Near-field scattering from PEC wedge excited by electric dipole in lossy medium

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Hülya Öztürk ◽  
Korkut Yegin
Keyword(s):  
Electric Fields ◽  
Green's Functions ◽  
Green’S Functions ◽  
Near Field ◽  
Dipole Source ◽  
Current Dipole ◽  
Content Type ◽  
Close Proximity ◽  
Lossy Medium ◽  
Asymptotic Forms

Purpose The purpose of this paper is to derive the dyadic representations of Green’s function in lossy medium because of the electric current dipole source radiating in close proximity of a PEC wedge and to reveal the effect of conductivity on the scattered electric field. Design/methodology/approach By using the scalarization procedure, the paraxial fields are obtained first and then scalar Green’s functions are used to derive asymptotic forms of the dyadic Green’s functions. The problem is also analyzed by the image theory and analytical derivations are compared. However, analytically calculated results are validated with FEKO, a commercially available numerical electromagnetic field solver. Findings The results indicate that excellent agreement is observed between analytical and numerical results. Moreover, it is found that the presence of conductivity introduces a reduction in scattered electric fields. Originality/value Asymptotically derived forms presented in this study can be used to calculate field distributions in the paraxial region of a wedge in a lossy medium.

Efficient Near-Field Interpolation of Mixed-Potential Green's Functions in Layered Media

2009 ◽  
Vol 8 ◽  
pp. 674-677 ◽  
Author(s):  
G. Valerio ◽  
P. Baccarelli ◽  
S. Paulotto ◽  
F. Frezza ◽  
A. Galli
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Near Field ◽  
Layered Media ◽  
Mixed Potential

Steklov approximations of Green’s functions for Laplace equations

2020 ◽  
Vol 39 (4) ◽  
pp. 991-1003 ◽  
Author(s):  
Manki Cho
Keyword(s):  
Boundary Value Problems ◽  
Laplace Operator ◽  
Green's Functions ◽  
Green’S Functions ◽  
Correction Term ◽  
Boundary Value ◽  
Content Type ◽  
The Laplace Operator ◽  
Steklov Eigenfunctions ◽  
Boundary Correction

Purpose This paper aims to present a meshless technique to find the Green’s functions for solutions of Laplacian boundary value problems on rectangular domains. This paper also investigates a theoretical basis for the Steklov series expansion methods to reduce and estimate the error of numerical approaches for the boundary correction kernel of the Laplace operator. Design/methodology/approach The main interest is how the Green's functions differ from the fundamental solution of the Laplace operator. Steklov expansion methods for finding the correction term are supported by the analysis that bases of the class of all finite harmonic functions can be formed using harmonic Steklov eigenfunctions. These functions construct a basis of the space of solutions of harmonic boundary value problems and their boundary traces generate an orthogonal basis of the trace space of solutions on the boundary. Findings The main conclusion is that the boundary correction term for the Green's functions is well-approximated by Steklov expansions with a few Steklov eigenfunctions. The error estimates for the Steklov approximations of the boundary correction term involved in Dirichlet or Robin boundary value problems are found. They appear to provide very good approximations in the interior of the region and become quite oscillatory close to the boundary. Originality/value This paper concentrates to document the first attempt to find the Green's function for various harmonic boundary value problems with the explicit Steklov eigenfunctions without concerns regarding discretizations when the region is a rectangle.

Co-seismic internal deformations in a spherical layered earth model

2020 ◽  
Vol 221 (3) ◽  
pp. 1515-1531
Author(s):  
Tai Liu ◽  
Guangyu Fu ◽  
Yawen She ◽  
Cuiping Zhao
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Near Field ◽  
Earth Model ◽  
Coulomb Stress ◽  
Far Field ◽  
Coulomb Stress Changes ◽  
Layered Earth ◽  
Stress Changes ◽  
Internal Deformation

SUMMARY Using a numerical integral method, we deduced a set of formulae for the co-seismic internal deformation in a spherically symmetric earth model, simultaneously taking self-gravitation, compressibility and realistically stratified structure of the Earth into account. Using these formulae, we can calculate the internal deformation at an arbitrary depth caused by an arbitrary seismic source. To demonstrate the correctness of our formulae, we compared our numerical solutions of radial functions with analytical solutions reported by Dong & Sun based on a homogeneous earth model; we found that two sets of results agree well with each other. Our co-seismic internal Green's functions in the near field agree well with the results calculated by the formulae of Okada, which also verifies our Green's functions. Finally, we calculated the Coulomb stress changes on the Japanese Islands and Northeast China induced by the Tohoku-Oki Mw 9.0 earthquake using the methods described above. We found that the effect of layered structure plays a leading role on the near field, while curvature occupies a dominant position on the deep region of the far field. Through a comparison of the Coulomb stress changes at a depth of 10 km on a layered earth model calculated by our method along with the corresponding results of Okada, we found that the discrepancy between them in near field was ∼31.5 per cent, and that of far field was >100 per cent of the signals.

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