3D integral equation modeling with a linear dependence on dimensions

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. F89-F94 ◽  
Author(s):  
Dmitry Avdeev ◽  
Sergei Knizhnik
Keyword(s):  
Integral Equation ◽  
Electromagnetic Fields ◽  
Linear Dependence ◽  
Integral Equation Method ◽  
Three Dimensions ◽  
Equation Method ◽  
Equation Modeling ◽  
Quadratic Dependence ◽  
Induction Logging ◽  
Model Size

We have improved the integral equation method for modeling 3D electromagnetic fields by using the separability of its inherent [Formula: see text] dyadic Green’s tensors. Conventional integral equation approaches exhibit a quadratic dependence on model size, at least for the vertical dimension. In contrast, our approach has a linear dependence on all three dimensions. We tested our method on an example of induction logging in deviated boreholes.

scholarly journals The boundary integral equation method with application to certain stress concentration problems in elasticity

1981 ◽  
Vol 22 (4) ◽  
pp. 381-393 ◽  
Author(s):  
F. J. Rizzo ◽  
D. J. Shippy
Keyword(s):  
Integral Equation ◽  
Stress Concentration ◽  
Boundary Integral Equation ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Three Dimensions ◽  
Boundary Integral Equation Method ◽  
Equation Method ◽  
Elliptic Type ◽  
Concentration Problem

AbstractThe essential aspects of the Boundary Integral Equation Method for the numerical solution of elliptic type boundary value problems are presented. A numerical example for a stress concentration problem in classical elasticity in three dimensions is given along with several examples for a class of scalar problems in elastic torsion of non-cylindrical bars. Some discussion and criticism of the method itself and in comparison with widely used field methods is also presented.

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