Time-domain analysis of electromagnetic wave fields by boundary integral equation method

An interpolation-based fast-multipole accelerated boundary integral equation method for the three-dimensional wave equation

Computation of dynamic stress intensity factors by the time domain boundary integral equation method—II. Examples

Boundary integral equation method for transient analysis of 3-D cavities and inclusions

In this book, analysis of electromagnetic (EM) field inside microwave cavities (e.g., oven, autoclave) is presented using finite difference time domain method (FDTD). In this regard, a domestic microwave oven is considered where EM field distribution inside its cavity is determined using FDTD method. Further, the leakage of RF field from the oven door is also estimated at different plane of the door.

A new hybrid finite-difference time-domain boundary integral equation (FDTD-BIE) method is proposed. The geometry under consideration is decomposed into several subregions. For some of the bounded subregions the FDTD technique is used to construct an interaction matrix, relating virtual electric and magnetic currents at the boundary of the subregion, for several frequencies at the same time. The remaining bounded and unbounded subregions are described by a boundary integral equation technique. An example is given to validate the new technique.

In this study, we propose a two-step approach to evaluate electromagnetic interference (EMI) with a wearable electrocardiogram (ECG) sensor. The two-step approach combines a quasi-static electromagnetic (EM) field analysis and an electric circuit analysis, and is applied to the EMI analysis at frequencies below 1 MHz for our developed wearable ECG to demonstrate its usefulness. The quasi-static EM field analysis gives the common mode voltage coupled from the incident EM field at the ECG sensing electrodes, and the electric circuit analysis quantifies a differential mode voltage at the differential amplifier output of the ECG detection circuit. The differential mode voltage has been shown to come from a conversion from the common mode voltage due to an unbalance between the contact impedances of the two sensing electrodes. It may achieve nearly 0.6 V at the differential amplifier output under 10-V/m plane-wave incident electric field, and completely mask the ECG signal. It is essential to reduce the unbalance as much as possible to not cause a significant interference voltage in the amplified ECG signal.

Applying the concept of minimum potential energy and the variational method proposed in this paper, one can derive the governing equation and transversality conditions for the critical slip surface of a cohesive land slope described by simplified Janbu's model where both horizontal and vertical inter-slice forces are neglected. The governing equation, transversality conditions and boundary conditions were solved by the boundary integral equation method, which is a one dimensional BIEM, so that the critical slip surface and its associated minimal factor of safety can be determined effectively. By comparison of the results gotten from the boundary integral equation method and other numerical methods, it can be concluded, that, for some simplified cases, by using the boundary integral equation method on slope stability analysis of a cohesive land slope, a more reasonable result can be obtained.

A hybrid formulation of the 2.5D elastodynamic scattering problem combining the finite-element method and boundary integral equation method is presented and validated. The formulation of the 2.5D boundary integral equation method that is used was presented in detail by Papageorgiou and Pei (1998) and is an extension of the discrete wavenumber boundary integral equation method originally proposed by Kawase (1988) for 2D scattering problems. Modeling of the wave field in the domain of the scatterer is based on the variational principle of virtual displacements, and discretization of the domain is accomplished using the finite-element method.The formulation may be used to study the wave field in models of sedimentary deposits (e.g., valleys) or topography (e.g., canyons or ridges) with a 2D variation in structure but obliquely incident plane waves. The hybrid method exploits the versatility of the finite element method for modeling the scatterer and the effectiveness of the boundary integral equation method for taking care of the radiation condition in the half-space. The advantage of the 2.5D formulation is that it provides the means for calculations of 3D wave fields in scattering problems by requiring a storage comparable to that of the corresponding 2D calculations.

The transient electromagnetic fields due to electrostatic discharge (ESD) between charged metals have wide‐band frequency spectra up to the microwave region, which create a serious malfunction for high‐tech information devices. For the above ESD fields, we previously analyzed them, using the finite‐difference time‐domain (FDTD) method, and showed that the metals enhance the field level according to the metal dimension. From the standpoint of reducing such ESD fields, the electromagnetic fields caused by the spark between the metals with ferrite core attachments were investigated. The FDTD method was also used to compute the ESD fields. An FDTD algorithm for the magnetic field inside the ferrite core was newly derived. The results show that the cores attached near the spark gap considerably reduce the magnetic field level, which is also confirmed experimentally. © 2001 Scripta Technica, Electr Eng Jpn, 138(1): 34–41, 2002

Electromagnetic field analysis is the basis for solving the engineering coupled electromagnetic and thermal field problems. Based on the low-frequency Maxwell’s equations, some key problems concerning the formulations and numerical implementations of typical 3-D eddy current analysis methods, using different potential sets, such as A-V-A (or employing a reduced vector magnetic potential Ar to convert to Ar-V-Ar) and T-Ψ-Ψ, are briefly explained. Furthermore, the numerical solvers based on different potential sets have been developed by the author’s group and verified in the Testing Electromagnetic Analysis Methods (TEAM) benchmarking practices. In this chapter, the Galerkin weighted residual method, a key technique in numerical implementation, is elaborated, and the effectiveness of edge element, for example, in effectively reducing computational cost in industrial applications is discussed. Strengthening the theoretical basis of finite element analysis of electromagnetic fields and correctly understanding the significance of the combination of advanced numerical computation with accurate material property modeling will be more helpful in improving the effectiveness of modeling and simulation and further promoting the use of simulation in industrial applications.

With the increase in electricity demand, new sources of power generation and transmission lines are needed. Thus, because of the need to meet the demand for electricity, transmission lines and substations are increasingly present in urban and local areas near the movement of people. Since electromagnetic fields are a result of the electrical installation, there are rules governing the field exposure levels due to the possibility of causing adverse health effects. The institution which sets the levels of exposure limits is ANEEL (Agência Nacional de Energia Elétrica), with the Normative Resolution n° 398. The analysis of electromagnetic fields can be performed by measurements, analytical calculations, or through computer numerical solutions. This study aims to determine the electromagnetic fields from computer numerical solutions of an output line of a gas-insulated substation, determining the minimum distances for operation and pedestrian traffic.

The principles and development of the boundary integral equation (BIE) method for solving engineering problems are reviewed, with particular emphasis on applications in three-dimensional stress analysis. Its use in problems of this type is illustrated with the aid of three examples, one a classical stress concentration problem, the other two involving cracked components. Compared with a finite-element method, the BIE approach is shown to be capable of being both more accurate and more economical to use in terms of competing resources required and the cost of data preparation. These advantages may, however, be less clear-cut when predictions of stresses and displacements at a large number of points within a component are required, or when the component concerned has a relatively high surface-to-volume ratio.

Acoustic wave scattering by scatterers in layered media is studied using a new method that combines the hybrid ray–mode and boundary integral equation methods. The latter is used to formulate the scattering process and the former is used to provide the Green’s function of the layered environment. Following standard procedures of the boundary integral equation method, integral equations are formulated first for field distributions along the boundaries of the obstacles. By expressing these unknown distributions in terms of appropriate basis functions, the integral equations are then reduced to algebraic equations that are solved numerically. In the integral equations, it is necessary to compute the Green’s function of the layered environment for various arrangements of locations of source and receiver. None of these conventional approaches (rays, modes, and spectral integration) to evaluate the Green’s function are satisfactory for all possible arrangements. Only the newly developed hybrid ray–mode method is best suited for this purpose because it combines rays and modes self-consistently within a single framework and optimizes the advantages of each. Numerical implementation illustrates these aspects.

Background. Ultrashort pulses of electromagnetic field are widely used in construction, archeology and demining, etc., by constructing effective georadars of the underlying surface, but theoretical study of physical processes of irradiation of medium is had a limit range of simplified model problems, usually in frequency domain. Therefore, the solutions of the problems of penetration of a pulsed wave with arbitrary time dependence into material medium are of special importance for understanding the possibilities and limitations of georadar’s study. Objectives. To obtain the analytical solution in time domain of the problems of reflection and propagation of a impulse electromagnetic wave through the interface of two media, which is the first model approximation to the description of physical processes that occur during operation of pulsed ultrawideband radar. Materials and methods. The problem of irradiation by nonstationary electric field of a lossless medium with a given permittivity is solved analytically by application of evolutionary approach. It consists in solving of Cauchy’s problem for the second-order partial differential equation Klein–Gordon type with respect to evolutionary coefficients. The components of the electromagnetic field in free space are found by integration by spectral parameters and summation by angular modes with appropriate combinations of basis functions. Results. Cauchy’s problems for differential equations that describe the behavior of reflected and refracted waves are solved. The electrical transverse components of the reflected and refracted waves as a function of time on the longitudinal axis were found for the case of irradiation with the step-like time dependence. Graphs of dependence of electric components on time and coordinates are plotted and analyzed. Conclusion. The phenomenon of an electromagnetic missiles in the medium that was irradiated by a pulsed electromagnetic wave of ultrashort duration was demonstrated for the first time. The obtained results can be generalized for the case of an arbitrary impulse by the Duhamel’s integral method. In addition, the electric field for observation point that do not lie on the longitudinal axis can be considered. An even more interesting continuation of the researches in terms of energy analysis is the study of the behavior of longitudinal electric and transverse magnetic components.

The rapid development and deployment of mobile communications focused the scientists attention on electromagnetic field distribution problem. Numerical techniques, such as finite element method integral equations method, finite difference time domain method( FDTD) and some hybrid methods have been taken into account. These approaches allow to obtain a good accuracy in the estimation of the electromagnetic (EM) field distribution in the given phantom. FDTD method required to evaluate six components of EM field and the time discretization, what demanded the powerful computer and long time to compute. The attempt to increase the accuracy of computation by increasing of cells number collided with convergence problem. To avoid this problem the integral equations method was chosen for research. The results of modeling confirmed the correctness and adequacy of proposed model for evaluation of electromagnetic field distribution from mobile phone in human head phantom.