scholarly journals Asymptotic Error Analysis of a Quadrature Method for Integral Equations with Green's Function Kernels

2000 ◽  
Vol 12 (4) ◽  
pp. 349-384 ◽  
Author(s):  
William F. Ford ◽  
James A. Pennline ◽  
Yuesheng Xu ◽  
Yunhe Zhao
Keyword(s):  
Error Analysis ◽  
Green’S Function ◽  
Integral Equations ◽  
Green's Function ◽  
Quadrature Method ◽  
Asymptotic Error ◽  
Asymptotic Error Analysis

scholarly journals Green's Function for A Piecewise Continous Potential via Integral Equations Method

2018 ◽  
Vol 24 (2) ◽  
pp. 20-35
Author(s):  
Benali Brahim ◽  
Mohammed Tayeb Meftah ◽  
Rai Vandana
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Integral Equations ◽  
Green's Function ◽  
Hamiltonian Operator ◽  
Potential Part ◽  
Piecewise Continuous ◽  
Discrete Spectra

The aim of this work is to provide Green's function for the Schrodingerequation. The potential part in the Hamiltonian is piecewise continuous operator.It is a zero operator on a disk of radius "a" and a constant V0 outside this disk (intwo dimensions). We have used, to construct the Green's function, the technique ofthe integral equations. We have respected the boundary conditions of the problem.The discrete spectra of the Hamiltonian operator have been also derived.

Integral equations and relations for Lamé functions and ellipsoidal wave functions

1968 ◽  
Vol 64 (1) ◽  
pp. 113-126 ◽  
Author(s):  
B. D. Sleeman
Keyword(s):  
Wave Function ◽  
Green’S Function ◽  
Integral Equations ◽  
Green's Function ◽  
Function Theory ◽  
Natural Generalization ◽  
Wave Functions ◽  
Linear Integral ◽  
First Time ◽  
Linear Integral Equations

AbstractNon-linear integral equations and relations, whose nuclei in all cases is the ‘potential’ Green's function, satisfied by Lamé polynomials and Lamé functions of the second kind are discussed. For these functions certain techniques of analysis are described and these find their natural generalization in ellipsoidal wave-function theory. Here similar integral equations are constructed for ellipsoidal wave functions of the first and third kinds, the nucleus in each case now being the ‘free space’ Green's function. The presence of ellipsoidal wave functions of the second kind is noted for the first time. Certain possible generalizations of the techniques and ideas involved in this paper are also discussed.

scholarly journals Numerical Green's Functions for Line Force and Dislocation around Multiple Cracks

2007 ◽  
Vol 2 (1) ◽  
Author(s):  
M Denda ◽  
P Quick
Keyword(s):  
Error Analysis ◽  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Crack Opening ◽  
Crack Tip ◽  
Function Technique ◽  
Multiple Cracks ◽  
Line Force

The numerical Green's function technique for an in¯nite isotropic domain with multiple cracks is developed. The singularities considered are the line force and dislocation. The Green's function is decomposed into the singular and the image terms. To obtain the image term we represent the crack opening displacement (COD) by the dislocation dipole distribution, embed the pr crack tip behavior, and integrate the resulting singular/hyper-singular integrals analytically. The re- sulting whole crack singular element (WCSE) consists of multiple independent crack opening modes and is strictly algebraic with the correct crack tip singular behavior but the magnitude for each mode is unknown. They are determined to give the negative of the crack surface traction induced by the singular term. Ex- tensive error analysis is performed for the line force and dislocation in an in¯nite domain with a single crack to identify the region where, when these singularities are placed, the solution achieves high accuracy. Following the guideline set by the error analysis, numerical Green's functions for a few multiple crack con¯gurations are obtained for the line force and dislocation.

scholarly journals On the condition number of integral equations in linear elasticity using the modified Green's function

2003 ◽  
Vol 44 (3) ◽  
pp. 431-446
Author(s):  
E. Argyropoulos ◽  
D. Gintides ◽  
K. Kiriaki
Keyword(s):  
Fundamental Solution ◽  
Green’S Function ◽  
Optimal Condition ◽  
Integral Equations ◽  
Green's Function ◽  
Condition Number ◽  
Linear Elasticity ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Function Technique

AbstractIn this work the modified Green's function technique for an exterior Dirichlet and Neumann problem in linear elasticity is investigated. We introduce a modification of the fundamental solution in order to remove the lack of uniqueness for the solution of the boundary integral equations describing the problems, and to simultaneously minimise their condition number. In view of this procedure the cases of the sphere and perturbations of the sphere are examined. Numerical results that demonstrate the effect of increasing the number of coefficients in the modification on the optimal condition number are also presented.

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