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This paper aims to examine the uniform diffracted fields from a perfectly magnetic conductive (PMC) surface with the extended theory of boundary diffraction wave (BDW) approach.

Miyamoto and Wolf’s symbolic expression of the vector potential was used in the extended theory of BDW integral. This vector potential is applied to the problem, and the nonuniform field expression found was made uniform. Here, the expression is made uniform, using the detour parameter with the help of the asymptotic correlation of the Fresnel function. The BDW theory for the PMC surface extended the diffracted fields, and the uniform diffracted fields were calculated.

The field expressions obtained were interpreted with the graphs numerically for different aperture radii and observation distances. It has been shown that the BDW is continuous behind the diffracting aperture. There does not exist any discontinuity at the geometrically light-to-shadow transition boundary, as is required by the theory.

The results were graphically compared with diffracted fields for other surfaces. As far as we know, the uniform diffracted fields from the circular aperture on a PMC surface were calculated for the first time with the extended theory of the BDW approach.

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.

To provide a detailed investigation about methods commonly used for the computation of high‐frequency electromagnetic fields in the vicinity of obstacles that can reflect or diffract them. This is useful to create an elementary block that can be used to evaluate with a high accuracy the propagation of high‐frequency electromagnetic waves in real urban environment.

The approach is based on a realistic application of the asymptotic theory of the uniform theory of diffraction. Therefore, the effect of material roughness and its electromagnetic properties on the reflection are taken into account.

Provides information about the mechanisms involved in electromagnetic field propagation in urban environment, and the relative importance of each one.

In urban environment the buildings obviously have finite dimensions. The diffraction equations examined in the paper are strictly valid only in the case of infinite wedges; therefore, the behaviour of real building edges has not been taken rigorously into account.

A source of information for researchers interested in the development of a simulator for the electromagnetic propagation in urban environment.

This paper is aimed at providing to researchers, in a more comprehensive way, all information needed for the study of electromagnetic propagation in an environment containing many close scatterers.

A new hybrid method based on three‐dimensional finite element idealization in the near field and a semi‐analytic scheme using the principles of wave propagation in multilayered half space in the far field is proposed for the dynamic soil‐structure interaction analysis. The distinguishing feature of this technique from direct or indirect boundary integral techniques is that in boundary integral techniques a distribution of sources are considered at the near field boundary. Strengths of these sources are then adjusted to satisfy the continuity conditions across the near‐field/far‐field interface. In the proposed method unknown sources are placed not at the near field boundary but at the location of the structure. Then the Saint‐Venant's principle is utilized to justify that at a distant point the effect of the structure's vibration can be effectively modelled by an equivalent vibrating point force and vibrating moment at the structure's position. Thus the number of unknowns can be greatly reduced here. For soil‐structure interaction analysis by this method one needs to consider only three unknowns (two force components and one in‐plane moment) for a general two‐dimensional problem and six unknowns (three force components and three moment components) for a general three‐dimensional problem. When a vertically propagating elastic wave strikes a structure which is symmetric about two mutually perpendicular vertical planes the structure can only vibrate vertically for dilatational waves and horizontally for shear waves. Under this situation the number of unknowns is reduced to only one whereas in boundary integral and boundary element techniques the number of unknowns is dependent on the number of nodes at the near field boundary, which is generally much greater than six. Several example problems are solved in this paper using this technique for both flexible and rigid structures in multilayered soil media.

The physical sciences, particularly wave motion and optics are examined in order to develop a set of analogies which can be applied to organisational theory and practice. Such concepts as diffraction and focus exhibit remarkable parallels in both form and content with many aspects of mainstream organisational and managerial theory. Furthermore, the pervasiveness of wave motion in the physical sciences is not dissimilar from the pervasiveness of organisations in the social sciences. A series of concepts is introduced and, with the aid of diagrams, placed in a managerial context.

This paper is concerned with infinite elements for dynamic problems, that is, those which change in time. It is a sequel to our earlier paper on static problems. The paper is in a number of sections. The first is an introduction. In the second the state‐of‐the‐art review of infinite elements is updated. In the third, ‘added mass’ type effects are considered. In the fourth, time dependent problems of the diffusion type, which only involve the first time derivative are considered. Wave problems are considered in the fifth and the necessary radiation conditions for such problems are summarized. Section six deals with dynamic problems of a repetitive nature, that is periodic or harmonic problems. In section seven completely transient problems are dealt with and some fundamental difficulties are noted. Conclusions are drawn in section eight.

The two‐dimensional discrete Huygens’ modelling or TLM simulation is presented for the TE electromagnetic field problems. The TLM element or node with variable traveling speed and characteristic impedance is applied to several practical problems including scattering at the edge of a wall and over periodic grids or grooves, wave propagation along a dielectric structure, and a mode coupling between two parallel optical waveguides. The TLM solutions are compared with the theoretical ones or the results of other numerical methods and reasonable agreement is achieved.

The purpose of this paper is to develop a new finite difference method for solving the seismic wave propagation in fluid-solid media, which can be described by the acoustic and viscoelastic wave equations for the fluid and solid parts, respectively.

In this paper, the authors introduced a coordinate transformation method for seismic wave simulation method. In the new method, the irregular fluid–solid interface is transformed into a horizontal interface. Then, a multi-block coordinate transformation method is proposed to mesh every layer to curved grids and transforms every interface to horizontal interface. Meanwhile, a variable grid size is used in different regions according to the shape and the velocity within each region. Finally, a Lebedev-standard staggered coupled grid scheme for curved grids is applied in the multi-block coordinate transformation method to reduce the computational cost.

The instability in the auxiliary coordinate system caused by the standard staggered grid scheme is resolved using a curved grid viscoelastic wave field separation strategy. Several numerical examples are solved using this new method. It has been shown that the new method is stable, efficient and highly accurate in solving the seismic wave equation defined on domain with irregular fluid–solid interface.

First, the irregular fluid–solid interface is transformed into a horizontal interface by using the coordinate transformation method. The conversion between pressures and stresses is easy to implement and adaptive to different irregular fluid–solid interface models, because the normal stress and shear stress vanish when the normal angle is 90° in the interface. Moreover, in the new method, the strong false artificial boundary reflection and instability caused by ladder-shaped grid discretion are resolved as well.

Partially‐decoupled upwind‐based total‐variation‐diminishing (TVD) finite‐difference schemes for the solution of the conservation laws governing two‐dimensional non‐equilibrium vibrationally relaxing and chemically reacting flows of thermally‐perfect gaseous mixtures are presented. In these methods, a novel partially‐decoupled flux‐difference splitting approach is adopted. The fluid conservation laws and species concentration and vibrational energy equations are decoupled by means of a frozen flow approximation. The resulting partially‐decoupled gas‐dynamic and thermodynamic subsystems are then solved alternately in a lagged manner within a time marching procedure, thereby providing explicit coupling between the two equation sets. Both time‐split semi‐implicit and factored implicit flux‐limited TVD upwind schemes are described. The semi‐implicit formulation is more appropriate for unsteady applications whereas the factored implicit form is useful for obtaining steady‐state solutions. Extensions of Roe's approximate Riemann solvers, giving the eigenvalues and eigenvectors of the fully coupled systems, are used to evaluate the numerical flux functions. Additional modifications to the Riemann solutions are also described which ensure that the approximate solutions are not aphysical. The proposed partially‐decoupled methods are shown to have several computational advantages over chemistry‐split and fully coupled techniques. Furthermore, numerical results for single, complex, and double Mach reflection flows, as well as corner‐expansion and blunt‐body flows, using a five‐species four‐temperature model for air demonstrate the capabilities of the methods.

The purpose of this paper is to compare exact and Physical‐Optics‐approximated results of the electromagnetic field scattered by a perfectly conducting semi‐infinite elliptic cone illuminated by a plane wave. The results are important for judging the reliability of Physical‐Optics based field estimations of electrically large environments which include tip‐like structures (e.g. airport scenarios).

The spherical‐multipole analysis is applied to determine the exact total field outside a perfectly conducting semi‐infinite elliptic cone. The underlying boundary‐value problem is solved by a separation of variables of the Helmholtz equation in sphero‐conal coordinates leading to a two‐parametric eigenvalue problem with two coupled Lamé differential equations. The exact scattered far field is determined from the exact surface current on the cone using a bilinear expansion of the dyadic Green's function. The Physical‐Optics (PO) field is evaluated similarly starting from a surface current which is directly found from the incident magnetic field.

The diffraction coefficients of the exact scattered field and the PO scattered field are compared for different parameters (polarization and angle of incidence) of the plane wave. Reasonably well corresponding results are obtained for those angles of incidence of the plane wave where the entire cone is illuminated, otherwise the error of the PO approximation is increasing not just in the shadow region.

If carefully applied, the Physical‐Optics method can be useful and sufficient to obtain fields scattered by cone‐like structures.