scholarly journals An integral equation formulation of the N-body dielectric spheres problem. Part 1: Numerical analysis

2020 ◽  
Author(s):  
Muhammad Hassan ◽  
Benjamin Stamm
Keyword(s):  
Integral Equation ◽  
Numerical Analysis ◽  
Error Analysis ◽  
Convergence Rates ◽  
A Priori ◽  
Approximation Error ◽  
Spherical Particles ◽  
Integral Equation Formulation ◽  
Dielectric Spheres ◽  
The Stability

In this article, we analyse an integral equation of the second kind that represents the solution of N interacting dielectric spherical particles undergoing mutual polarisation. A traditional analysis can not quantify the scaling of the stability constants- and thus the approximation error- with respect to the number N of involved dielectric spheres. We develop a new a priori error analysis that demonstrates N-independent stability of the continuous and discrete formulations of the integral equation. Consequently, we obtain convergence rates that are independent of N.

scholarly journals An integral equation formulation of the N-body dielectric spheres problem. Part 2: Complexity analysis

2020 ◽  
Author(s):  
Bérenger Bramas ◽  
Muhammad Hassan ◽  
Benjamin Stamm
Keyword(s):  
Integral Equation ◽  
Linear System ◽  
Boundary Integral Equation ◽  
Convergence Rates ◽  
Computational Cost ◽  
Boundary Integral ◽  
Spherical Particles ◽  
Electrostatic Energy ◽  
Surface Charges ◽  
Integral Equation Formulation

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 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.

scholarly journals Approximate conversion of Bézier curves

1995 ◽  
Vol 51 (1) ◽  
pp. 153-162 ◽  
Author(s):  
Yungeom Park ◽  
U Jin Choi ◽  
Ha-Jine Kimn
Keyword(s):  
Error Analysis ◽  
A Priori ◽  
Approximation Error ◽  
Bézier Curve ◽  
Bezier Curve ◽  
A Priori Bounds ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Geometric Properties

The methods for generating a polynomial Bézier approximation of degree n − 1 to an nth degree Bézier curve, and error analysis, are presented. The methods are based on observations of the geometric properties of Bézier curves. The approximation agrees at the two endpoints up to a preselected smoothness order. The methods allow a detailed error analysis, providing a priori bounds of the point-wise approximation error. The error analysis for other authors’ methods is also presented.

New Error Estimates of Nonconforming Finite Element Methods for the Poisson Problem with Low Regularity Solution

2014 ◽  
Vol 6 (2) ◽  
pp. 179-190 ◽  
Author(s):  
Youai Li
Keyword(s):  
Finite Element ◽  
Error Analysis ◽  
Finite Element Methods ◽  
A Priori ◽  
Approximation Error ◽  
Posteriori Error ◽  
Nonconforming Finite Element ◽  
Poisson Problem ◽  
Posteriori Error Analysis ◽  
Nonconforming Finite Element Methods

AbstractIn this paper, we revisit a priori error analysis of nonconforming finite element methods for the Poisson problem. Based on some techniques developed in the context of the a posteriori error analysis, under two reasonable assumptions on the nonconforming finite element spaces, we prove that, up to some oscillation terms, the consistency error can be bounded by the approximation error. We check these two assumptions for the most used lower order nonconforming finite element methods. Compared with the classical error analysis of the nonconforming finite element method, the a priori analysis herein only needs the H1 regularity of the exact solution.

Stability Analysis of the Nanjung Water Diversion Twin Tunnels based on Convergence Measurement

2019 ◽  
Vol 1 (1) ◽  
pp. 49-60
Author(s):  
Simon Heru Prassetyo ◽  
Ganda Marihot Simangunsong ◽  
Ridho Kresna Wattimena ◽  
Made Astawa Rai ◽  
Irwandy Arif ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Convergence Rate ◽  
Critical Strain ◽  
Convergence Rates ◽  
Strain Analysis ◽  
Water Diversion ◽  
Tunnel Face ◽  
Tunnel Stability ◽  
The Stability ◽  
Twin Tunnels

This paper focuses on the stability analysis of the Nanjung Water Diversion Twin Tunnels using convergence measurement. The Nanjung Tunnel is horseshoe-shaped in cross-section, 10.2 m x 9.2 m in dimension, and 230 m in length. The location of the tunnel is in Curug Jompong, Margaasih Subdistrict, Bandung. Convergence monitoring was done for 144 days between February 18 and July 11, 2019. The results of the convergence measurement were recorded and plotted into the curves of convergence vs. day and convergence vs. distance from tunnel face. From these plots, the continuity of the convergence and the convergence rate in the tunnel roof and wall were then analyzed. The convergence rates from each tunnel were also compared to empirical values to determine the level of tunnel stability. In general, the trend of convergence rate shows that the Nanjung Tunnel is stable without any indication of instability. Although there was a spike in the convergence rate at several STA in the measured span, that spike was not replicated by the convergence rate in the other measured spans and it was not continuous. The stability of the Nanjung Tunnel is also confirmed from the critical strain analysis, in which most of the STA measured have strain magnitudes located below the critical strain line and are less than 1%.

Adsorption on heterogeneous surfaces: Numerical analysis of models for the Dubinin-Radushkevich equation

1981 ◽  
Vol 46 (8) ◽  
pp. 1709-1721 ◽  
Author(s):  
Miloš Smutek ◽  
Arnošt Zukal
Keyword(s):  
Integral Equation ◽  
Numerical Analysis ◽  
Numerical Method ◽  
Adsorption Behaviour ◽  
Heterogeneous Surfaces ◽  
Strong Energy ◽  
Adsorption On Heterogeneous Surfaces ◽  
Heterogeneity Parameter ◽  
Adsorption Energies ◽  
Mobile Adsorption

A numerical method, based on the integral equation of the adsorption on energy heterogeneous surfaces, is suggested for the evaluation of overall isotherm. It is shown that for the distribution of adsorption energies given by Eq. (1.11) and different models of the adsorption behaviour, the overall isotherms obey approximately the Dubinin-Radushkevich equation. The strong energy heterogeneity smears effectively the differences between the localized and mobile adsorption and leads to the same character of the overall isotherm with only a slightly changed heterogeneity parameter.

Sign in / Sign up

Export Citation Format

Share Document