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Rotational‐translational addition theorems for the vector spheroidal wave functions Ma(i)mn(h; ξ, η, φ) and Na(i)mn(h; ξ, η, φ), i = 1,2,3,4, are derived from those for the corresponding scalar spheroidal wave functions ψ(i)mn(h; ξ, η, φ). A vector spheroidal wave function defined in one spheroidal coordinate system (h; ξ, η, φ) is expressed in terms of a series of vector spheroidal wave functions defined in another spheroidal coordinate system (h′; ξ′, η′, φ′), which is rotated and translated with respect to the first one. These theorems allow a rigorous treatment of boundary value problems relative to time‐harmonic vector field waves in the presence of a system of spheroids with arbitrary orientations. As a special case, general rotational‐translational addition theorems for vector spherical wave functions are also presented.

The purpose of this paper is to propose a stable high-order absorbing boundary condition (ABC) based on new continued fraction for scalar wave propagation in 2D and 3D unbounded layers.

The ABC is obtained based on continued fraction (CF) expansion of the frequency-domain dynamic stiffness coefficient (DtN kernel) on the artificial boundary of a truncated infinite domain. The CF which has been used to the thin layer method in [69] will be applied to the DtN method to develop a time-domain high-order ABC for the transient scalar wave propagation in 2D. Furthermore, a new stable composite-CF is proposed in this study for 3D unbounded layers by nesting the above CF for 2D layer and another CF.

The ABS has been transformed from frequency to time domain by using the auxiliary variable technique. The high-order time-domain ABC can couple seamlessly with the finite element method. The instability of the ABC-FEM coupled system is discussed and cured.

This manuscript establishes a stable high-order time-domain ABC for the scalar wave equation in 2D and 3D unbounded layers, which is based on the new continued fraction. The high-order time-domain ABC can couple seamlessly with the finite element method. The instability of the coupled system is discussed and cured.

The finite element method (FEM) is used to calculate the two-dimensional anti-plane dynamic response of structure embedded in D’Alembert viscoelastic multilayered soil on the rigid bedrock. This paper aims to research a time-domain absorbing boundary condition (ABC), which should be imposed on the truncation boundary of the finite domain to represent the dynamic interaction between the truncated infinite domain and the finite domain.

A high-order ABC for scalar wave propagation in the D’Alembert viscoelastic multilayered media is proposed. A new operator separation method and the mode reduction are adopted to construct the time-domain ABC.

The derivation of the ABC is accurate for the single layer but less accurate for the multilayer. To achieve high accuracy, therefore, the distance from the truncation boundary to the region of interest can be zero for the single layer but need to be about 0.5 times of the total layer height of the infinite domain for the multilayer. Both single-layered and multilayered numerical examples verify that the accuracy of the ABC is almost the same for both cases of only using the modal number excited by dynamic load and using the full modal number of infinite domain. Using the ABC with reduced modes can not only reduce the computation cost but also be more friendly to the stability. Numerical examples demonstrate the superior properties of the proposed ABC with stability, high accuracy and remarkable coupling with the FEM.

A high-order time-domain ABC for scalar wave propagation in the D’Alembert viscoelastic multilayered media is proposed. The proposed ABC is suitable for both linear elastic and D’Alembert viscoelastic media, and it can be coupled seamlessly with the FEM. A new operator separation method combining mode reduction is presented with better stability than the existing methods.

Notes that Scalar digital plane waves are made of a finite or infinite sequence of discrete pulses which are solutions of a wave equation. Discusses the 1D and 2D wave equations and shows how the 1D and 2D Laplace transforms may be used in connection with digital signals. Gives some examples of digital plane waves and, as an illustration, gives three different applications of this technique.

We have developed a two‐dimensional model for quantum‐well lasers which solves, self‐consistently, the semiconductor equations together with the complex scalar wave equation and the photon rate equation. To predict the threshold current accurately we have included the wavelength‐ and position‐dependence of the gain and the spontaneous emission. For the complex wave equation successive over relaxation (SOR) is used with two adaptive acceleration parameters for the complex wave amplitude and for the eigenvalue. Since the rate equation near threshold can be driven into divergence during iteration for a steady state solution, we have introduced a special damping technique to overcome this problem. Our model enables us to predict the characteristics of a quantum‐well laser with a minimal number of empirical constants. The output of the model includes light‐current characteristics, and the current and optical field intensity distributions. We show the results of a calculation for a graded‐index separate‐confinement heterostructure single quantum‐well (GRIN‐SCH SQW) laser.

To extend to electromagnetism the acoustic wave reflections on time reversal mirrors used in medical imaging, nondestructive testing and underwater acoustics.

Recent works (1993‐2004) analyse the reflection of acoustic waves on time reversal mirror. To perform the same job in electromagnetism, the behaviour of the electromagnetic field tensor under the space and time inversions of the referential is investigated and also, when in addition an exchange of two coordinates exists. All these reflections are supposed obtained from perfect but unconventional mirrors.

Electromagnetic reflections on unconventional mirrors have remarquable features since some of them give birth to a real twin source of the incident source with an opposite polarization.

The techniques used in acoustic to manufacture time reversal mirrors can be used in electromagnetism with possible applications of such mirrors for instance in cameras to avoid reversed photographs but no information on practical realizations has appeared in the open literature.

Extends research on electromagnetism.

This paper aims to present a modified precise integration time domain (PITD) method for the numerical solution of 2D scalar wave equation.

The split step (SS) scheme is applied to factorize the conventional PITD calculation into two sub-steps procedures and then field components can be updated along one spatial direction only in each sub-step. The perfectly matched layer (PML) absorber is extended to this method for modeling open region problems by using the stretched coordinate approach.

It is shown that this method requires less computation time and storage space in comparison with the conventional PITD method, yet maintains the numerical stability despite using large time steps.

The WE-PITD method requires the divergence free region, which may be a limit on its usage. Hence, there is a challenge of using this technique in the 3D problems.

Based on the SS scheme, the PITD method is used to solve the scale wave equation rather than Maxwell's equations, leading to a significant reduction in the computation time and memory usage.

This paper aims to show that simple geometry‐based hp‐algorithms using an explicit a posteriori error estimator are efficient in wave propagation computation of complex structures containing geometric singularities.

Four different hp‐algorithms are compared with common h‐ and p‐adaptation in electrostatic and time‐harmonic problems regarding efficiency in number of degrees of freedom and runtime. An explicit a posteriori error estimator in energy norm is used for adaptive algorithms.

Residual‐based error estimation is sufficient to control the adaptation process. A geometry‐based hp‐algorithm produces the smallest number of degrees of freedom and results in shortest runtime. Predicted error algorithms may choose inappropriate kind of refinement method depending on p‐enrichment threshold value. Achieving exponential error convergence is sensitive to the element‐wise decision on h‐refinement or p‐enrichment.

Initial mesh size must be sufficiently small to confine influence of phase lag error.

Information on implementation of hp‐algorithm and use of explicit error estimator in electromagnetic wave propagation is provided.

The paper is a resource for developing efficient finite element software for high‐frequency electromagnetic field computation providing guaranteed error bound.

Survey of period infinite element developments The first infinite elements for periodic wave problems, as stated in Part 1, were developed by Bettess and Zienkiewicz, the earliest publication being in 1975. These applications were of ‘decay function’ type elements and were used in surface waves on water problems. This was soon followed by an application by Saini et al., to dam‐reservoir interaction, where the waves are pressure waves in the water in the reservoir. In this case both the solid displacements and the fluid pressures are complex valued. In 1980 to 1983 Medina and co‐workers and Chow and Smith successfully used quite different methods to develop infinite elements for elastic waves. Zienkiewicz et al. published the details of the first mapped wave infinite element formulation, which they went on to program, and to use to generate results for surface wave problems. In 1982 Aggarwal et al. used infinite elements in fluid‐structure interaction problems, in this case plates vibrating in an unbounded fluid. In 1983 Corzani used infinite elements for electric wave problems. This period also saw the first infinite element applications in acoustics, by Astley and Eversman, and their development of the ‘wave envelope’ concept. Kagawa applied periodic infinite wave elements to Helmholtz equation in electromagnetic applications. Pos used infinite elements to model wave diffraction by breakwaters and gave comparisons with laboratory photogrammetric measurements of waves. Good agreement was obtained. Huang also used infinite elements for surface wave diffraction problems. Davies and Rahman used infinite elements to model wave guide behaviour. Moriya developed a new type of infinite element for Helmholtz problem. In 1986 Yamabuchi et al. developed another infinite element for unbounded Helmholtz problems. Rajapalakse et al. produced an infinite element for elastodynamics, in which some of the integrations are carried out analytically, and which is said to model correctly both body and Rayleigh waves. Imai et al. gave further applications of infinite elements to wave diffraction, fluid‐structure interaction and wave force calculations for breakwaters, offshore platforms and a floating rectangular caisson. Pantic et al. used infinite elements in wave guide computations. In 1986 Cao et al. applied infinite elements to dynamic interaction of soil and pile. The infinite element is said to be ‘semi‐analytical’. Goransson and Davidsson used a mapped wave infinite element in some three dimensional acoustic problems, in 1987. They incorporated the infinite elements into the ASKA code. A novel application of wave infinite elements to photolithography simulation for semiconductor device fabrication was given by Matsuzawa et al. They obtained ‘reasonably good’ agreement with observed photoresist profiles. Häggblad and Nordgren used infinite elements in a dynamic analysis of non‐linear soil‐structure interaction, with plastic soil elements. In 1989 Lau and Ji published a new type of 3‐D infinite element for wave diffraction problems. They gave good results for problems of waves diffracted by a cylinder and various three dimensional structures.

In this paper, a modified meshless method, as one of the numerical techniques that has recently emerged in the area of computational electromagnetics, is extended to solving time-domain wave equation. The paper aims to discuss these issues.

In space domain, the fields at the collocation points are expanded into a series of new Shepard's functions which have been suggested recently and are treated with a meshless method procedure. For time discretization of the second-order time-derivative, two finite-difference schemes, i.e. backward difference and Newmark-β techniques, are proposed.

Both schemes are implicit and always stable and have unconditional stability with different orders of accuracy and numerical dispersion. The unconditional stability of the proposed methods is analytically proven and numerically verified. Moreover, two numerical examples for electromagnetic field computation are also presented to investigate characteristics of the proposed methods.

The paper presents two unconditionally stable schemes for meshless methods in time-domain electromagnetic problems.