A method to reconstruct the surface shape of a scatterer from the relative intensity of the scattered field is proposed. Reconstruction of the scatterer shape has been studied as an inverse problem. An approach that employs boundary-integral equations can determine the scatterer shape with low computation resources and high accuracy. In this method, the reconstruction process is performed so that the error between the measured far field of the sample and the computed far field of the estimated scatterer shape is minimized. The amplitude of the incident wave at the sample is required to compute the scattered field of the estimated shape. However, measurement of the incident wave at the sample (measurement without the sample) is inconvenient, particularly when the output power of the wave source is temporally unstable. In this study, we improve the reconstruction method with boundary-integral equations for practical use and expandability to various types of samples. First, we propose new boundary-integral equations that can reconstruct the sample shape from the relative intensity at a finite distance. The relative intensity is independent from the amplitude of the incident wave, and the reconstruction process can be performed without measuring the incident field. Second, the boundary integral equation for reconstruction is discretized with boundary elements. The boundary elements can flexibly discretize various shapes of samples, and this approach can be applied to various inverse scattering problems. In this paper, we present a few reconstruction processes in numerical simulations. Then, we discuss the reason for slow-convergence conditions and introduce a weighting coefficient to accelerate the convergence. The weighting coefficient depends on the distance between the sample and the observation points. Finally, we derive a formula to obtain an optimum weighting coefficient so that we can reconstruct the surface shape of a scatterer at various distances of the observation points.

The Time Domain Boundary Element Method (TDBEM) has its advantages in the analysis of transient electromagnetic fields (wake fields) induced by a charged particle beam with curved trajectory in a particle accelerator. On the other hand, the TDBEM has disadvantages of huge required memory and computation time compared with those of the Finite Difference Time Domain (FDTD) method or the Finite Integration Technique (FIT). This paper presents a comparison of the FDTD method and 4-D domain decomposition method of the TDBEM based on an initial value problem formulation for the curved trajectory electron beam, and application to a full model simulation of the bunch compressor section of the high-energy particle accelerators.

A numerical investigation revealed the relation between the groove randomness of actual-size diffraction gratings and the diffraction efficiencies. The diffraction gratings we treat in this study have around 10000 grooves. When the illumination wavelength is 600 nm, the entire grating size becomes 16.2 mm. The simulation was performed using the difference-field boundary element method (DFBEM). The DFBEM treats the vectorial field with a small amount of memory resources as independent of the grating size. We firstly describe the applicability of DFBEM to a considerably large-sized structure; regularly aligned grooves and a random shallow-groove structure are calculated by DFBEM and compared with the results given by standard BEM and scalar-wave approximation, respectively. Finally we show the relation between the degree of randomness and the diffraction efficiencies for two orthogonal linear polarizations. The relation provides information for determining the tolerance of fabrication errors in the groove structure and measuring the structural randomness by acquiring the irradiance of the diffracted waves.

The main purpose of this paper is to apply the boundary integral equation (BIE) method to the analysis of spoof localized surface plasmons (spoof LSPs) excited in a perfectly conducting cylinder with longitudinal corrugations. Frequency domain BIE schemes based on electric field integral equation (EFIE), magnetic field integral equation (MFIE) and combined field integral equation (CFIE) formulations are used to solve two-dimensional electromagnetic (EM) problems of scattering from the cylinder illuminated by a transverse electric plane wave. In this approach effects of spoof LSPs are included in the secondary surface current and charge densities resulting from the interaction between the plane wave and the cylinder. Numerical results obtained with the BIE schemes are validated by comparison with that of a recently proposed modal solution based on the metamaterial approximation.

Streak cameras are now widely used for measurements of ultra short phenomena, such as those in semi conductor luminescence and plasma gaseous discharge. To further improve the temporal resolution and carry out higher-dimensional measurements, it is necessary to understand the electron beam behavior in detail. Thus, numerical simulations play an important role in the analysis of the streak camera. The authors have been working on the development of a numerical simulation code that uses the finite difference method (FDM) for electric field analysis, the Runge-Kutta (R-K) method for charged particle motion determination, and the particle-in-cell (PIC) method for charge density calculation. However, the use of the PIC method leads to inaccuracy in the charge density calculation in cases of high-density electron beams. To improve the accuracy of the conventional analysis of the streak camera, we perform the boundary element (BE) analysis of the streak camera.

This paper presents the iterative progressive numerical methods (IPNMs) based on the induced dimension reduction (IDR) theorem. The IDR theorem is mainly utilized for the development of new nonstationary linear iterative solvers. On the other hand, the use of the IDR theorem enables to revise the classical linear iterative solvers like the Jacobi, the Gauss-Seidel (GS), the relaxed Jacobi, the successive overrelaxation (SOR), and the symmetric SOR (SSOR) methods. The new IPNMs are based on the revised solvers because the original one is similar to the Jacobi method. In the new IPNMs, namely the IDR-based IPNMs, we repeatedly solve linear systems of equations by using a nonstationary linear iterative solver. An initial guess and a stopping criterion are discussed in order to realize a fast computation. We treat electromagnetic wave scattering from 27 perfectly electric conducting spheres and reports comparatively the performance of the IDR-based IPNMs. However, the IDR-based SOR- and the IDR-based SSOR-type IPNMs are not subject to the above numerical test in this paper because of the problem with an optimal relaxation parameter. The performance evaluation reveals that the IDR-based IPNMs are better than the conventional ones in terms of the net computation time and the application range for the distance between objects. The IDR-based GS-type IPNM is the best among the conventional and the IDR-based IPNMs and converges 5 times faster than a standard computation by way of the boundary element method.

This paper presents various types of iterative progressive numerical methods (IPNMs) for the computation of electromagnetic (EM) wave scattering from many objects and reports comparatively the performance of these methods. The original IPNM is similar to the Jacobi method which is one of the classical linear iterative solvers. Then the modified IPNMs are based on other classical solvers like the Gauss-Seidel (GS), the relaxed Jacobi, the successive overrelaxation (SOR), and the symmetric SOR (SSOR) methods. In the original and modified IPNMs, we repeatedly solve linear systems of equations by using a nonstationary iterative solver. An initial guess and a stopping criterion are discussed in order to realize a fast computation. We treat EM wave scattering from 27 perfectly electric conducting (PEC) spheres and evaluate the performance of the IPNMs. However, the SOR- and SSOR-type IPNMs are not subject to the above numerical test in this paper because an optimal relaxation parameter is not possible to determine in advance. The evaluation reveals that the IPNMs converge much faster than a standard BEM computation. The relaxed Jacobi-type IPNM is better than the other types in terms of the net computation time and the application range for the distance between objects.

Authors have been working in particle accelerator wake field analysis by using the Time Domain Boundary Element Method (TDBEM). A stable TDBEM scheme was presented and good agreements with conventional wake field analysis of the FDTD method were obtained. On the other hand, the TDBEM scheme still contains difficulty of initial value setting on interior region problems for infinitely long accelerator beam pipe. To avoid this initial value setting, we adopted a numerical model of beam pipes with finite length and wall thickness on open scattering problems. But the use of such finite beam pipe models causes another problem of unwanted scattering fields at the beam pipe edge, and leads to the involvement of interior resonant solutions. This paper presents a modified TDBEM scheme, Scattered-field Time Domain Boundary Element Method (S-TDBEM) to treat the infinitely long beam pipe on interior region problems. It is shown that the S-TDBEM is able to avoid the excitation of the edge scattering fields and the involvement of numerical instabilities caused by interior resonance, which occur in the conventional TDBEM.

Efficient extraction of interconnect parasitic parameters has become very important for present deep submicron designs. In this paper, the improved boundary element method (BEM) is presented for 3-D interconnect resistance extraction. The BEM is accelerated by the recently proposed quasi-multiple medium (QMM) technology, which quasi-cuts the calculated region to enlarge the sparsity of the overall coefficient matrix to solve. An un-average quasi-cutting scheme for QMM, advanced nonuniform element partition and technique of employing the linear element for some special surfaces are proposed. These improvements considerably condense the computational resource of the QMM-based BEM without loss of accuracy. Experiments on actual layout cases show that the presented method is several hundred to several thousand times faster than the well-known commercial software Raphael, while preserving the high accuracy.

Common-mode excitation caused by an imperfect ground plane on a printed circuit board (PCB) has been conventionally explained with the 'current driven' scheme, in which the common-mode current is driven by the ground voltage across the unintentional inductance of the ground plane. We have developed an alternative method for estimating common-mode excitation that is driven by the difference of the common-mode voltages for two connected transmission lines. A parameter called current division factor (CDF) that represents the degree of imbalance of a transmission line explains the common-mode voltage. In this paper, we calculate the CDF with two-dimensional (2-D) static electric field analysis by using the boundary element method (BEM) for asymmetric transmission lines with an arbitrary cross-section. The proposed 2-D method requires less time than three-dimensional simulations. The EMI increase due to a signal line being close to the edge of the ground pattern was evaluated through CDF calculation. The estimated increase agreed well--within 2 dB--with the measured one.

The boundary element method (BEM), a representative method of numerical calculation of electromagnetic wave scattering, has been used for solving boundary integral equations. Using BEM, however, we finally have to solve a linear system of L equations expressed by dense coefficient matrix. The floating-point operation is O(L2) due to a matrix-vector product in iterative process. Greengard-Rokhlin's fast multipole algorithm (GRFMA) can reduce the operation to O(L). In this paper, we describe GRFMA and its floating-point operation theoretically. Moreover, we apply the fast Fourier transform to the calculation processes of GRFMA. In numerical examples, we show the experimental results for the computation time, the amount of used memory and the relative error of matrix-vector product expedited by GRFMA. We also discuss the convergence and the relative error of solution obtained by the BEM with GRFMA.

Simple expressions for constriction resistance of multitude conducting spots were analytically formulated by Greenwood. These expressions, however, include some approximations. Nakamura presented that the constriction resistance of one circular spot computed using the BEM is closed to Maxwell's exact value. This relative error is only e=0. 00162 [%]. In this study, the constriction resistances of two, five and ten conducting spots are computed using the boundary element method (BEM), and compared with those obtained using Greenwood's expressions. As the conducting spots move close to each other, the numerical deviations between constriction resistances computed using Greenwood's expressions and the BEM increase. As a result, mutual resistance computed by the BEM is larger than that obtained from Greenwood's expressions. The numerical deviations between the total resistances computed by Greenwood's expressions and that by the BEM are small. Hence, Greenwood's expressions are valid for the total constriction resistance calculation and can be applied to problems where only the total resistance of two contact surfaces, such as a relay and a switch, is required. However, the numerical deviations between the partial resistances computed by Greenwood's expression and that by the BEM are very large. The partial resistance calculations of multitude conducting spots are beyond the applicable range of Greenwood's expression, since Greenwood's expression for constriction resistance of two conducting spots is obtained by assuming that the conducting spots are equal size. In particular, the deviation between resistances of conducting spots, which are close to each other, is very large. In the case of partial resistances which are significant in semiconductor devices, Greenwood's expressions cannot be used with high precision.

A new configuration of high gain circularly polarized microstrip antenna with a diagonal short and its analysis using boundary element method with a radiation load are presented. The center of a radiating patch is shorted with a 45-degree diagonal offset for not only obtaining a high gain but exciting a circular polarization. This configuration leads to achieving high gain with keeping a very low profile configuration. Boundary element method with radiation load which takes into account the effect of radiation loss is employed to analyze this complicated configuration. The radiation load, which is very important when boundary element method is applied to antenna analyses, can be obtained from radiation admittance using recurring technique, so that the accuracy of the antenna characteristic calculations can be improved. This antenna was designed and tested in the L-band and good characteristics, axial ratios and radiation patterns, have been verified.

In this paper, we present an analysis of microstrip line with a trapezoidal dielectric ridge in multilayered media. The method employed in this characterization is called partial-boundary element method (p-BEM) which provides an efficient technique to the analysis of the structures with multilayered media. To improve the convergence of the Green's function used in the analysis with the P-BEM, we employ a technique based on a combination of the Fourier series expansion and the method of images. Treatment on convergence for the boundary integrals is also described. After this treatment, it requires typically one tenth or one hundredth of Fourier terms to obtain the same accuracy compared with the original Green's function. Numerical results are presented for two microstrip lines that have a trapezoidal dielectric ridge placed on a one-layered substrate and a two-layered substrate. These numerical results demonstrate the effects on the characteristics of the microstrip line due to the existence of the dielectric ridge as well as the second layer between the ridge and the fundamental substrate.

A numerical scheme to analyze a three-dimensional perfectly conducting body that has edges and corners is presented. The geometry of the body can be arbitrary. A new formulation using boundary element method has been developed. This formulation allows that a scatterer has edges and corners, where the behavior of the electromagnetic fields become singular.

In this paper, we presented an analysis of single and coupled microstrip lines covered with protective dielectric film which is usually used in the microwave integrated circuits. The method employed in the characterization is called partial-boundary element method (p-BEM). The p-BEM provides an efficient means to the analysis of the structures with multilayered media or covered with protective dielectric film. The numerical results show that by changing the thickness of the protective dielectric films such as SiO2, Si and Polyimide covered on these lines on a GaAs substrate, the coupled microstrip lines vary within 10% on the characteristic impedance and within 25% on the effective dielectric constant for the odd mode of coupled microstrip line, respectively, in comparison with the structures without the protective dielectric film. In contrast, the single microstrip lines vary within 4% on the characteristic impedance and within 8% on the effective dielectric constant, respectively. The protective dielectric film affects the odd mode of the coupled lines more strongly than the even mode and the characteristics of the single microstrip lines.

The electric or electronic circuits have many contact devices such as relay and switch. The contact between two nominally conducting flat surface has a lot of micro contact spots. The constriction resistance of the contact is known to determine the sum of the parallel resistance of the micro contacts and the interaction of them. The constriction resistance of two circular conducting spots was approximately formulated by Greenwood. This formulation shows that the interacted resistance of two circular spots is in inverse proportion to the distance between two conducting spots. It was known that this effect is introduced by the interaction between two conducting spots. However, the condition of interaction in the spots is not clear. Calculating the current density distribution in the spots is important to clarify the condition of interaction. The numerical analysis is very suitable to calculate the current density in the spots. In the fundamental case of the computation of the current density the boundary element method (BEM) is more efficient and accurate than that of the finite element method (FEM) because the boundary condition at the infinite is naturally satisfied and is not required a great number of the element in a wide space. In this paper the current density in the square spots is computed by the BEM. As the distance between two conducting spots becomes small, the current density in the two spots decreases. It becomes clear that the constriction resistance of conducting spots is increased by this effect. The decrease of current density by interaction is not uniformly, that at the near location to the opposite spot is larger than that at the far location in the same spot. In this paper the constriction resistance of two conducting spots is also considered. It was known that the constriction resistance of one conducting spot is not influenced by the form of spot very much. However, that of two conducting spots is not clear. The constriction resistance of two square spots is also computed by the BEM. The computed values of the constriction resistance of two square spots are compared with that of two circular spots by Greenwood's formulation and other results. As the result, it is clear that they have the considerable discrepancy. However, the trend of the variations is almost agree each other.

To study the biological effects of the ion-current commonly found under ultra-high voltage DC transmission lines, a technique was developed to evaluate the human exposure to the ion-current field. This technique is based on numerical analysis using the boundary element method. The difficulty of handling the space charge in the calculation was overcome by assuming a lumped source ion-current. This technique is applicable to a three-dimensionally complex object such as a human body. In comparison with theoretical values, the accuracy of this technique was evaluated to be satisfactory for our purposes. It was then applied to a human body in an ion-current field. The distribution of the electric field along the body surface was obtained. The general characteristics of the field distribution were essentially the same as in those without space charges. However, it was found that the strength of the field concentration was significantly enhanced by the space charges. Further, the field exposure when a human body was charged by an ion-current was evaluated. As the charged voltage increases, the position of the field concentration moves from a human's head toward his legs. But the shock of micro spark increases. This technique provides a useful tool for the study of biological effects and safety standards of ion-current fields.