Please sign up or login with your details

Forgot password? Click here to reset