Covariance Operator = Green’s Function = Resolvent Kernel = Euclidean Propagator = Fundamental Solution

1981 ◽  
pp. 123-143 ◽  
Author(s):  
James Glimm ◽  
Arthur Jaffe
Keyword(s):  
Fundamental Solution ◽  
Green’S Function ◽  
Green's Function ◽  
Covariance Operator ◽  
Resolvent Kernel

Interaction of Circular Lining and Interior Linear Crack by Incident SH-Wave

2007 ◽  
Vol 348-349 ◽  
pp. 521-524 ◽  
Author(s):  
Hong Liang Li ◽  
Guang Cai Han ◽  
Hong Li
Keyword(s):  
Stress Concentration ◽  
Fundamental Solution ◽  
Green’S Function ◽  
Green's Function ◽  
Dynamic Stress ◽  
Dynamic Stress Concentration ◽  
Elastic Space ◽  
Sh Wave ◽  
Out Of Plane ◽  
Train Of Thought

In this paper, the method of Green’s function is used to investigate the problem of dynamic stress concentration of circular lining and interior linear crack impacted by incident SH-wave. The train of thought for this problem is that: Firstly, a Green’s function is constructed for the problem, which is a fundamental solution of displacement field for an elastic space possessing a circular lining while bearing out-of-plane harmonic line source force at any point in the lining. In terms of the solution of SH-wave’s scattering by an elastic space with a circular lining, anti-plane stresses which are the same in quantity but opposite in direction to those mentioned before, are loaded at the region where the crack existent actually, we called this process “crack-division”. Finally, the expressions of the displacement and stress are given when the lining and the crack exist at the same time. Then, by using the expressions, some example is provided to show the effect of crack on the dynamic stress concentration around circular lining.

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.

scholarly journals Green's functions and Riemann's method

1965 ◽  
Vol 14 (4) ◽  
pp. 293-302 ◽  
Author(s):  
A. G. Mackie
Keyword(s):  
Fundamental Solution ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Elliptic Equations ◽  
Green's Functions ◽  
Green’S Functions ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Auxiliary Function

Methods for solving boundary value problems in linear, second order, partial differential equations in two variables tend to be somewhat rigidly partitioned in some of the standard text-books. Problems for elliptic equations are sometimes solved by finding the fundamental solution which is defined as a solution with a given singularity at a certain point. Another approach is by way of Green's functions which are usually defined as solutions of the original homogeneous equations now made inhomogeneous by the introduction of adelta function on the right hand side. The Green's function coincides with the fundamental solution for elliptic equations but exhibits a totally different type of singularity for parabolic or hyperbolic equations. Boundary value problems for hyperbolic equations can often by solved by Riemann's method which depends on the existence of an auxiliary function called the Riemann or sometimes the Riemann-Green function. The main object of this paper is to show the close relationship between Riemann's method and the method of Green's functions. This not only serves to unify different methods of solution of boundary value problems but also provides an additional method of determining Riemann functions for given hyperbolic equations. Before establishing these relationships we shall survey the general approach to boundary value problems through the use of the Green's function.

GREEN'S FUNCTION MATCHING METHOD FOR REALISTIC CALCULATIONS OF INTERFACES

1985 ◽  
Vol 46 (C4) ◽  
pp. C4-321-C4-329 ◽  
Author(s):  
E. Molinari ◽  
G. B. Bachelet ◽  
M. Altarelli
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Matching Method

THE ATOMISTIC GREEN'S FUNCTION METHOD FOR INTERFACIAL PHONON TRANSPORT

2014 ◽  
Vol 17 (N/A) ◽  
pp. 89-145 ◽  
Author(s):  
Sridhar Sadasivam ◽  
Yuhang Che ◽  
Zhen Huang ◽  
Liang Chen ◽  
Satish Kumar ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Phonon Transport ◽  
Green’S Function Method
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