Showing papers on "Computational electromagnetics published in 2003"

Numerical methods in electromagnetic scattering theory

Abstract: An overview is given over some of the most widely used numerical techniques for solving the electromagnetic scattering problem that start from rigorous electromagnetic theory. In particular, the theoretical foundations of the separation of variables method, the finite-difference time-domain method, the finite-element method, the method of lines, the point matching method, the method of moments, the discrete dipole approximation, and the null-field method (or extended boundary condition method) are reviewed, and the advantages and disadvantages of the different methods are discussed. Aspects concerning the T matrix formulation and the surface Green's function formulation of the electromagnetic scattering problem are addressed.

Electromagnetic Modeling by Finite Element Methods

Abstract: PREFACE MATHEMATICAL PRELIMINARIES Introduction The Vector Notation Vector Derivation The Gradient The Divergence The Rotational Second-Order Operators Application of Operators to More than One Function Expressions in Cylindrical and Spherical Coordinates MAXWELL EQUATIONS, ELECTROSTATICS, MAGNETOSTATICS, AND MAGNETODYNAMIC FIELDS Introduction The EM Quantities Local Form of the Equations The Anisotropy The Approximation of Maxwell's Equations The Integral Form of Maxwell's Equations Electrostatic Fields Magnetostatic Fields Magnetodynamic Fields BRIEF PRESENTATION OF THE FINITE ELEMENT METHOD Introduction The Galerkin Method - Basic Concepts A First-Order Finite Element Program Generalization of the Finite Element Method Numerical Integration Some 2D Finite Elements Coupling Different Finite Elements Calculation of Some Terms in the Field Equation A Simplified 2D Second-Order Finite Element Program THE FINITE ELEMENT METHOD APPLIED TO 2D ELECTROMAGNETIC CASES Introduction Some Static Cases Application to 2D Eddy Current Problems Axi-Symmetric Application Advantages and Limitation of 2D Formulations Non-Linear Applications Geometric Repetition of Domains Thermal Problems Voltage-Fed Electromagnetic Devices Static Examples Dynamic Examples COUPLING OF FIELD AND ELECTRICAL CIRCUIT EQUATIONS Introduction Electromagnetic Equations Equations for Different Conductor Configurations Connections Between Electromagnetic Devices and External Feeding Circuits Examples MOVEMENT MODELING FOR ELECTRICAL MACHINES Introduction The Macro-Element The Moving Band The Skew Effect in Electrical Machines Using 2D Simulation Examples INTERACTION BETWEEN ELECTROMAGNETIC AND MECHANICAL FORCES Introduction Methods Based on Direct Formulations Methods Based on the Force Density Electrical Machine Vibrations Originated by Magnetic Forces Example of Coupling Between the Field and Circuit Equations, Including Mechanical Transients IRON LOSSES Introduction Eddy Current Losses Hysteresis Anomalous or Excess Losses Total Iron Losses The Jiles-Atherton Model The Inverse Jiles-Atherton Model Including Iron Losses in Finite Element Calculations BIBLIOGRAPHY INDEX

Nonorthogonal PEEC formulation for time- and frequency-domain EM and circuit modeling

Abstract: Electromagnetic solvers based on the partial element equivalent circuit (PEEC) approach have proven to be well suited for the solution of combined circuit and EM problems. The inclusion of all types of Spice circuit elements is possible. Due to this, the approach has been used in many different tools. Most of these solvers have been based on a rectangular or Manhattan representation of the geometries. In this paper, we systematically extend the PEEC formulation to nonorthogonal geometries since many practical EM problems require a more general formulation. Importantly, the model given in this paper is consistent with the classical PEEC model for rectangular geometries. Some examples illustrating the application of the approach are given for both the time and frequency domain.

Unconditionally stable Crank-Nicolson scheme for solving two-dimensional Maxwell's equations

Abstract: The Crank-Nicolson method is an unconditionally stable, implicit numerical scheme with second-order accuracy in both time and space. When applied to solve Maxwell's equations in two-dimensions, the resulting matrix is block tri-diagonal, which is very expensive to solve. The Douglas-Gunn algorithm is used to subdivide the update procedure into two sub-steps. At each sub-step only a tri-diagonal matrix needs to be solved for one field component. The other two field components are updated explicitly in one step. The numerical dispersion relations are given for the original Crank-Nicolson scheme and for the Douglas-Gunn modification. The predicted numerical dispersion is shown to agree with numerical experiments, and its numerical anisotropy is shown to be much smaller than that of the ADI-FDTD.

10 million unknowns: is it that big? [computational electromagnetics]

Abstract: At the Center for Computational Electromagnetics at the University of Illinois, we recently solved a very-large-scale electromagnetic scattering problem. We computed the bistatic radar cross-section of a full-size aircraft at 8 GHz, involving the solution of a dense matrix equation with nearly 10.2 million unknowns. We regarded this as the "ultimate test" of a massively parallel implementation of the multilevel fast multipole algorithm (MLFMA), called ScaleME. In this paper, we narrate the technical difficulties faced and the experience gained from a very informal point of view. We describe the various methods developed for surmounting each of the obstacles.

Genetic algorithm (GA) and particle swarm optimization (PSO) in engineering electromagnetics

Abstract: Modern antenna designers are constantly challenged to seek for optimum solutions for complex electromagnetic device designs. The temptation has grown because of ever increasing advances in computational power. The standard brute force design techniques are systematically being replaced by the state-of-the-art optimization techniques. The ability of using numerical methods to accurately and efficiently characterizing the relative quality of a particular design has excited the EM engineers to apply stochastic global optimizers. The genetic algorithm (GA) is the most popular of the so-called evolutionary methods in the electromagnetics community. Recently, a new stochastic algorithm called particle swarm optimization (PSO) has been shown to be a valuable addition to the electromagnetic design engineer's toolbox. In this paper we provide an overview of both techniques and present some representative examples. Most of the material incorporated in this invited plenary session paper is based on the earlier publication work by the author and his students at UCLA.

Higher order hierarchical curved hexahedral vector finite elements for electromagnetic modeling

Abstract: A novel higher order finite-element technique based on generalized curvilinear hexahedra with hierarchical curl-conforming polynomial vector basis functions is proposed for microwave modeling. The finite elements are implemented for geometrical orders from 1 to 4 and field-approximation orders from 1 to 10 in the same Galerkin-type finite-element method and applied to eigenvalue analysis of arbitrary electromagnetic cavities. Individual curved hexahedra in the model can be as large as approximately 2/spl lambda//spl times/2/spl lambda//spl times/2/spl lambda/, which is 20 times the traditional low-order modeling discretization limit of /spl lambda//10 in each dimension. The examples show excellent flexibility and efficiency of the higher order (more precisely, low-to-high order) method at modeling of both field variation and geometrical curvature, and its excellent properties in the context of p-refinement of solutions, for models with both flat and curved surfaces. The reduction in the number of unknowns is by an order of magnitude when compared to low-order solutions.

High-order accurate methods in time-domain computational electromagnetics: A review

Abstract: Publisher Summary This chapter reviews the Maxwell's equations in the time domain and discusses boundary conditions, various simplifications, and standard normalizations. The chapter provides an overview of the classical phase-error analysis as a way of motivating the need to consider high-order accurate methods in time-domain electromagnetics, particularly as problems increase in size and complexity. The extensions of the Yee scheme and other more complex finite difference schemes are discussed. Higher-order schemes allow a significant reduction of the degrees of freedom with accuracy. For some applications it may be natural to consider the ultimate limit, leading to global or spectral methods. The chapter discusses the elements of spectral multidomain methods, which combine the accuracy of global methods with the geometric flexibility of a multielement formulation. The recent efforts on the development of high-order finite volume methods for the solution of Maxwell's equations are reviewed. The issues related to high-order time stepping and discrete stability are also discussed.

Well-conditioned asymptotic waveform evaluation for finite elements

Abstract: The frequency-domain finite-element method (FEM) results in matrix equations that have polynomial dependence on the frequency of excitation. For a wide-band fast frequency sweep technique based on a moment-matching model order reduction (MORe) process, researchers generally take one of two approaches. The first is to linearize the polynomial dependence (which will either limit the bandwidth of accuracy or require the introduction of extra degrees of freedom) and then use a well-conditioned Krylov subspace technique. The second approach is to work directly with the polynomial matrix equation and use one of the available, but ill-conditioned, asymptotic waveform evaluation (AWE) methods. For large-scale FEM simulations, introducing extra degrees of freedom, and therefore increasing the length of the MORe vectors and the amount of memory required, is not desirable; therefore, the first approach is not alluring. On the other hand, an ill-conditioned AWE process is unattractive. This paper presents a novel MORe technique for polynomial matrix equations that circumvents these problematic issues. First, this novel process does not require any additional unknowns. Second, this process is well-conditioned. Along with the presentation of the novel algorithm, which is called well-conditioned AWE (WCAWE), numerical examples modeled using the FEM are given to illustrate its accuracy.

A fully high-order finite-element simulation of scattering by deep cavities

Abstract: A fully high-order finite element algorithm is presented for simulating electromagnetic scattering by a deep cavity using curvilinear tetrahedral elements. Unlike the previously developed algorithm based on mixed-order triangular prism elements, this new algorithm can significantly suppress numerical dispersion errors in all directions, thus resulting in a more accurate and efficient simulation of complex wave propagation inside a deep cavity. Moreover, the use of tetrahedral elements removes limitations on the modeling of complex cavities imposed by the use of triangular prism elements. Numerical examples and experimental results are presented to demonstrate the advantages of the new algorithm.

Generation of FDTD subcell equations by means of reduced order modeling

Abstract: Adapted finite-difference time-domain (FDTD) update equations exist for a number of objects that are smaller than the grid step, such as wires and thin slots. We provide a technique that automatically generates new FDTD update equations for small objects. Our presentation focusses on 2D-FDTD. We start from the FDTD equations in a fine grid where the time derivative is not discretised. This yields a large state-space model that is drastically reduced with a reduced order modeling technique. The reduced state-space model is then translated into new FDTD update equations that can be used in an FDTD simulation in the same way as the existing update equations for wires and thin slots. This technique is applied to a number of numerical problems showing the accuracy and versatility of the proposed method.

Numerical electromagnetic analysis of lightning-induced voltage over ground of finite conductivity

Abstract: Numerical Electromagnetics Code (NEC-2), which is a computer code to analyze the three-dimensional electromagnetic (EM) field around thin wires in the frequency domain, has been successfully used in lightning-related studies such as lightning surge analyses or lightning EM pulse calculations over a perfectly conducting ground. NEC-2 is still more useful in investigating lightning-induced effects over ground of finite conductivity. This application of NEC-2 is investigated by comparing calculated results with an experiment over lossy ground. The advantages of the analysis using NEC-2 are that it can accurately compute the current distribution along a wire structure with small amount of postulation. It automatically incorporates coupling between a lightning channel and transmission lines, and it can also take account of finitely conducting ground in transient condition. In addition, it can also model conductors in any arbitrary angles, and it is available in the public domain.

Electromagnetic modeling using the partial element equivalent circuit method

Abstract: This thesis presents contributions within the field of numerical simulations of electromagnetic properties using the Partial Element Equivalent Circuit (PEEC) method. Numerical simulations of ele ...

High Order Finite Difference Approximations of Electromagnetic Wave Propagation Close to Material Discontinuities

Abstract: Electromagnetic wave propagation close to a material discontinuity is simulated by using summation by part operators of second, fourth and sixth order accuracy The interface conditions at the discontinuity are imposed by the simultaneous approximation term procedure Stability is shown and the order of accuracy is verified numerically

Hardware implementation of a three-dimensional finite-difference time-domain algorithm

Abstract: In order to take advantage of the significant benefits afforded by computational electromagnetic techniques, such as the finite-difference time-domain (FDTD) method, solvers capable of analyzing realistic problems in a reasonable time frame are required. Although software-based solvers are frequently used, they are often too slow to be of practical use. To speed up computations, hardware-based implementations of the FDTD method have recently been proposed. Although these designs are functionally correct, to date, they have not provided a practical and scalable solution. To this end, we have developed an architecture that not only overcomes the limitations of previous accelerators, but also represents the first three-dimensional FDTD accelerator implemented in physical hardware. We present a high-level view of the system architecture and describe the basic functionality of each module involved in the computational flow. We then present our implementation results and compare them with current PC-based FDTD solutions. These results indicate that hardware solutions will, in the near future, surpass existing PC throughputs, and will ultimately rival the performance of PC clusters.

Fast integral equation solvers in computational electromagnetics of complex structures

Abstract: This paper reviews the recent progress of fast integral equation solvers at the Center for Computational Electromagnetics and Electromagnetics laboratory, University of Illinois at Urbana-Champaign. We will demonstrate the ability to solve a variety of electromagnetic problems for complex structures and low-frequency structures as well as large scale scattering problems with over 10 million unknowns.

Characteristic basis function method for solving large problems arising in dense medium scattering

Abstract: Electromagnetic scattering from a dense medium consists of a large number of dielectric scatterers is of great interest. For these dense media, multiple scattering and coherent wave mutual interactions must be taken into account and many exiting analytical and approximation theories may require the use of pair distribution function and/or configurational symmetries. To incorporate mutual coupling effects, the use of characteristic basis functions (CBFs) has recently been proposed (R. Mittra et al., IEEE MTT-S Microwave Symp. Workshop, 2002). In this method, the mutual coupling effects are included through the use of higher-level basis functions, referred to the primary and secondary CBFs. The coefficients of these CBFs are solved directly using the Galerkin method. In this paper, we implement the CBF method for dense medium scattering. These CBFs, however, are constructed differently using the Foldy-Lax equations (L. Tsang et al., Optics Lett., vol. 17, no. 5, pp. 314-316, 1992) in which mutual coupling effects among all scatterers can be included systematically. Our results in this paper show that a small number of CBFs is sufficient.

Comprehensive broadband electromagnetic modeling of on-chip interconnects with a surface discretization-based generalized PEEC model

Abstract: This paper proposes a comprehensive integral equation electromagnetic field solver for broadband modeling of on-chip interconnects. Instead of the computationally intensive volumetric discretization model, which appears to be currently the most popular method of choice for handling the tall and narrow cross sections of the on-chip wiring and capturing correctly the impact of adjacent wiring coupling and skin effect, the proposed generalized partial element equivalent circuit (PEEC) methodology utilizes a computationally more efficient conductor surface discretization. Key to the success of such a surface discretization model is the definition of a position- and frequency-dependent surface impedance used to relate the tangential electric field and current on the wire surface. A novel strategy for the identification of loops in the resulting discrete model leads to a numerically-stable and efficient mesh analysis-based PEEC formulation in support of on-chip interconnect electromagnetic modeling from DC to multi-GHz frequencies.

Extremely short electromagnetic pulses in a resonant medium with a permanent dipole moment

Abstract: The propagation of an extremely short (one cycle long) pulse of an electromagnetic field in a medium whose resonant transition is characterized by both diagonal and off-diagonal matrix elements of the dipole-moment operator is considered theoretically. The set of Maxwell-Bloch equations without the approximation of the slowly varying envelopes is used. Two types of solutions of this set, which are found describing the steady-state propagation of an electromagnetic pulse in such a medium.

An improved compact 2-D finite-difference frequency-domain method for guided wave structures

Abstract: An improved compact two-dimensional (2-D) finite-difference frequency-domain method is presented to determine the dispersion characteristics of guided wave structures. Eigenvalue equations that contain only two transverse electric field components are derived from Maxwell's differential equations. Compared to the traditional 2-D FDFD containing four or six field components, both the order and number of nonzero elements of the coefficient matrix are reduced simultaneously. The method is verified by two application examples.

A reciprocity approach for calculating radiation patterns of arbitrarily shaped microstrip antennas mounted on circularly cylindrical platforms

Abstract: The paper presents a convenient and efficient approach, based on the reciprocity theorem, for calculating the radiation patterns of arbitrarily shaped microstrip antennas with dielectric substrate and superstrate layers mounted on circularly cylindrical platforms. A detailed theoretical development followed by examples with numerical and graphical results illustrate the versatility of the technique. The reciprocity approach presented is very flexible and may be used in conjunction with any of the commonly employed computational electromagnetics modeling approaches such as the method of moments, finite-element methods, and finite-difference time-domain techniques.

MLFMA analysis of scattering from multiple targets in the presence of a half-space

Abstract: The multilevel fast multipole algorithm (MLFMA) is applied to the analysis of plane-wave scattering from multiple conducting and/or dielectric targets, of arbitrary shape, situated in the presence of a dielectric half-space. The multiple-target scattering problem is solved in an iterative fashion. In particular, the fields exciting each target are represented as the incident fields plus the scattered fields from all other targets. The scattered fields from each target are updated iteratively, until the induced currents on all targets have converged. The model is validated with an independent scattering algorithm, and results are presented for several example multitarget scattering scenarios.

The influence of the measurement probe on the evaluation of electromagnetic fields

Abstract: In this paper, the influence of the measurement probe on the evaluation of the far and near field of an electromagnetic source is characterized. While measuring, the electromagnetic field will be disturbed by the measurement probes themselves. Therefore, not the true, free-space field but the disturbed field will be measured. The disturbance can not be fully taken into account by the calibration, especially in the near field. It is found that in the near field, these disturbances are much higher than in the far field for a large sensitive measurement probe. This paper will show that when the disturbance must be limited to a predefined value (e.g., 5%), a suitable measurement probe with maximum sensitivity can be selected. The characterization was performed using a numerical electromagnetic computational program.

Automatic generation of geometrically parameterized reduced order models for integrated spiral RF-inductors

Abstract: We describe an approach to generating low-order models of spiral inductors that accurately capture the dependence on both frequency and geometry (width and spacing) parameters. The approach is based on adapting a multiparameter Krylov-subspace based moment matching method to reducing an integral equation for the three dimensional electromagnetic behavior of the spiral inductor. The approach is demonstrated on a typical on-chip rectangular inductor.

Finite formulation and domain-integrated field relations in electromagnetics - a synthesis

Abstract: Complementary formulations of the integral type have established themselves as the most adequate approach to computational electromagnetics. This paper proposes a computational strategy that benefits from the advantages offered by the finite formulation of the electromagnetic (EM) field, employing integral field quantities and dual meshes, and by the domain-integrated field relations approach to EM field computation.

A study of mlfma for large-scale scattering problems

Abstract: This research is centered in computational electromagnetics with a focus on solving large-scale problems accurately in a timely fashion using first principle physics. Error control of the translation operator in 3-D is shown. A parallel implementation of the multilevel fast multipole algorithm (MLFMA) was studied as far as parallel efficiency and scaling. The large-scale scattering program (LSSP), based on the ScaleME library, was used to solve ultra-large-scale problems including a 200λ sphere with 20 million unknowns. As these large-scale problems were solved, techniques were developed to accurately estimate the memory requirements. Careful memory management is needed in order to solve these massive problems. The study of MLFMA in large-scale problems revealed significant errors that stemmed from inconsistencies in constants used by different parts of the algorithm. These were fixed to produce the most accurate data possible for large-scale surface scattering problems. Data was calculated on a missile-like target using both high frequency methods and MLFMA. This data was compared and analyzed to determine possible strategies to increase data acquisition speed and accuracy through multiple computation method hybridization.

FEMSTER: an object oriented class library of discrete differential forms

Abstract: The FEMSTER finite element class library described in this paper is unique in several aspects. First, it is based upon the language of differential forms. This language provides a unified description of a great variety of PDEs and thus leads us directly to a concise and abstract interface to finite element methods. This language also unifies the seemingly disparate Lagrange, H(curl) and H(div) basis functions that are used in computational electromagnetics. Secondly, FEMSTER utilizes higher-order elements, bases, and integration rules. Higher-order elements are important for accurate modeling of curved surfaces. The use of higher-order basis functions reduces the demands put upon mesh generation, e.g. a billion element mesh is no longer required for a numerically converged solution. The FEMSTER class library is ideally suited for researchers who wish to experiment with unstructured-grid, higher-order solution of Poisson's equation, the Helmholtz equation, Maxwell equations, and related PDEs that employ the standard gradient, curl, and divergence operators.

Electrodynamics in deformable solids for electromagnetic forming

Abstract: The behaviour of matter in an electromagnetic field may be considered as a very complex problem, involving not only electromagnetism but also mechanics and thermodynamics. The interaction field-matter is not simple even for a rigid body, and it becomes more complicated for a deforming body, as long as all the physical quantities that characterize the process are changing both in time and space and also in their interdependence. It is well known that conducting bodies can move and/or can be deformed when they are subjected to strong electromagnetic fields. One of the practical applications of these phenomena is the electromagnetic forming, i.e. shaping objects using strong electromagnetic fields. The electromagnetic forming is a high-velocity forming procedure and it has many advantages that make it an attractive alternative to conventional forming systems or even to other high-velocity forming systems. Since the early 20-th century this has been used at an industrial level, though without a well developed theory about all the phenomena involved in the process. In this thesis, an analytical model of the electromagnetic forming process performed for shaping of hollow circular cylindrical objects, has been developed. The model applies both for electromagnetic compression and expansion of hollow circular cylindrical objects. Additionally, for expansion, an experimental model has been developed to design a set-up for an experimental investigation of electromagnetic forming of steel beverage cans, which was used for verification of the various aspects of the developed analytical model.

Hybridization of FDTD and device behavioral-modeling techniques [interconnected digital I/O ports]

Abstract: We present a systematic methodology for the electromagnetic modeling of interconnected digital I/O ports. Digital drivers and receivers are represented through behavioral models based on radial basis functions expansions. Such a technique allows a very accurate representation of nonlinear/dynamic effects as well as switching behavior of real-world components by means of carefully identified discrete-time models. The inclusion of these models into a finite-difference time-domain solver for full-wave analysis of interconnected systems is presented. A rigorous stability analysis shows that use of nonlinear/dynamic discrete-time models can be easily integrated with standard full-wave solvers, even in the case of unmatched sampling time. A set of numerical examples illustrates the feasibility of this method.