The contrast-source stress-velocity integral-equation formulation of three-dimensional time-domain elastodynamic scattering problems: A structured approach using tensor partitioning

2009 ◽  
Vol 126 (3) ◽  
pp. 1095-1100 ◽  
Author(s):  
Adrianus T. de Hoop ◽  
Aria Abubakar ◽  
Tarek M. Habashy
Keyword(s):  
Integral Equation ◽  
Time Domain ◽  
Three Dimensional ◽  
Scattering Problems ◽  
Equation Formulation ◽  
Integral Equation Formulation ◽  
Structured Approach

A well-posed integral equation formulation for three-dimensional rough surface scattering

2006 ◽  
Vol 462 (2076) ◽  
pp. 3683-3705 ◽  
Author(s):  
Simon N Chandler-Wilde ◽  
Eric Heinemeyer ◽  
Roland Potthast
Keyword(s):  
Integral Equation ◽  
Rough Surface ◽  
Double Layer ◽  
Inverse Operator ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Wave Number ◽  
Layer Potential ◽  
Equation Formulation ◽  
Integral Equation Formulation

We consider the problem of scattering of time-harmonic acoustic waves by an unbounded sound-soft rough surface. Recently, a Brakhage–Werner type integral equation formulation of this problem has been proposed, based on an ansatz as a combined single- and double-layer potential, but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half-space Green's function. Moreover, it has been shown in the three-dimensional case that this integral equation is uniquely solvable in the space when the scattering surface does not differ too much from a plane. In this paper, we show that this integral equation is uniquely solvable with no restriction on the surface elevation or slope. Moreover, we construct explicit bounds on the inverse of the associated boundary integral operator, as a function of the wave number, the parameter coupling the single- and double-layer potentials, and the maximum surface slope. These bounds show that the norm of the inverse operator is bounded uniformly in the wave number, κ , for κ >0, if the coupling parameter η is chosen proportional to the wave number. In the case when is a plane, we show that the choice is nearly optimal in terms of minimizing the condition number.

An enhanced integral-equation formulation for accurate analysis of frequency-selective structures

2012 ◽  
Vol 4 (3) ◽  
pp. 365-372 ◽  
Author(s):  
Guido Valerio ◽  
Alessandro Galli ◽  
Donald R. Wilton ◽  
David R. Jackson
Keyword(s):  
Integral Equation ◽  
Multilayered Structures ◽  
Accurate Analysis ◽  
Scattering Problems ◽  
Equation Formulation ◽  
Acceleration Techniques ◽  
Full Wave ◽  
Integral Equation Formulation ◽  
Different Types ◽  
Frequency Selective

In this work, a very efficient mixed-potential integral-equation formulation is implemented for the rigorous analysis of multilayered structures with arbitrarily shaped two-dimensional periodic metallic and/or dielectric inclusions. Original acceleration techniques have been developed for the computation of the components of the scalar and dyadic Green's functions, based on different types of asymptotic extractions according to the potential considered. The theoretical approach and its computational convenience have been validated through different full-wave analyses concerning both scattering problems and complex-mode dispersive behaviors in various frequency-selective structures for microwave applications.

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