3-D computation of E fields by the volume-surface integral equation(VSIE) method in comparison with the finite-integration theory (FIT)method [clinical hyperthermia application]

An algorithm has been developed for calculation of 3-D electric (E) fields by the volume-surface integral equation (VSIE) method. Integration over surface elements is performed using elementary analytical formulas, assuming a linear interpolation of surface charges. Grid points at electrical interfaces are split off, taking into account the E field behavior at these contours, specifically at sharp bends and multimedia junctions. Averaging procedures are utilized in order to avoid undefined or infinite values at critical points. The VSIE is solved by iteration using the GMRES (general minimum residuum) solver on a SUN workstation SPARC-IPX or Cray XMP, whereby convergence speed decreases considerably as the heterogeneity of the problem increases. Results for 3-D test cases (plane wave illuminating a layered cylinder) generally agree well with the finite-integration-theory (FIT) method if high E field gradients occur perpendicular to electrical boundaries. The VSIE method predicts slightly higher E fields only in critical regions. On the other hand, the FIT method at present is more efficient with respect to computation time for large domains with high cell numbers (>100000 cells)     

A General Three-Dimensional Tensor FDTD-Formulation for Electrically Inhomogeneous Lossy Media Using the Z-Transform

A general three-dimensional tensor finite-difference time-domain (TFDTD) formulation is derived to model electrically inhomogeneous lossy media of arbitrary shapes. The time domain representation of electric losses is achieved using Z-transforms. The regular cubical grid structure is maintained everywhere in the calculation domain by defining a 3-D face-fraction based 3 x 3 permittivity tensor on the interfaces that describes the relationship between the (known) average flux density vector and the (unknown) local electric field vector. For electrically lossy media, this tensor is complex in the frequency domain. However, it can be modified for use with the Z-transform. Only this modified real form is inverted, then transformed from the frequency into the Z-domain, and finally into the time domain. Furthermore, a local interface matrix is used to describe the relationship between the local electric field in the grid node and its counterpart on the other side of the interface. This matrix is complex in the frequency domain for lossy media. By applying the Z-transform, this matrix can also be transformed into the time domain using only real modified matrix elements. The accuracy of the method is confirmed by comparisons with analytical solutions.     

Electromagnetic Scattering by Arbitrarily Shaped PEC Targets Coated with Anisotropic Media Using Equivalent Dipole-Moment Method

The equivalent dipole-moment method (EDM) is extended and applied in the analysis of electromagnetic (EM) scattering by arbitrarily shaped perfect electric conductor (PEC) targets coated with electric anisotropic media in this paper. The scattering targets are discretized into tetrahedral volume elements in the material region and into triangle patches on the conducting surface, where the volume-surface integral equation (VSIE) is set up. Then the method of moments (MoM) is employed to solve the VSIE. In the impedance matrix, the near field interaction elements are computed by the conventional MoM while the far field interaction elements are modeled by the EDM. The proposed approach is sufficiently versatile in handling arbitrarily shaped objects coated with general electric anisotropic media and is easily constructed through a simple procedure. Numerical results are given to demonstrate the accuracy and efficiency of this method.     

Theory of aperture-coupled hemispherical dielectric resonator antennas with radiating elements

A new approach based on hybrid volume-surface integral equation (VSIE) formulation in combination with spherical dyadic Green's function (DGF) is presented in this paper to analyze aperture-coupled multilayer hemispherical dielectric resonator antennas (DRA) with conformal conducting patches. Hybrid VSIE is used for the planar part of the structure and is solved with the aid of spatial-domain method of moments (MoM) in order to compute magnetic surface current in a slot cut in a finite planar perfect electric conductor (PEC) sheet. Multilayer spherical electromagnetic DGFs are used to compute loading effects of hemispherical dielectric resonators and conformal patches on antenna characteristics. The effects of variation in some parameters of the structure on the return loss of the antenna are studied. Accuracy of the presented method is validated by comparing the results obtained from the proposed method with those of CAD simulations.     

A hybrid finite element-boundary integral method for the analysisof cavity-backed antennas of arbitrary shape

An edge-based hybrid finite element-boundary integral (FE-BI) formulation using tetrahedral elements is described for scattering and radiation analysis of arbitrarily shaped cavity-backed patch antennas. By virtue of the finite element method (FEM), the cavity irregularities, the dielectric super/substrate inhomogeneities, and the diverse excitation schemes inside the cavity may be readily modeled when tetrahedral elements are used to discretize the cavity. On the aperture, the volume mesh reduces to a triangular grid allowing the modeling of nonrectangular patches. Without special handling of the boundary integral system, this formulation is typically applicable to cavity-backed antenna systems with moderate aperture size. To retain an O(N) memory requirement, storage of the full matrix due to the boundary integral equation is avoided by resorting to a structured triangular aperture grid and taking advantage of the integral's convolutional property. If necessary, this is achieved by overlaying a structured triangular grid on the unstructured triangular grid and relating the edge field coefficients between the two grids via two narrow banded transformation matrices. The combined linear system of equations is solved via the biconjugate gradient (BICG) method, and the FFT algorithm is incorporated to compute the matrix-vector product efficiently, with minimal storage requirements     

Hybrid2: combining the three-dimensional hybrid finiteelement-boundary integral technique for planar multilayered media withthe uniform geometrical theory of diffraction

The fully three-dimensional (3-D) hybrid finite element (FE)-boundary integral (BI) technique is extended by further hybridization with the uniform geometrical theory of diffraction (UTD) resulting in a so-called hybrid² FE-BI-UTD approach. The formulation is capable of modeling arbitrarily shaped strongly inhomogeneous objects together with electrically large obstacles of relatively simple shape within the common environment of a planar-multilayered medium. The arbitrarily shaped inhomogeneous objects are discretized by finite elements, whereas, the electrically-large obstacles are described by the UTD and both of these models are included into an integral equation derived from the equivalence principle for planar-multilayered media. Thus, full-electromagnetic coupling is realized between all parts of the formulation. The integral equation is implemented using mixed potentials with appropriate Green's functions derived from Sommerfeld integral representations for planar-multilayered media. The UTD contributions are accounted for by corresponding modifications of the Green's functions and the FE technique is coupled to the integral equation via introduction of equivalent surface current densities in the bounding surfaces of the discretized objects. After presenting the formulation of this novel fully 3-D hybrid² technique, the implemented computer code is validated against conventional hybrid FE-BI computations and a wireless base station antenna is analyzed in several situations of complex real world, microcell environments     

A simplified two-dimensional numerical analysis of MOS devices—DC case

A simplified two-dimensional numerical analysis program has been developed for MOS devices. The calculation speed of this program is an order of magnitude faster than that of the finite-difference or finite-element methods due to the reduced number of analysis node points. The method solves only a one-dimensional current-continuity equation along the channel. Poisson's equation in two dimensions is replaced by an initial solution and a boundary-value problem formulation for the incremental potential and charge. In this method, the nodes are allocated only along the boundaries and the channel; therefore, it has a much smaller number of nodes than that required for other methods. MOS characteristics are simulated and compared with results from the finite-difference program [2], [9]. The agreement is satisfactory within 10 percent over a wide range of the substrate doping concentrations and channel lengths.     

A fast solver for the Helmholtz equation on long, thin structures

We present a fast solver for the Helmholtz equation on long, thin structures. It operates on an integral equation formulation of the problem, in which the solution is represented as a superposition of fields generated by sources on the structure (usually on the boundary or boundaries of the structure). It uses a standard iterative solver for linear equations, in conjunction with a novel method for applying the forward matrix, whose computational complexity is O(N), where N is the number of points on which the integral equation is solved. The algorithm is suitable for structures in either two dimensions (2-D) or three dimensions. It does not depend in any great detail on the specifics of the Helmholtz equation, and, thus, is also suitable for similar equations. We demonstrate the algorithm by using it to simulate scattering in 2-D from dielectric structures, using an integral equation formulation constructed using a combination of single-layer and double-layer potentials, yielding a second-kind integral equation. Numerical results show the algorithm to be efficient and accurate.     

A hybrid symmetric FEM/MOM formulation applied to scattering byinhomogeneous bodies of revolution

A new symmetric formulation of the hybrid finite element method (HFEM) is described which combines elements of the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) for the exterior region along with the finite element solution for the interior region. The formulation is applied to scattering by inhomogeneous bodies of revolution. To avoid spurious modes in the interior region a combination of vector and nodal based finite elements are used. Integral equations in the exterior region are used to enforce the Sommerfeld radiation condition by matching both the tangential electric and magnetic fields between interior and exterior regions. Results from this symmetric formulation as well as formulations based solely on the EFIE or MFIE are compared to exact series solutions and integral equation solutions for a number of examples. The behaviors of the symmetric, EFIE, and MFIE solutions are examined at potential resonant frequencies of the interior and exterior regions, demonstrating the advantage of this symmetric formulation     

Grid‐Enabled Parallel Simulation Based on Parallel Equation Formulation

Parallel simulation is an efficient way to cope with long runtimes and high computational requirements in simulations of modern complex integrated electronic circuits and systems. This paper presents an algorithm for parallel simulation based on parallelization in equation formulation and simultaneous calculation of matrix contributions for nonlinear analog elements. In addition, the paper describes the development of a grid interface for a parallel simulator that enables a designer to perform simulations on distant computer clusters. Performances of the developed parallel simulation algorithm are evaluated by simulation of a microelectromechanical system.     

Hierarchal vector boundary elements and p-adaption for 3-Delectromagnetic scattering

This paper describes the development of new vector boundary elements for solving electromagnetic (EM) scattering problems. The new elements are suitable for the magnetic field integral equation (MFIE), electrical field integral equation (EFIE), or the combination field integral equation (CFIE). The basis functions are assigned to the edges of an element, rather than to its nodes. The new element guarantees the continuity of the normal component of the surface current across element edges. Furthermore, the basis functions are hierarchical from linear to higher order, which enables one to use the new elements in a p-adaption scheme     

A novel grid-robust higher order vector basis function for themethod of moments

A set of novel, grid-robust, higher order vector basis functions is proposed for the method-of-moments (MoM) solution of integral equations for three-dimensional (3-D) electromagnetic (EM) problems. These basis functions are defined over curvilinear triangular patches and represent the unknown electric current density within each patch using the Lagrange interpolation polynomials. The highlight of these basis functions is that the Lagrange interpolation points are chosen to be the same as the nodes of the well-developed Gaussian quadratures. As a result, the evaluation of the integrals in the MoM is greatly simplified. Additionally, the surface of an object to be analyzed can be easily meshed because the new basis functions do not require the side of a triangular patch to be entirely shared by another triangular patch, which is a very stringent requirement for traditional vector basis functions. The proposed basis functions are implemented with point matching for the MoM solution of the electric-field integral equation, the magnetic-field integral equation, and the combined-field integral equation. Numerical examples are presented to demonstrate the higher order convergence and the grid robustness for defective meshes using the new basis functions     

Single integral equation for electromagnetic scattering bythree-dimensional homogeneous dielectric objects

A single integral equation formulation for electromagnetic scattering by three-dimensional (3-D) homogeneous dielectric objects is developed. In this formulation, a single effective electric current on the surface S of a dielectric object is used to generate the scattered fields in the interior region. The equivalent electric and magnetic currents for the exterior region are obtained by enforcing the continuity of the tangential fields across S. A single integral equation for the effective electric current is obtained by enforcing the vanishing of the total field due to the exterior equivalent currents inside S. The single integral equation is solved by the method of moments. Numerical results for a dielectric sphere obtained with this method are in good agreement with the exact results. Furthermore, the convergence speed of the iterative solution of the matrix equation in this formulation is significantly greater than that of the coupled integral equations formulation     

Scattering from planar structures containing small features usingthe adaptive integral method (AIM)

Fast integral equation algorithms such as the adaptive integral method (AIM) have been demonstrated to reduce memory and execution time associated with moment-method solutions for arbitrarily shaped three-dimensional (3-D) geometries. In this paper, we examine the efficiency of AIM in modeling planar structures that contain small and intricate details as is the case with spirals and slot antennas. Such geometries require high tessellation due to the inclusion of very small features resulting in a large number of unknowns. AIM with its capability to translate the original grid to an equivalent sparser uniform grid is uniquely suited for the analysis of such geometries. In the latter part of the paper, we demonstrate the application of AIM in connection with a finite-element boundary-integral formulation for cavity-backed antennas     

金属介质混合目标电磁特性的快速分析

将自适应积分算法与基于体面混合积分方程的矩量法相结合快速分析任意结构金属/介质混合目标的电磁散射和辐射特性.通过将传统矩量法的阻抗矩阵分为两部分且采用不同的方法进行处理计算,提高了矩量法的计算速度并大幅度缩减了需要的计算机内存占用量.最后,分别用传统的矩量法与结合自适应积分快速算法的矩量法计算了三个典型例子,通过比较充分说明了文中方法的有效性.     

Distributed Synchronization for OFDMA‐Based Wireless Mesh Networks

In this paper, we propose a distributed synchronization algorithm for wireless mesh networks based on orthogonal frequency division multiple access. For time and frequency synchronization, a node requests its neighbor nodes for a change of fast Fourier transform starting points, transmission times, and carrier frequencies needed for synchronization. The node also updates its own time and frequency elements through simple formulas based on request messages received from neighbor nodes using a guard interval and a cyclic prefix. This process with the cooperation of neighbor nodes leads to a gradual synchronization of all nodes in the network. Through a performance comparison with a conventional scheme, we obtain simulation results indicating that the proposed scheme outperforms the conventional scheme in random topologies and a grid topology.     

An MFIE-based tabulated interaction method for UHF terrainpropagation problems

Approximations are introduced into a magnetic field integral equation (MFIE) formulation of a two-dimensional (2-D) terrain scattering problem, which allow most of the integrals inherent in the MFIE to be performed analytically. The implementation of the method is discussed and an example is given comparing its performance against a reference solution and measured data. The new formulation applies to both TM^z and TE^z polarizations and is an improvement over the electric field integral equation (EFIE) formulation of the tabulated interaction method (TIM) in that far-field patterns can be calculated analytically leading to increased flexibility of the method     

On the testing of the magnetic field integral equation with RWGbasis functions in method of moments

For electromagnetic analysis using method of moments (MoM), three-dimensional (3-D) arbitrary conducting surfaces are often discretized in Rao, Wilton and Glisson basis functions. The MoM Galerkin discretization of the magnetic field integral equation (MFIE) includes a factor Ω₀ equal to the solid angle external to the surface at the testing points, which is 2π everywhere on the surface of the object, except at the edges or tips that constitute a set of zero measure. However, the standard formulation of the MFIE with Ω₀=2π leads to inaccurate results for electrically small sharp-edged objects. This paper presents a correction to the Ω₀ factor that, using Galerkin testing in the MFIE, gives accuracy comparable to the electric field integral equation (EFIE), which behaves very well for small sharp-edged objects and can be taken as a reference     

A thin-rod approximation for the improved modeling of bare and insulated cylindrical antennas using the FDTD method

A general and consistent integral finite-difference time-domain (FDTD) formulation on cubical grids for modeling of cylindrical antennas with or without dielectric coating is derived. No additional grid points or modifications of the integral paths are necessary. Instead, effective material properties are modified in the FDTD grid. Thus, even for insulated antennas, the simple cubical structure is maintained. Special integral factors are defined on cubical elements, which take into account the behavior of fields in all directions in the neighborhood of the antenna. Applying these factors to the gap region and along the antenna's axis allows a correct modeling of the influence of the antenna's thickness. Furthermore, integral factors derived for the antenna's ends improve the modeling of the antenna's length. The accuracy of the method is confirmed by a systematic comparison with analytical and numerical results.