Three-dimensional finite-element method with edge elements forelectromagnetic waveguide discontinuities

When three-dimensional electromagnetic problems are solved by the finite-element method based on a functional with three components of electric or magnetic field, spurious solutions appear if the traditional tetrahedral elements are used. It is shown in the present work that the finite-element method using edge elements succeeds in suppressing spurious solutions and that it succeeds in analyzing three-dimensional electromagnetic waveguide problems in the case of metal wedges     

Thin sheet modeling using shell elements in the finite-element time-domain method

The ability to model features that are small relative to the cell size is often important in electromagnetic simulations. In this paper, the focus is on modeling of thin material sheets and coatings in the finite-element time-domain method. The proposed method is based on degenerated prism elements, so-called shell elements. For a dielectric sheet the thickness is assumed small compared to the wavelength for all frequencies of interest. An important characteristic of the method is that it takes the discontinuity of the normal electric field component at a dielectric interface into account. The accuracy of the method is demonstrated for three different scattering cases. Comparisons are made with analytical data and results obtained on grids for which the thickness of the sheets is resolved. Good agreement is observed in all cases.     

A subgridding method for the time-domain finite-difference methodto solve Maxwell's equations

A modification to the time-domain finite-difference method (TDFDM) that uses a variable step size is investigated. The entire computational volume is divided into a coarse grid with a large step size. A fine grid with a small step size is introduced only around discontinuities. The corresponding time increments are related to the spatial increments with the same ratio in order to minimize the numerical dispersion. The fields within the coarse and fine grids are found using the TDFDM, while an interpolation in space and time is utilized to calculate the tangential electric field on the coarse-fine grid boundary. This subgridding decreases the required computer memory and therefore expands the capability of the TDFDM. The technique is shown to be numerically stable and does not entail any extra numerical error. The method is applied to the calculation of waveguides and microstrips     

A special higher order finite-element method for scattering by deepcavities

A special higher order finite-element method is presented for the analysis of electromagnetic scattering from a large, deep, and arbitrarily shaped open cavity. This method exploits the unique features of the finite-element equations and, more importantly, the unique features of the problem of scattering by a large and deep cavity. It is designed in such a manner that it uses minimal memory, which is proportional to the maximum cross section of the cavity and independent of the depth of the cavity, and its computation time increases only linearly with the depth of the cavity. Furthermore, it computes the scattered fields for all angles of incidence without requiring significant additional time. The technique is implemented with higher order tetrahedral and mixed-order prism elements, both having curved sides to allow for accurate modeling of arbitrary geometries. Numerical results show that higher order elements yield a remarkably more accurate and efficient solution for scattering by three-dimensional (3-D) cavities. Of the two kinds of element, the mixed-order prism is optimal for the proposed special solver     

Implementation of radiation boundary conditions in the finiteelement analysis of electromagnetic wave propagation

Radiation boundary conditions are formulated which permit the simulation of two-dimensional electromagnetic wave phenomena with the finite-element method using conventional elements over a bounded domain. Implementation of such boundary conditions preserves the symmetry of the global stiffness matrix with all the advantages that this implies, including economy of storage and solution. A number of wire-antenna systems have been modeled with this technique in a finite-element computer program called FEAST. The results demonstrate good agreement with published reference data     

Model of a nonlinear electromagnetic crystal

2D electromagnetic crystal with lumped nonlinear elements is considered. An electrodynamic model with a rectangular grid is developed for a crystal that is infinite in one coordinate and finite in the other. In the case when the structure is excited by a plane wave, linear boundary value problems are formulated for electromagnetic fields at multiples of the fundamental frequency. The nonlinear problem is solved by means of the harmonic balance method. A system of nonlinear equations for the amplitudes of voltage harmonics at nonlinear elements is derived. Results of numerical solution of the system are presented for resistive and capacitive nonlinear elements.     

Infinite elements and base functions for rotationally symmetricelectromagnetic waves

The finite-element method is applicable to infinite domains if the outermost `finite' elements are infinite and their base functions satisfy the boundary conditions at infinity. Appropriate infinite elements fitted to triangular or quadratic finite-element net and corresponding base functions satisfying Sommerfield's radiation condition of electromagnetic waves are introduced. The application of the defined infinite elements is illustrated for the problem of the radiation of a coaxial cable to a half-space. The results are in very good agreement with those found in the literature     

The complementary derivatives method: a second-order accurate interpolation scheme for non-uniform grid in FDTD simulation

Non-uniform grid in finite-difference time-domain methods, which is typically used to resolve fine structures, can reduce the computational domain and therefore lead to a reduction of the computational cost. However, for high-accuracy problems, such as partially-filled parallel plate waveguide and resonators, using different grid size increases the truncation error at the boundary of domains having different grid size. To address this problem, in this work, we introduce the complementary derivatives method (CDM). Theoretical discussion and numerical results will be presented to show that the CDM can maintain second-order accuracy throughout the computational domain.     

Hierarchical multilevel potential preconditioner for fast finite-element analysis of microwave devices

A robust hierarchical multilevel preconditioning technique is presented for the fast finite-element analysis of microwave devices. The proposed preconditioner is based on a hierarchical multilevel scheme for the vector-scalar potential finite-element formulation of electromagnetic problems. Numerical experiments from the application of the new preconditioner to the finite-element analysis of microwave devices are used to demonstrate its superior numerical convergence and efficient memory usage.     

Numerical Solution of Dielectric Loaded Waveguides: I-Finite-Element Analysis

A variational expression of the electromagnetic fields in dielectric loaded waveguides is derived. This expression is discretized using the finite-element method and an electromagnetic coupling matrix is derived and evaluated. No restriction is placed on the shapes of the triangular elements or the order of the polynomial approximation. A general finite-element computer program is described and dispersion curves and field plots of some dielectric loaded waveguides are presented.     

Analysis of Waveguiding Structures Employing Surface Magnetoplasmons by the Finite-Element Method (Short Paper)

The dispersion relation and electromagnetic field distributions for a gyroelectrically loaded waveguiding structure are obtained utilizing finite-element techniques. The structure considered consists of two layers, one a dielectric and the other a semiconductor, bounded by two perfectly conducting planes. The finite-element solution for the lowest real branches in the dispersion spectrum was compared against a numerical solution of the exact dispersion equation, and excellent agreement was found between the two. The structure, exhibiting nonreciprocal behavior, provides a suitable canonical model for the design of circuit components such as circulators, isolators, and phase shifters.     

Nested multigrid vector and scalar potential finite element method for fast computation of two-dimensional electromagnetic scattering

Nested multigrid techniques are combined with the ungauged vector and scalar potential formulation of the finite-element method to accelerate the convergence of the numerical solution of two-dimensional electromagnetic scattering problems. The finite-element modeling is performed on nested meshes of the same computational domain. The conjugate gradient method is used to solve the resultant finite-element matrix for the finest mesh, while the nested multigrid vector and scalar potential algorithm acts as the preconditioner of the iterative solver. Numerical experiments are used to demonstrate the superior numerical convergence and efficient memory usage of the proposed algorithm.     

Two-dimensional singular vector elements for finite-elementanalysis

The finite-element method (FEM) exhibits a reduced convergence rate when used for the analysis of geometries containing sharp edges where the electromagnetic field is singular. The convergence of the method can be-improved by introducing singular elements that model analytically predicted singular behavior. A number of authors have developed singular elements that are compatible with the scalar FEM. In this paper, we propose a new singular element that is compatible with edge-based vector finite elements and can cope with any order of singularity while preserving the sparsity of the FEM equations. Edge-based singular elements more correctly model singular fields and thus require fewer unknowns, while avoiding the introduction of spurious modes in the numerical solution. Numerical results verify that the convergence of the FEM is significantly improved     

Computed basis functions for finite element analysis based on tomographic data

In bioelectromagnetics, the structures in which the electromagnetic field is to be computed are sometimes defined by a fine grid of voxels (3-D cells) whose tissue types are obtained by tomography. A novel finite element method is proposed for such cases. A simple, regular mesh of cube elements is constructed, each containing the same, integer number of voxels. There may be several different tissues present within an element, but this is accommodated by computing element basis functions that approximately respect the interface conditions between different tissues. Results are presented for a test model of 128 (3) voxels, consisting of nested dielectric cubes, driven by specified charges. The electrostatic potential computed with the new method agrees well with that of a conventional finite element code: the rms difference along the sample line is 1.5% of the highest voltage. Results are also presented for the potential due to a current dipole placed in a brain model of 181 × 217 × 181 voxels, derived from MRI data. The new method gives potentials that are different to those obtained by treating each voxel as an element by 1% of the peak voltage, yet the global finite element matrix has a dimension which is more than 50 times smaller.     

Some experiences from FDTD analysis of infinite and finite multi-octave phased arrays

Some experiences from finite-differences time-domain (FDTD) analysis of infinite and finite multi-octave phased arrays are presented. First, a more unified derivation of equations suitable for unit-cell analysis of phased arrays or other types of periodic structures using FDTD is presented. Second, results from FDTD calculations of small to very large multi-octave finite arrays are summarized in order to answer the question of how large an array model must be in order to capture the characteristics of both the interior and the edge elements of a large multi-octave phased array. It is found that a considerably larger number of elements is required in the broad-band case than in the normal narrow-band case, and it is also found that FDTD is well suited for such calculations. Third, simple methods to save computer memory using locally fine grids in an otherwise coarse FDTD grid to model finite-phased arrays are explored. The two local grid methods tested were found in our application to suffer from numerical instabilities.     

Universal fatigue life prediction equation for ceramic ball grid array (CBGA) packages

A traditional approach to predicting solder joint fatigue life involves finite-element simulations in combination with experimental data to develop a Coffin–Manson type predictive equation. The finite-element simulations often require good understanding of finite-element modeling, physics-based failure models, and time-, temperature-, and direction-dependent material constitutive behavior. Also, such simulations are computationally expensive and time-consuming. Microelectronic package designers often do not have the time and the expertise to perform such simulations. The traditional solder joint fatigue predictive equations fall short of ideal because: (1) they are not applicable to others due to numerical modeling issues, (2) they require a mature understanding of mechanics, numerical modeling, and reliability theory, and (3) they are difficult to implement into the design process. This includes both design of an individual electronic component and selecting which type of existing component to include in an application.Therefore, this work develops universal predictive equations that are: (1) simple, quick, and accurate, (2) require only a basic understanding of reliability and mechanics, (3) require no special software; easy to implement in a spreadsheet or current reliability tools, (4) information rich in regards to design parameters, and (5) maximize available information from experimental tests and numerical models. Using experimental data and finite-element simulations as a basis, this work has developed a predictive equation for solder joint fatigue life in lead-containing ceramic ball grid array (CBGA) package. The developed equation has been validated with other experimental data with good success. Efforts are underway to develop similar equations for other packages and Pb-free CBGAs.     

Moment method with isoparametric elements for three-dimensionalanisotropic scatterers

A new method for computing the frequency-domain electromagnetic fields scattered from, and penetrating into, arbitrarily shaped, three-dimensional, lossy, inhomogeneous anisotropic scatterers is presented. The method is based on a general volume integro-differential formulation of the scattering problem, and consists of the numerical solution of the coupled integral equations by the moment method and point matching. A particularly powerful feature of this method is that the numerical model of the scatterer is obtained by parametric volume elements and the basis functions used to represent the field within each element are the same used in the finite-element method. Element integration problems due to the singular kernel of the integral equations are treated in some detail. Numerical results for both the isotropic and the anisotropic spherical scatterer are presented, including comparisons with results obtained by different numerical methods for the isotropic cases considered. The capability of the numerical code presented here to deal with cases where the material parameters of the scatterer are given by singular matrices is discussed for two particular examples     

On wire-grid representation of solid metallic surfaces

This work deals with the wire-grid representation of metallic surfaces in numerical electromagnetic modeling. We discuss in particular the adequacy of the well known and widely used equal area rule (EAR) to calculate the radii of wire-grid models. We show that the EAR is accurate as long as the wire grid consists of a simple rectangular mesh. For more complex body-fitted meshes, using other polygons such as triangles, the EAR appears to be less accurate in reproducing the electromagnetic field scattered by metallic bodies. The conclusions of the paper are supported by numerical simulations performed using a parallel version of the numerical electromagnetics code and experimental data obtained on a vehicle illuminated by an electromagnetic pulse simulator.     

Do covariant projection elements really satisfy the inclusioncondition?

Spurious modes which often are found among finite-element solutions of electromagnetic eigenvalue problems do not occur when covariant projection elements are used. It has been claimed that this happens because covariant projection elements satisfy the inclusion condition, but they do not satisfy it-as is proven in this paper     

用于电磁波多尺度问题求解的高效FDTD-PITD混合算法北大核心CSCD

针对电磁波多尺度问题的高效仿真需求,提出了基于亚网格技术的时域有限差分(FDTD)方法与时域精细积分(PITD)方法的混合数值算法。该混合算法的基本思想是采用局部亚网格技术分别对精细结构区域以及其他区域进行剖分,并应用FDTD方法和PITD方法分别对粗网格区域与细网格区域进行求解,同时构建信息交互策略交换细网格区域与粗网格区域的计算信息。一方面该方法减少了电磁波多尺度问题的网格剖分数目,显著降低了内存需求;另一方面由于应用于细网格区域的PITD方法不受Courant-Friedrich-Levy(CFL)数值稳定性条件的限制,该混合方法能够采用较大的时间步长进行仿真,减少了迭代步数以及CPU执行时间。数值计算结果验证了混合算法的稳定性、可行性以及高效性。