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Considering the vector Helmholtz equation in three dimensions, this paper aims to present a novel approach for coupling the finite element method and a boundary integral formulation. It is demonstrated that the method is well-suited for many realistic three-dimensional problems in high-frequency engineering.

The formulation is based on partial solutions fulfilling the global boundary conditions and the iterative interaction between them. In comparison to other coupling formulation, this approach avoids the typical singularity in the integral kernels. The approach applies ideas from domain decomposition techniques and is implemented for a parallel calculation.

Using confirming elements for the trace space and default techniques to realize the infinite domain, no additional loss in accuracy is introduced compared to a monolithic finite element method approach. Furthermore, the degree of coupling between the finite element method and the integral formulation is reduced. The accuracy and convergence rate are demonstrated on a three-dimensional antenna model.

This approach introduces additional degrees of freedom compared to the classical coupling approach. The benefit is a noticeable reduction in the number of iterations when the arising linear equation systems are solved separately.

This paper focuses on multiple heterogeneous objects surrounded by a homogeneous medium. Hence, the method is suited for a wide range of applications.

The novelty of the paper is the proposed formulation for the coupling of both methods.

The purpose of this paper is to provide an analytical solution to the plane eddy current problem inside conductive bars with rectangular cross‐section.

Eddy currents inside conductive materials have been investigated for a very long time, using measurements and mathematical modelling. This paper provides an analytical solution to the plane eddy current problem inside conductive bars with rectangular cross‐section.

The paper's approach solves the given plane eddy current problem with the boundary integral equation method. The Helmholtz' equation for vector potential inside the rectangle is solved by separation. The solution is inserted into the remaining boundary integral equation for the exterior vector potential in the domain surrounding the conductor yielding a system of linear equations. Results match existing solutions.

The method discussed provides a new way to solve the EC problem and is slightly faster than the available commercial codes; yet, it is limited to rectangular bars of cross‐section.

This meshless collocation method is applicable not only to the Helmholtz equation with Dirichlet boundary condition but also mixed boundary conditions. It can calculate not only the high wavenumber problems, but also the variable wave number problems.

In this paper, the authors developed a meshless collocation method by using barycentric Lagrange interpolation basis function based on the Chebyshev nodes to deduce the scheme for solving the three-dimensional Helmholtz equation. First, the spatial variables and their partial derivatives are treated by interpolation basis functions, and the collocation method is established for solving second order differential equations. Then the differential matrix is employed to simplify the differential equations which is on a given test node. Finally, numerical experiments show the accuracy and effectiveness of the proposed method.

The numerical experiments show the advantages of the present method, such as less number of collocation nodes needed, shorter calculation time, higher precision, smaller error and higher efficiency. What is more, the numerical solutions agree well with the exact solutions.

Compared with finite element method, finite difference method and other traditional numerical methods based on grid solution, meshless method can reduce or eliminate the dependence on grid and make the numerical implementation more flexible.

The Helmholtz equation has a wide application background in many fields, such as physics, mechanics, engineering and so on.

This meshless method is first time applied for solving the 3D Helmholtz equation. What is more the present work not only gives the relationship of interpolation nodes but also the test nodes.

The purpose of this paper is to provide a brief introduction of the finite difference based parabolic equation (PE) modeling to the advanced engineering students and academic researchers.

A three-dimensional parabolic equation (3DPE) model is developed from the ground up for modeling wave propagation in the tunnel via a rectangular waveguide structure. A discussion of vector wave equations from Maxwell’s equations followed by the paraxial approximations and finite difference implementation is presented for the beginners. The obtained simulation results are compared with the analytical solution.

It is shown that the alternating direction implicit finite difference method (FDM) is more efficient in terms of accuracy, computational time and memory than the explicit FDM. The reader interested in maximum details of individual contributions such as the latest achievements in PE modeling until 2021, basic PE derivation, PE formulation’s approximations, finite difference discretization and implementation of 3DPE, can learn from this paper.

For the purpose of this paper, a simple 3DPE formulation is presented. For simplicity, a rectangular waveguide structure is discretized with the finite difference approach as a design problem. Future work could use the PE based FDM to study the possibility of utilization of meteorological techniques, including the effects of backward traveling waves as well as making comparisons with the experimental data.

The proposed work is directly applicable to typical problems in the field of tunnel propagation modeling for both national commercial and military applications.

The purpose of this paper is to show the possibility of using the quartz regular surface profile in the form of protrusions and troughs of a triangular shape instead of a random surface profile characterized by a Gaussian correlation function when analyzing the electromagnetic field parameters above the quartz surface to determine the conditions of the effective surface subnano-polishing.

The numerical determination of the evanescent field optimal configuration formed near the quartz rough surface coated with an aqueous solution of calcium hypochlorite when illuminated from the side of the solution has been considered. The finite-element approach is used to solve the Helmholtz two-dimensional vector equation.

Conditions of effective photochemical polishing of rough surface with profile in the form of triangular protrusions and troughs to a sub-nanometer level of roughness are found. These optimal conditions are achieved when the light falls normally on the quartz surface and the height of the surface protrusions is small (up to 20 nm).

This paper shows the possibility of simplifying electrodynamic calculations and analyzing an evanescent field near a quartz surface for the purpose of photochemical polishing by replacing the random profile function with a deterministic periodic function. That is, the novelty of this paper, which supplements the works published earlier [Journal of Modern Optics, 67(3) (2020):242–251; Optik, 207 (2020):164438].

The evaluation of eddy currents in cylindrical geometries is examined analytically by using a method, which utilises the second order magnetic vector potential. As an example the three‐dimensional problem of the calculation of eddy currents inside a long conducting cylinder excited by a saddle shaped coil is studied.

This paper investigates new technological devices to be utilised in future optical communications, by means of variational method (FEM) and multipole scattering approach (Rayleigh method). This last one provides interesting asymptotic results in the long‐wavelength limit. The so‐called photonic crystal fibres (PCF) possess radically different guiding properties due to photonic band gap guidance: removing a hole within a macro‐cell leads to a defect state within the gap. In the case of multi‐core PCF, the localised modes start talking to each other which possibly leads to a new generation of multiplexer/demultiplexers.

A computational methodology, based on the coupling of the finite element and boundary element methods, is developed for the solution of magnetothermal problems. The finite element formulation and boundary element formulation, along with their coupling, are discussed. The coupling procedure is also presented, which entails the application of the LU decomposition to eliminate the need for the direct inversion of matrices resulting from FE‐BE formulation, thereby saving computation time and storage space. Corners for both FE‐BE interface and BE regions, where discontinuous fluxes exist, are treated using the double flux concept. Numerical results are presented for three different systems and compared with analytical solutions when available. Numerical experiments suggest that for magnetothermal problems involving small skin depths, a careful mesh distribution is critical for accurate prediction of the field variables of interest. It is found that the accuracy of the temperature distribution is strongly dependent upon that of the magnetic vector potential. A small error in the magnetic vector potential can produce significant errors in the subsequent temperature calculations. Thus, particular attention must be paid to the design of a suitable mesh for the accurate prediction of vector potentials. From all the cases examined, 4‐node linear elements with adequate progressive coarsening of meshes from the surface gave the results with best accuracy.

The dyadic Green's function for a horizontally stratified dielectric medium is computed. The general electric field integral equation describing the scattering from an arbitrary dielectric scatterer embedded in one of the layers is formulated using the dyadic Green's function of the respective layer. For the numerical solution of the equation the method of moments is used. Numerical results are given for the case of a cylinder buried in the middle of a five‐layer space for various cases of plane wave excitation.

This paper is devoted to the presentation of a new finite element formulation for spectral problems arising in the determination of propagating modes in dielectric waveguides and particularly in optical fibers. As an example, we compute the coupling between two parallel optical wave guides. The originality of the paper lies in the fact that we take into account both the vector character of the problem (no weak coupling assumption) and the unboundness of the domain.