Method of hypersingular integral equations in a three-dimensional problem of diffraction of electromagnetic waves on a piecewise homogeneous dielectric body

2015 ◽  
Vol 51 (9) ◽  
pp. 1197-1210 ◽  
Author(s):  
E. V. Zakharov ◽  
A. V. Setukha ◽  
E. N. Bezobrazova
Keyword(s):  
Integral Equations ◽  
Electromagnetic Waves ◽  
Three Dimensional ◽  
Dimensional Problem ◽  
Dielectric Body ◽  
Hypersingular Integral ◽  
Hypersingular Integral Equations

Diffraction by a plane screen

1950 ◽  
Vol 202 (1069) ◽  
pp. 277-284 ◽  
Keyword(s):  
Integral Equation ◽  
Boundary Conditions ◽  
Integral Equations ◽  
Half Plane ◽  
Arbitrary Function ◽  
Electromagnetic Waves ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Dimensional Problem ◽  
Conducting Plane

The integral-equation method of solving the problem of the diffraction of electromagnetic waves by a perfectly conducting plane screen has been criticized by C. J. Bouwkamp, who claims that it is valid only when certain boundary conditions are satisfied on the edge of the screen. This criticism is answered. It is also shown that, since the equations to be solved are differential-integral equations, an arbitrary function arises in the solution and that this arbitrary function may be chosen so that, although there are singularities at the edge of the screen, there is no radiation of energy from the edge. As an illustration, the three-dimensional problem of diffraction by a half-plane is solved.

Analysis of a Three-Dimensional Crack Terminating at an Interface Using a Hypersingular Integral Equation Method

2002 ◽  
Vol 69 (5) ◽  
pp. 626-631 ◽  
Author(s):  
T. Y. Qin ◽  
N. A. Noda
Keyword(s):  
Integral Equations ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Stress Singularity ◽  
Basic Density ◽  
Hypersingular Integral Equation ◽  
Singular Stress ◽  
Hypersingular Integral ◽  
Rectangular Crack ◽  
Hypersingular Integral Equations

Using a body force method and the finite-part integral concepts, a set of hypersingular integral equations for a vertical crack terminating at an interface in a three-dimensional infinite bimaterial subjected to arbitrary loads are derived. The stress singularity orders and singular stress fields around the crack front terminating at the interface are obtained by the main-part analytical method of hypersingular integral equations. Then, a numerical method for the solution of the hypersingular integral equations in case of a rectangular crack is proposed, in which the crack displacement discontinuities are approximated by the product of basic density functions and polynomials. Numerical solutions for the stress intensity factors of some examples are given.

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