Showing papers on "Computational electromagnetics published in 2001"

Fast and Efficient Algorithms in Computational Electromagnetics

Abstract: From the Publisher: Here's a cutting-edge resource that brings you up-to-date with all the recent advances in computational electromagnetics. You get the most-current information available on the multilevel fast multipole algorithm in both the time and frequency domains, as well as the latest developments in fast algorithms for low frequencies and specialized structures, such as the planar and layered media. These algorithms solve large electromagnetics problems with shorter turn around time, using less computer memory. Complex problems that once required a supercomputer to solve, can now be solved on a workstation or personal computer with the innovative methods taught in this resource. The book introduces you to new advances in the perfectly matched layer absorbing boundary conditions, and offers you a thorough understanding of error analysis of numerical methods, fast-forward and inverse solvers for inverse problems, hybridization in computational electromagnetics, and asymptotic waveform evaluation.

Acoustic and electromagnetic equations : integral representations for harmonic problems

Abstract: Preface * 1 Some wave equations * 2 Harmonic Helmholtz equation * 3 Integral representations and Integral equations * 4 Singular integral operators * 5 Maxwell equations and electromagnetic waves * References

Point Sources and Multipoles in Inverse Scattering Theory

Abstract: INTRODUCTION AND TOOLS A Survey About Inverse Scattering Theory Basic Definitions and Tools DIRECT SCATTERING PROBLEMS Acoustic Obstacle Scattering The Inhomogeneous Acoustic Medium Electromagnetic Scattering by a Perfect Conductor The Electromagnetic Inhomogeneous Medium Scattering by Orthotropic Media Anisotropic Electromagnetic Media UNIQUENESS AND STABILITY IN INVERSE SCATTERING Acoustic Scattering Electromagnetic Scattering THE CASE OF FINITE DATA Finite Data in Inverse Acoustic Scattering Inverse Electromagnetic Scattering THE POINT-SOURCE METHOD AND APPLICATIONS Reconstruction Of Acoustic Scatters Inverse Electromagnetic Scattering Reconstruction of the Boundary Values of Scattered Fields Convergence of a Regularized Newton Method SINGULAR SOURCES AND SHAPE RECONSTRUCTION Acoustic Scattering Electromagnetic Scattering LINEAR SAMPLING METHODS The Original Linear Sampling Method Spectral Theory and a Modified Linear Sampling Method Shape Reconstruction for Orthotropic Media Anisotropic Electromagnetic Media REFERENCES INDEX

Progress in the methodologies for the electrical modeling of interconnects and electronic packages

Abstract: The rapid growth of the electrical modeling and analysis of the interconnect structure, both at the electronic chip and package level, can be attributed to the increasing importance of the electromagnetic properties of the interconnect circuit on the overall electrical performance of state-of-the-art very large scale integration (VLSI) systems. With switching speeds well below 1 ns in today's gigahertz processors, and VLSI circuit complexity exceeding the 100 million transistors per chip mark, power and signal distribution is characterized by multigigahertz bandwidth pulses propagating through a tightly coupled three-dimensional wiring structure that exhibits resonant behavior at the upper part of the spectrum. Consequently, in addition to the inductive and capacitive coupling, present between adjacent wires across the entire frequency bandwidth, distributed electromagnetic effects, manifested as interconnect-induced delay, reflection, radiation, and long-range nonlocal coupling, become prominent at high frequencies, with a decisive impact of overall system performance. The electromagnetic nature of such high-frequency effects, combined with the geometric complexity of the interconnect structure, make the electrical design of today's performance-driven systems extremely challenging. Its success is heavily dependent on the availability of sophisticated electromagnetic modeling methodologies and computer-aided design tools. This paper presents an overview of the different approaches employed today for the development of an electromagnetic modeling and simulation framework that can effectively tackle the complexity of the interconnect circuit and facilitate its design. In addition to identifying the current state of the art, an assessment is given of the challenges that lie ahead in the signal integrity-driven electrical design of tomorrow's performance- and/or portability-driven, multifunctional ULSI systems.

Finite Formulation of the Electromagnetic Field

Abstract: This paper shows that the equations of electromagnetism can be directly obtained in a finite (=discrete) form, i.e. without going throught the differential formulation. This finite formulation is a natural extension of the network theory to electromagnetic field and it is suitable for computational electromagnetics.

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

Abstract: 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.

Simple phenomenological models for wideband frequency-domain electromagnetic induction

Abstract: The authors propose three phenomenological models for wideband electromagnetic induction (EMI) response of buried conductors, such as unexploded ordnance (UXO) or metal parts in landmines. The models are based on analytic solutions for spheres, cylinders, and wire loops, and produce physically reasonable predictions for a variety of targets at all frequencies of interest including matches to theory in the low- and high-frequency limits. All three produce excellent fits to test data and run quickly enough to be of practical use in data inversion schemes. The authors present a three-parameter model capable of exactly matching permeable spheres and cylinders, a four-parameter version which adds the capability to match wire loops, and a five-parameter version which adds the capability to match signals due to driving bands, a feature found only on UXO. Driving bands, also called rotating bands, are soft metal rings near the tail of a projectile designed to engage rifles in the gun bore when the projectile Is fired. The author observe that driving bands produce a distinctive loop-like signal in EMI spectra, possibly because they are in the shape of a loop and typically have much greater conductivity than the body of the UXO. They demonstrate that the five-parameter model is capable of accurately fitting this signal and expressing its presence or absence through model fit parameters.

'Generalized Finite Differences' in Computational Electromagnetics

Abstract: The geometrical approach to Maxwell's equations promotes a way to discretize them that can be dubbed Generalized Finite Differences, which has been realized independently in several computing codes. The main features of this method are the use of two grids in duality, the metric-free formulation of the main equations (Ampere and Faraday), and the concentration of metric information in the discrete representation of the Hodge operator. The specific role that finite elements have to play in such an approach is emphasized, and a rationale for Whitney forms is proposed, showing why they are the finite elements of choice.

Stationary phase method application for the analysis of radiation of complex 3-D conducting structures

Abstract: The stationary phase method is used to calculate the radiation pattern of antennas on complex structures. Physical optics (PO) approximation has been applied for the induced currents. The problem is stated directly over the parametric surfaces used to model the geometry and no translation of geometrical formats is required. The integral comes from the contribution of certain points on the surface (specular, boundary and vertices) where the phase term of the integrand presents a stationary behavior. In general, the asymptotic integration behaves similar to the numerical one but being more efficient in execution time than the latter.

Numerical methods in computational electrodynamics : linear systems in practical applications

Abstract: 1.Classical Electrodynamics.- 2. Numerical Field Theory.- 3. Numerical Treatment of Linear Systems.- 4. Applications from Electrical Engineering.- 5. Applications from Accelerator Physics.- Summary.- References.- Symbols.

Underground electromagnetic fields generated by the return strokes of lightning flashes

Abstract: In this paper, equations are developed in the time domain to represent lightning generated electromagnetic (EM) fields at different depths below the ground surface. The equations connect underground EM fields to surface fields that can easily be measured or calculated. Numerous examples are given to illustrate how the signature of the electric and magnetic field vary as a function of depth as well as conductivity.

Time-Domain Methods for the Maxwell Equations

Abstract: The most widespread time-domain method for the numerical simulation of the Maxwell equations is the finite-difference time-domain method (FD-TD). It has been widely used for electromagnetic simulation, for instance in radar cross section computations and electromagnetic compatibility investigations. The FD-TD method is second-order accurate and very efficient for simple geometries. A major drawback with the FD-TD method is its inability to accurately handle curved boundaries. Such boundaries are approximated with so-called staircasing to fit into the Cartesian FD-TD grid. Staircasing introduces errors that destroy the secondorder accuracy of the FD-TD method. We present three different methodologies to tackle the errors caused by staircasing. They are parallelization, hybridization with unstructured grids, and regularization of material interfaces. By using parallel computers it is possible to lower the staircasing errors by using a grid with many cells. We examine the scale-up and speed-up properties of the FD-TD method and demonstrate that it can be used to solve gigantic problems. This is shown by a one-billion-cell computation of an aircraft. We also present a new hybridization strategy. We hybridize FD-TD with methods for unstructured tetrahedral grids. On the unstructured grid we use either an explicit finite volume method or an implicit finite element method, depending one the size of the smallest tetrahedron in the unstructured grid. The implicit method is used on grids with tetrahedra that are much smaller than the hexahedra in the FD-TD grid. Otherwise the explicit method is used. In two dimensions, our hybrid methods are second-order accurate and stable. This is demonstrated by extensive numerical experimentation. In three dimensions, our hybrid methods have been successfully used on realistic geometries such as a generic aircraft model. The methods show super-linear convergence for a vacuum test case. However, they are not second-order accurate. This is shown to be caused by the interpolation when sending values from the FD-TD grid to the unstructured grid. Our hybrid methods have been implemented in a code package that is used in an industrial environment. The hybridization strategy is successful but can be expensive in terms of memory and arithmetic operations needed per cell in the grids. We present a new regularization procedure for material interfaces that restore second-order accuracy without adding any extra memory or arithmetic operations during the timestepping. By replacing the discontinuous material function with a properly chosen continuous function prior to the discretization, we can restore second-order accuracy. This is shown for a circular dielectric cylinder for the TMz polarization of the Maxwell equations. ISBN 91-7283-043-3 • TRITA-NA-0101 • ISSN 0348-2952 • ISRN KTH/NA/R--01/01--SE

Power electronic converter EMC analysis through state variable approach techniques

Abstract: A technique based on the state vector approach and a simple switch device model is proposed for electromagnetic compatibility (EMC) analysis in converter design. The conducted noise spectrum is straightforward computed in the frequency domain for hard switching converters with alternating or direct current input sources. The results are compared with PSpice time-domain simulations mixed with the fast Fourier transform, considering a buck converter. The technique proposed in this paper is appropriate for applications where calculation speed is preferred rather than high precision.

High-order/spectral methods on unstructured grids I. Time-domain solution of Maxwell's equations

Abstract: We present an ab initio development of a convergent high-order accurate scheme for the solution of linear conservation laws in geometrically complex domains As our main example we present a detailed development and analysis of a scheme suitable for the time-domain solution of Maxwell''s equations in a three-dimensional domain The fully unstructured spatial discretization is made possible by the use of a high-order nodal basis, employing multivariate Lagrange polynomials defined on the triangles and tetrahedra Careful choices of the unstructured nodal grid points ensure high-order/spectral accuracy, while the equations themselves are satisfied in a discontinuous Galerkin form with the boundary conditions being enforced weakly through a penalty term Accuracy, stability, and convergence of the semi-discrete approximation to Maxwell''s equations is established rigorously and bounds on the global divergence error are provided Concerns related to efficient implementations are discussed in detail This sets the stage for the presentation of examples, verifying the theoretical results, as well as illustrating the versatility, flexibility, and robustness when solving two- and three-dimensional benchmarks in computational electromagnetics Pure scattering as well as penetration is discussed and high parallel performance of the scheme is demonstrated

On the spectrum of the electric field integral equation and the convergence of the moment method

Abstract: Existing convergence estimates for numerical scattering methods based on boundary integral equations are asymptotic in the limit of vanishing discretization length, and break down as the electrical size of the problem grows. In order to analyse the efficiency and accuracy of numerical methods for the large scattering problems of interest in computational electromagnetics, we study the spectrum of the electric field integral equation (EFIE) for an infinite, conducting strip for both the TM (weakly singular kernel) and TE polarizations (hypersingular kernel). Due to the self-coupling of surface wave modes, the condition number of the discretized integral equation increases as the square root of the electrical size of the strip for both polarizations. From the spectrum of the EFIE, the solution error introduced by discretization of the integral equation can also be estimated. Away from the edge singularities of the solution, the error is second order in the discretization length for low-order bases with exact integration of matrix elements, and is first order if an approximate quadrature rule is employed. Comparison with numerical results demonstrates the validity of these condition number and solution error estimates. The spectral theory offers insights into the behaviour of numerical methods commonly observed in computational electromagnetics. Copyright © 2001 John Wiley & Sons, Ltd.

A new finite element model for reduced order electromagnetic modeling

Abstract: This paper introduces a new formulation suitable for direct model order reduction of finite element approximations of electromagnetic systems using Krylov subspace methods. The proposed formulation utilizes a finite element model of Maxwell's curl equations to generate a state-space representation of the electromagnetic system most suitable for the implementation of model order reduction techniques based on Krylov subspaces. It is shown that, with a proper selection of the finite element interpolation functions for the fields, the proposed formulation is equivalent to the commonly used approximation of the vector wave equation with tangentially continuous vector finite elements. This equivalence is exploited to improve the computational efficiency of the model order reduction process.

Multilevel fast multipole method solution of volume integral equations using parametric geometry modeling

Abstract: Field computations for problems involving inhomogeneous materials have mostly been confined to either analytical approximations for canonical problem geometries or differential equation solvers, such as the finite element (FE) method. Integral equation formulations for inhomogeneous materials have not been exploited due to their high computational cost. However, recent developments in fast algorithms, such as the multilevel fast multipole method (MLFMM) have enabled direct method of moments (MoM) solutions of volumetric integral equation formulations. This paper outlines the MLFMM solution of a volume integral equation for scattering by arbitrarily shaped inhomogeneous dielectric structures. The approach uses three-dimensional conformal parametric subdomains to ensure fidelity of the geometrical representation. This low complexity computer code can be used in various areas of applied computational electromagnetics, ranging from microwave circuit simulations to remote sensing applications.

Hybrid Time-Domain Methods and Wire Models for Computational Electromagnetics

Abstract: The Finite-Difference Time-Domain (FD-TD) method is the most commonly used time-domain method for solving the Maxwell equations. The FD-TD method pioneered by K.S. Yee 1966 is an explicit finite-difference scheme using central differences on a staggered Cartesian grid (Yee grid) and is second-order accurate in both space and time. It has been attractive for industrial users since the early 1980s because the basic method is relatively simple to program and the geometry handling is fairly straightforward. The main drawback of the FD-TD method is its inability to accurately model curved objects and small geometrical features. The Cartesian FD-TD grid leads to a staircase approximation of the geometry and parts smaller than an FD-TD cell might be neglected by the grid generator. We present three different methodologies to minimize this drawback of FD-TD but still benefit from its advantages. They are parallelization, hybridization with unstructured grids, and subcell models for thin wires. Parallel computers can solve very large FD-TD problems. This is illustrated by a lightning problem for a real aircraft where more than one billion FD-TD cells are used. The cell size is one inch which gives a very fine grained grid. This type of simulation is important for electromagnetic compatibility problems where the complexity of the geometry requires small cells to give accurate results. The idea behind our hybridization method is to use unstructured boundary fitted grids to resolve the geometrical features and Yee grid elsewhere. In this way we avoid the staircasing problems, and small parts can be resolved but still keep the efficiency of FD-TD. In two dimensions, our hybrid methods are second-order accurate and stable. This is demonstrated by extensive numerical experiments. In three dimensions, our hybrid methods have been successfully used on realistic geometries such as a generic aircraft model. The methods show super-linear convergence for a vacuum test case and almost second-order convergence for a perfect electric sphere. However, they are not second-order accurate. This is shown to be caused by the interpolation needed when sending values from the Yee grid to the unstructured grid. Stability issues are also discussed. The cross-section of thin wires are smaller than the Yee cells and hence subcell models for thin wires have been developed for FD-TD. We present a new model for arbitrarily oriented thin wires. Previously published models for FD-TD require the wire to be oriented along the edges of the grid and hence a staircasing error is introduced. The new model avoids these errors. Results are presented illustrating the superiority of the new thin-wire subcell model. ISBN 91-7283-058-1 • TRITA-NA-0106 • ISSN 0348-2952 • ISRN KTH/NA/R--01/06--SE

Generalized PEEC models for three-dimensional interconnect structures and integrated passives of arbitrary shapes

Abstract: This paper presents the generalization of the Partial Element Equivalent Circuit method that facilitates its application to the modeling of structures of arbitrary shapes. This is achieved through the development of partial element equivalent circuit models using triangular cells and prisms as the fundamental building blocks for modeling conductor surfaces and conductor/dielectric volumes. The new Partial Element Equivalent Circuit models are demonstrated through their application to the quantification of electromagnetic coupling in crossing wires.

Evaluation of the effects of an external incident electromagnetic wave on metallic enclosures with rectangular apertures

Abstract: An analytical model is presented, which is useful to evaluate the shielding effectiveness of a rectangular metallic enclosure with a rectangular aperture. The aperture is modeled as a coplanar transmission line, and the enclosure is modeled as a length of a rectangular waveguide ended by a short. The effects of the incident electromagnetic wave are taken into account by using suitable forcing terms in the equations related to the aperture model. The method provides an approximated solution in closed form, and is useful to achieve a fast evaluation of the shielding effectiveness, which can be computed as a function of the enclosure dimensions, the aperture dimensions, and the characteristics of the incident electromagnetic wave. Numerical simulation results are in good agreement with the results given by other theoretical models. Results also compare well with measurement data. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 28: 289–293, 2001.

A quasi three-dimensional distributed electromagnetic model for complex power distribution networks

Abstract: This paper describes a systematic methodology for the electromagnetic modeling of complex power distribution networks. The proposed methodology uses locally three-dimensional modifications to an otherwise two-dimensional description of the behavior of electromagnetic fields between power/ground plane pairs, to model correctly the field behavior at discontinuities such as vias, pins, as well as splits in the power/ground plane structure. Furthermore, a systematic synthesis methodology is presented for the direct generation of a SPICE-compatible multi-port macro-model for the power distribution network from its discrete quasi three-dimensional model. The proposed modeling and equivalent circuit synthesis methodologies are validated through a specific numerical simulation study of the transient electromagnetic analysis of a power/ground plane pair during switching.

Topological Approach to Computational Electromagnetism

Abstract: Software systems designed to solve Maxwell's equations need abstractions that accurately explain what different kinds of electromagnetic problems really do have in common. Computational electromagnetics calls for higher level abstractions than what is typically needed in ordinary engineering problems. In this paper Maxwell's equations are described by exploiting basic concepts of set theory. Although our approach unavoidably increases the level of abstraction, it also simplifies the overall view making it easier to recognize a topological problem behind all boundary value problems modeling the electromagnetic phenomena. This enables us also to construct an algorithm which tackles the topological problem with basic tools of linear algebra.

Scattering by a groove in a conducting plane-a PO-MoM hybrid formulation and wavelet analysis

Abstract: A novel method is presented to solve the two-dimensional (2-D) problem of scattering of an electromagnetic plane wave by a groove in a perfectly conducting infinite plane. In this method, the unknown induced current is expressed in terms of the known physical optics solution of the unperturbed problem of scattering by an infinite conducting plane plus a yet to be determined localized correction current placed in the vicinity of the groove. It is then shown that a good approximation of the induced current can be obtained using only a few dominant functions in the wavelet expansion of the correction current. Moreover, the same set of dominant wavelet functions serves the purpose of approximating the induced current at different angles of incidence. A numerical example demonstrates these various features of the proposed method of solution.

Coupled electromagnetic-circuit simulation of arbitrarily-shaped conducting structures

Abstract: This paper presents a triangular surface mesh-based formulation of the Partial Element Equivalent Circuit (PEEC) approach. Rao-Wilton-Glisson (RWG) basis functions defined on triangular tessellations are used to model arbitrarily-shaped conducting structures via SPICE compatible netlists. This approach is potentially useful for modeling on-chip electromagnetic interactions.

Far-region electromagnetic radiation with a vertical magnetic dipole in sea

Abstract: Great attention has been paid to conveniently calculating the electromagnetic (EM) field due to a vertical magnetic dipole (VMD) buried in stratified media. It is quite difficult because this topic involves the computation of Sommerfeld (1949) type integrals (SI). In this paper closed-form expressions for the far field of a VMD embedded below the sea surface are obtained easily by using a new technique to evaluate the SI with the aid of complex image theory. The present approach can be also used to get the far field formulas for other similar cases.

Electromagnetic, thermal, and structural analysis of RF cavities using ANSYS

Abstract: We report on techniques developed for producing electromagnetic, thermal, and structural solutions to RF cavity design problems in ANSYS, using one model. Methods for preparing imported geometry from solid modeling programs are discussed, and meshing techniques are suggested. A study of mesh density is presented, comparing mesh size with heat flux and Q factor convergence. The general analysis protocol is presented in a stepwise fashion, describing the macros that are used for conducting RF calculations. Finally, these techniques are applied to a proposed RF cavity for the NLC damping rings, which is shown as an example.

The layered medium Green's function—A new look

Abstract: This paper describes an alternate method to formulate the layered medium Green's function suitable for computational electromagnetics. The Green's function is symmetrized so that the reciprocity theorem becomes obvious. Also, the vector differential operators are explicit so that they can be transferred to operate on the basis function and the testing function, as is often done in the method of moments. This alternative formulation of the layered medium Green's function makes it simple to integrate with other computational electromagnetic methods. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 252–255, 2001.

The effects of tall buildings on the measurement of electromagnetic fields due to lightning return strokes

Abstract: A theoretical method is presented to study the effects of tall buildings on the measurement of lightning electromagnetic fields. It is shown that the perturbed electromagnetic fields due to the presence of the metallic structure of a building can be determined using an electric field integral equation in time domain. Simulation results depict that the presence of a tall building can considerably affect the measurement results. However, for a given building, it is possible to calculate the associated antenna enhancement factor in order to correct the measurement results.

Electromagnetic scattering from infinite periodic structures with a localized impurity

Abstract: An accurate hybrid technique for the analysis of electromagnetic scattering from an infinite periodic structure containing an impurity is presented in this paper. The hybrid formulation proposed combines a finite element method/Floquet modal expansion with the method of moments solution of a surface integral equation in the framework of an iterative approach. The impurity within the infinite periodic structure can be constituted by an arbitrary material with an arbitrary shape.