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Based on the governing equations of magneto‐electro‐elastic media, the general solutions in the case of distinct eigenvalues and is introduced and expressed in four harmonic functions. Then, the Green’s functions for point forces, point charge and point current acting in the interior of a two‐phase infinite magneto‐electro‐elastic plane in the case of distinct or multiple eigenvalues are given using the method of mirror image source.

A convenient form of spatial‐domain Green’s function for a point charge in multilayered dielectric medium enclosed by a conducting cylinder of circular cross‐section is presented in this paper. Green’s function expression is obtained by solving Poisson differential equation in cylindrical coordinates and applying analogies with multistep electrical transmission lines. Convergence of the proposed expression obtained in the form of a double infinite sum is investigated and compared with triple‐sum solution for the same problem obtained by standard variable separation method. The numerical investigation has shown that the proposed expression has much faster convergence than the standard solution. Also, contrary to the variable separation method, increasing the number of dielectric layers is not an obstacle in determining of proposed Green’s functions, as it is shown for the three layers dielectric structure.

The aim of this paper is to present two independent ways in which a simple approximation to a Green's function for a differential equation can be used to improve the performance of well‐known iterative methods for linear equations.

In 1993 the 200th anniversary of George Green, a great physicist and mathematician's, birth was celebrated. His contribution to world's science is beyond the question. This can best be seen in the frequency of mentioning his name and quoting his works in other physicists' and mathematicians' works. Some of historians of science and researchers are deeply convinced that George Green together with Maxwell originated modern electromagnetism. George Green is also famous for his inventions as far as light, stress and accoustic theories are concerned but electromagnetism ows him most of all. Indeed, none of those who have ever dealt with mathematical electromagnetism will question George Green's part and position. In nearly each paper referring to it, Green's function or Green's identities are the terms that are mentioned or quoted. Without these notions contemporary numerical techniques such as finite element method (first Green's identity) or boundary element method (second Green's identity) or integral methods (Green's function) are hard to imagine.

This paper aims to develop an efficient numerical method for nonlinear transient heat conduction problems with local radiation boundary conditions and nonlinear heat sources.

Based on the physical characteristic of the transient heat conduction and the distribution characteristic of the Green’s function, a quasi-superposition principle is presented for the transient heat conduction problems with local nonlinearities. Then, an efficient method is developed, which indicates that the solution of the original nonlinear problem can be derived by solving some nonlinear problems with small structures and a linear problem with the original structure. These problems are independent of each other and can be solved simultaneously by the parallel computing technique.

Within a small time step, the nonlinear thermal loads can only induce significant temperature responses of the regions near the positions of the nonlinear thermal loads, whereas the temperature responses of the remaining regions are very close to zero. According to the above physical characteristic, the original nonlinear problem can be transformed into some nonlinear problems with small structures and a linear problem with the original structure.

An efficient and accurate numerical method is presented for transient heat conduction problems with local nonlinearities, and some numerical examples demonstrate the high efficiency and accuracy of the proposed method.

Analysis of the frequency selective surface (FSS) is of great significance. In the method of moments, when the electric size of the FSS increases, huge in-core memory and CPU time are required. The purpose of this paper is to efficiently analyze the finite FSS backed by dielectric substrate utilizing sub-entire-domain (SED) basis function method.

Different types of SED basis functions are generated according to the locations of the cells in the entire structure, and a reduced system is constructed and solved. The couplings of all cells of the FSS are taken into account by using Green’s function and Galerkin’s test procedure. The spatial Green’s function is obtained with the discrete complex image method. The reflection and transmission coefficients of the FSS are calculated using the far field of the FSS and the metallic plate with the same size.

Moderate problems of the finite FSS backed by dielectric substrate are solved with the SED basis function method. The original problem can be simplified to two smaller problems. It enables a significant reduction to the matrix size and storage, and efficient analysis of FSS can be performed. The band-stop type of FSS can be composed of periodic conductive patch cells on the dielectric substrate, and shows total reflection property at the resonant frequency.

The SED basis function method is mostly used to analyze periodic PEC structures in free space. The layered medium Green’s function is successfully employed and several dielectric substrate backed finite FSSs are discussed in this paper. The calculation of reflection and transmission coefficients, which are more effective rather than far field scattering of the FSS, are described.

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.

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.

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.

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.

Accurate numerical differentiation of approximate data by methods based on Green's second identity often involves singular or nearly singular integrals over domains or their boundaries. This paper applies the finite part integration concept to evaluate such integrals and to generate suitable quadrature formulae. The weak singularity involved in first derivatives is removable; the strong singularities encountered in computing higher derivatives can be reduced. To find derivatives on or near the edge of the integration region, special treatment of boundary integrals is required. Values of normal derivative at points on the edge are obtainable by the method described. Example results are given for derivatives of analytically known functions, as well as results from finite element analysis.

The purpose of this paper is to present a time‐domain technique to compute the electromagnetic wave field and to reconstruct the permittivity and electric conductivity profile of a one‐dimensional slab of finite length.

The forward scattering problem is solved by a Green's function formulation to generate synthetic data that are used as a testbed for the inversion scheme. The inverse scattering problem is solved by reconstructing the unknown permittivity and electric conductivity profile of the medium with the help of an invariant embedding method.

The Green's operator maps the incident field on either side of the medium to the field at an arbitrary observation point inside the slab and hence, the internal fields can be computed directly without computing the wave field throughout the entire medium. The invariant embedding method requires a finite time trace of reflection data and therefore it is suitable for reconstructing the material parameters in real‐time.

The implemented methods have been validated against synthetic and measured time domain reflectometry data.

This paper fulfils an identified need to determine unknown one‐dimensional profiles and thus plays an important role in electromagnetics, non‐destructive testing, and geophysics.

This paper is concerned with static problems, i.e. those which do not change with time. Dynamic problems will be considered in a sequel. The historical development of infinite elements is described. The two main developments, decay function infinite elements and mapped infinite elements, are described in detail. Results obtained using various infinite elements are given, followed by a discussion of possibilities and likely developments.