Fast numerical method for electromagnetic scattering by rough layered interfaces: Propagation-inside-layer expansion method

2006 ◽  
Vol 23 (2) ◽  
pp. 359 ◽  
Author(s):  
Nicolas Déchamps ◽  
Nicole de Beaucoudrey ◽  
Christophe Bourlier ◽  
Serge Toutain
Keyword(s):  
Numerical Method ◽  
Electromagnetic Scattering ◽  
Expansion Method ◽  
Inside Layer ◽  
Layered Interfaces

Self-Similar Crack Expansion Method for Three-Dimensional Cracks Under Mixed-Mode Loading Conditions

1998 ◽  
Vol 65 (3) ◽  
pp. 557-565 ◽  
Author(s):  
Yonglin Xu ◽  
B. Moran ◽  
T. Belytschko
Keyword(s):  
Numerical Method ◽  
Mixed Mode ◽  
Three Dimensional ◽  
Expansion Method ◽  
Shear Loading ◽  
Boundary Integral ◽  
Normal Displacement ◽  
Loading Conditions ◽  
Mixed Mode Loading ◽  
Self Similar

Three-dimensional planar cracks under mixed-mode loading conditions are investigated by using the selfsimilar crack expansion method with the boundary integral equation technique. For a planar crack under general loading (tensile and shear) conditions, the normal displacement and tangential displacements on the crack surface exhibit uncoupled characteristics. However, the tangential displacements in the two directions are generally coupled. In this paper, two coupled boundary integral equations for a crack subject to shear loading are solved using the analytically numerical method, where the integrals on elements’ are estimated by using the explicit expression of the close form of the integrals. Combination of the self-similar crack expansion method and the analytically numerical method results in good accuracy, with errors in stress intensity factors of penny-shaped cracks and elliptical cracks less than one percent. This numerical analysis is applicable to the analysis of cracks with arbitrary geometry.

scholarly journals Analytical Method and Semianalytical Method for Analysis of Scattering by Anisotropic Sphere: A Review

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Chao Wan ◽  
Hongning Li
Keyword(s):  
Electromagnetic Scattering ◽  
Expansion Method ◽  
Scattering Field ◽  
Significant Phenomenon ◽  
History Of ◽  
T Matrix ◽  
Cartesian Coordinate ◽  
Semianalytical Method ◽  
Variable Separation Method ◽  
Angular Expansion

The history of methods for the electromagnetic scattering by an anisotropic sphere has been reviewed. Two main methods, angular expansion method and T-matrix method, which are widely used for the anisotropic sphere, are expressed in Cartesian coordinate firstly. The comparison of those and the further exploration on the scattering field are illustrated afterwards. Based on the most general form concluded by variable separation method, the coupled electric field and magnetic field of radial anisotropic sphere can be derived. By simplifying the condition, simpler case of uniaxial anisotropic media is expressed with confirmed coefficients for the internal and external field. Details of significant phenomenon are presented.

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