Showing papers on "Computational electromagnetics published in 2011"

Efficient Modeling of Modular Multilevel HVDC Converters (MMC) on Electromagnetic Transient Simulation Programs

Abstract: The number of semiconductor switches in a modular multilevel converter (MMC) for HVDC transmission is typically two orders of magnitudes larger than that in a two or three level voltage-sourced converter (VSC). The large number of devices creates a computational challenge for electromagnetic transient simulation programs, as it can significantly increase the simulation time. The paper presents a method based on partitioning the system's admittance matrix and deriving an efficient time-varying Thevenin's equivalent for the converter part. The proposed method does not make use of approximate interfaced models, and mathematically, is exactly equivalent to modelling the entire network (converter and external system) as one large network. It is shown to drastically reduce the computational time without sacrificing any accuracy. The paper also presents control algorithms and other modelling aspects. The efficacy of the proposed method is demonstrated by simulating a point-to-point VSC-MMC-based HVDC transmission system.

Differential Evolution as Applied to Electromagnetics

Abstract: In electromagnetics, optimization problems generally require high computational resources and involve a large number of unknowns. They are usually characterized by non-convex functionals and continuous spaces suitable for strategies based on Differential Evolution (DE). In such a framework, this paper is aimed at presenting an overview of Differential Evolution-based approaches used in electromagnetics, pointing out novelties and customizations with respect to other fields of application. Starting from a general description of the evolutionary mechanism of Differential Evolution, Differential Evolution-based techniques for electromagnetic optimization are presented. Some hints on the convergence properties and the sensitivity to control parameters are also given. Finally, a comprehensive coverage of different Differential Evolution formulations in solving optimization problems in the area of computational electromagnetics is presented, focusing on antenna synthesis and inverse scattering.

Introduction to the Finite-Difference Time-Domain (Fdtd) Method for Electromagnetics

Abstract: Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics provides a comprehensive tutorial of the most widely used method for solving Maxwell's equations -- the Finite Difference Time-Domain Method. This book is an essential guide for students, researchers, and professional engineers who want to gain a fundamental knowledge of the FDTD method. It can accompany an undergraduate or entry-level graduate course or be used for self-study. The book provides all the background required to either research or apply the FDTD method for the solution of Maxwell's equations to practical problems in engineering and science. Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics guides the reader through the foundational theory of the FDTD method starting with the one-dimensional transmission-line problem and then progressing to the solution of Maxwell's equations in three dimensions. It also provides step by step guides to modeling physical sources, lumped-circuit components, absorbing boundary conditions, perfectly matched layer absorbers, and sub-cell structures. Post processing methods such as network parameter extraction and far-field transformations are also detailed. Efficient implementations of the FDTD method in a high level language are also provided. Table of Contents: Introduction / 1D FDTD Modeling of the Transmission Line Equations / Yee Algorithm for Maxwell's Equations / Source Excitations / Absorbing Boundary Conditions / The Perfectly Matched Layer (PML) Absorbing Medium / Subcell Modeling / Post Processing

Electromagnetic Field Theory

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Multiscale Compressed Block Decomposition for Fast Direct Solution of Method of Moments Linear System

Abstract: The multiscale compressed block decomposition algorithm (MS-CBD) is presented for highly accelerated direct (non iterative) solution of electromagnetic scattering and radiation problems with the method of moments (MoM). The algorithm is demonstrated to exhibit N2 computational complexity and storage requirements scaling with N1.5, for electrically large objects. Several numerical examples illustrate the efficiency of the method, in particular for problems with multiple excitation vectors. The largest problem presented in this paper is the monostatic RCS of the NASA almond at 50 GHz, for one thousand incidence angles, discretized using 442,089 RWG basis functions. Being entirely algebraic, MS-CBD is independent of the Greens function of the problem.

Parallel and Explicit Finite-Element Time-Domain Method for Maxwell's Equations

Abstract: We construct a parallel and explicit finite-element time-domain (FETD) algorithm for Maxwell's equations in simplicial meshes based on a mixed E- B discretization and a sparse approximation for the inverse mass matrix. The sparsity pattern of the approximate inverse is obtained from edge adjacency information, which is naturally encoded by the sparsity pattern of successive powers of the mass matrix. Each column of the approximate inverse is computed independently, allowing for different processors to be used with no communication costs and hence linear (ideal) speedup in parallel processors. The convergence of the approximate inverse matrix to the actual inverse (full) matrix is investigated numerically and shown to exhibit exponential convergence versus the density of the approximate inverse matrix. The resulting FETD time-stepping is explicit is the sense that it does not require a linear solve at every time step, akin to the finite-difference time-domain (FDTD) method.

An efficient method for computer aided analysis of noisy electromagnetic fields

Abstract: This work presents an efficient method for the numerical simulation of noisy electromagnetic fields, accounting for arbitrary correlations between the noise radiation sources. It allows us to compute the spatial distribution of the spectral energy density. Method of moments is applied to model noisy electromagnetic fields by network methods using correlation matrix techniques. The method can be combined with available electromagnetic modeling tools. Numerical examples, demonstrating the strong influence of the correlation between the sources on the spatial distribution of the radiated noise field are presented.

Theory of electromagnetic fields

Abstract: We discuss the theory of electromagnetic fields, with an emphasis on aspects relevant to radiofrequency systems in particle accelerators. We begin by reviewing Maxwell's equations and their physical significance. We show that in free space, there are solutions to Maxwell's equations representing the propagation of electromagnetic fields as waves. We introduce electromagnetic potentials, and show how they can be used to simplify the calculation of the fields in the presence of sources. We derive Poynting's theorem, which leads to expressions for the energy density and energy flux in an electromagnetic field. We discuss the properties of electromagnetic waves in cavities, waveguides and transmission lines.

Using GPU With CUDA to Accelerate MoM-Based Electromagnetic Simulation of Wire-Grid Models

Abstract: In this letter, a CUDA-enabled graphics processing unit (GPU) accelerated implementation of the method of moments (MoM) for electromagnetic simulation of wire-grid models of arbitrary configurations of conducting surfaces and wires is presented. The solution based on the frequency-domain electric field integral equation (EFIE) discretized using piecewise-linear (triangular) functions for expansion and testing is considered. Some issues pertinent to porting a single-CPU sequential code to an inherently parallel GPU platform are addressed. The GPU numerical results for a user-created benchmark structure are backed up with comparison to CPU results. A noticeable speedup (about 6t) of the overall MoM simulation is achieved due to employing GPU.

Efficient Implementation for 3-D Laguerre-Based Finite-Difference Time-Domain Method

Abstract: When the Laguerre-based finite-difference time-domain (FDTD) method is used for electromagnetic problems, a huge sparse matrix equation results, which is very expensive to solve. We previously introduced an efficient algorithm for implementing an unconditionally stable 2-D Laguerre-based FDTD method. We numerically verified that the efficient algorithm can save CPU time and memory storage greatly while maintaining comparable computational accuracy. This paper presents new efficient algorithm for implementing unconditionally stable 3-D Laguerre-based FDTD method. To do so, a factorization-splitting scheme using two sub-steps is adopted to solve the produced huge sparse matrix equation. For a full update cycle, the presented scheme solves six tri-diagonal matrices for the electric field components and computes three explicit equations for the magnetic field components. A perfectly matched layer absorbing boundary condition is also extended to this approach. In order to demonstrate the accuracy and efficiency of the proposed method, numerical examples are given.

On the use of the method of moments in plasmonic applications

Abstract: [1] In the last 40 years the method of moments (MOM) has been a cornerstone in the field of computational electromagnetics. Traditionally, this method has been used to solve integral equations formulated for antennas and other components in the microwave frequency range and below. In this paper, the application of MOM in the field of plasmonics is briefly reviewed. First, existing literature is referenced. Then the differences with the classical implementations are pointed out. Finally, its applicability, advantages, and disadvantages are discussed. This is done by comparing it with a numerical finite difference time domain solver well-known in the plasmonics research community for a number of example structures. It is shown that also at these higher frequencies, namely in the IR and optical range, MOM is a very powerful technique.

Implicit Runge-Kutta Methods for the Discretization of Time Domain Integral Equations

Abstract: Implicit Runge-Kutta based schemes are proposed for solving the time domain integral equations of electromagnetic theory. The proposed technique maps a Laplace-domain equation to a Ƶ-domain equation using the Butcher tableau of the implicit Runge-Kutta scheme. A discrete time domain system is recovered by computing the inverse Ƶ-transform numerically. The resulting technique is capable of third- or fifth-order accuracy in time, and is stable independent of time step. Numerical results illustrate the accuracy and stability of the technique.

A Semianalytical Spectral Element Method for the Analysis of 3-D Layered Structures

Abstract: A semianalytical spectral element method (SEM) is proposed for electromagnetic simulations of 3-D layered structures. 2-D spectral elements are employed to discretize the cross section of a layered structure, and the Legendre transformation is then used to cast the semidiscretized problem from the Lagrangian system into the Hamiltonian system. A Riccati equation-based high precision integration method is utilized to perform integration along the longitudinal direction, which is the undiscretized direction, to generate the stiffness matrix of the whole layered structure. The final system of equations by the semianalytical SEM will take the form of a set of linear equations with a block tri-diagonal matrix, which can be solved efficiently by the block Thomas algorithm. Numerical examples demonstrate the high efficiency and accuracy of the proposed method.

Efficient Modeling of Three-Dimensional Reverberation Chambers Using Hybrid Discrete Singular Convolution-Method of Moments

Abstract: Efficient modeling of a three-dimensional reverberation chamber (RC) is achieved by combining the discrete singular convolution (DSC) method and the method of moments (MoM). An RC usually consists of a metallic cavity and one or two conducting stirrers, whose size is normally small compared to the chamber size. The large cavity is efficiently modeled by the DSC method, and the stirrer is simulated by the flexible MoM. Exploiting the property of RWG basis, solutions from the two methods are combined together using the equivalence principle. The validity and advantages of the proposed hybrid technique are shown through comparisons with the commercial software FEKO. Employing the high efficiency of the DSC method, the hybrid technique can analyze one stirrer position of a medium-sized RC in a few hundred seconds on a single personal computer, for which FEKO needs thousands of seconds CPU time. The memory requirement of the proposed method is also less than that of FEKO. Furthermore, our hybrid method provides efficient calculation of electric field strength at a large number of field points, which is of great interest in RC analysis. Simulations show that our method only takes 1.7 seconds to compute electric field strength at 4026 field points.

A Meshless Local Petrov–Galerkin Method for Three-Dimensional Scalar Problems

Abstract: In this paper, we apply a meshless method based on local boundary integral equations (LBIEs) to solve electromagnetic problems. The discretization process is carried out through the use of special basis functions that, unlike the Finite Element Method, are not confined to an element and do not require the support of an underlying mesh. The approach herein developed can be applied to general three-dimensional scalar boundary value problems arising in electromagnetism.

FDTD Modeling of Dispersive Bianisotropic Media Using Z-Transform Method

Abstract: The finite-difference time-domain (FDTD) technique for simulating electromagnetic wave interaction with a dispersive chiral medium is extended to include the simulation of dispersive bianisotropic media. Due to anisotropy and frequency dispersion of such media, the constitutive parameters are represented by frequency-dependent tensors. The FDTD is formulated using the Z-transform method, a conventional approach for applying FDTD in frequency-dispersive media. Omega medium is considered as an example of bianisotropic media, the frequency-dependent tensors of which are based on analytical models. The extended FDTD method is used to determine the reflection and transmission coefficients of co- and cross-polarized electromagnetic waves from omega slabs, illuminated by normally incident plane waves. Three cases are simulated: 1) a slab of uniaxial omega medium with its optical axis parallel to the propagation vector; 2) a slab of rotated uniaxial omega medium with its optical axis not parallel to the propagation vector; and 3) a slab of biaxial omega medium. The results are validated by means of comparisons with analytical solutions.

New Development of Parallel Conformal FDTD Method in Computational Electromagnetics Engineering

Abstract: In this paper, we summarize the new development of hardware-acceleration techniques and a parallel conformal Finite-Difference Time-Domain (FDTD) method in computational electromagnetics engineering. We investigate the performance of a parallel conformal FDTD method on different hardware platforms, such as Intel and AMD processors, with vector-arithmetic logic unit (VALU) acceleration, a regular PC cluster, a high-performance server cluster, the use of a graphics-processing unit (GPU), and an IBM CELL processor. The FDTD method, which is parallel in nature, is one of the best candidate numerical methods for using multiple-core processors and computer clusters to efficiently simulate various electromagnetic problems. Several representative examples, such as a UWB (ultra-wideband) antenna array and reflector antennas, are employed to demonstrate the engineering applications of the parallel conformal FDTD method.

Electromagnetic modeling of massively coupled through silicon vias for 3D interconnects

Abstract: This article presents a full-wave electromagnetic approach for analyzing the electrical performance of massively coupled through silicon vias (TSV). The TSVs are modeled with SiO2 insulation coating and are placed in the sandwiched SiO2-Si-SiO2 substrate. The planar guided wave is analyzed to determine the fundamental mode and high order modes in stratified media. Cylindrical wave expansions and Foldy-Lax equations for multiple scattering techniques are adapted to the TSV problems. The effect of SiO2 coating around the via is modeled by the general expression of T-matrix coefficients. Both dispersive silicon loss and copper loss are included in this approach. Numerical simulation of a 4-by-4 TSV array is demonstrated to show the signal performance and crosstalk. It shows that the coupling issues among the TSVs will become significant beyond 15 GHz. The results are in excellent agreement with general purpose field solver. V C 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:1204-1206, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/ mop.26021

A Practical Guide to 3D Electromagnetic Software Tools

Abstract: This chapter considers the numerical analysis of planar antennas. First the fundamental theoretical techniques widely used in the general area of computational electromagnetics are discussed. The focus is on the specific case of planar antennas. Second, several simulation tools implementing these techniques are overviewed. Both commercial and non-commercial tools are considered. Examples found in literat ure are given. Third, three planar antennas are benchmarked, using a variety of tools, in order to show the reader the quality and matureness of the existing tools, and to prove that the analysis of planar antennas is by no means always straightforward. Remaining challenges that still need to be faced and “missing links” are identified, and suggestions are given for the future. In the strictest sense a planar antenna means an antenna flat compared to the wavelength. Although the height of the antennas considered is different from traditional antennas, in most cases no special modeling techniques or software tools are used for planar antennas. Almost all planar antennas reported in literat ure have been designed / analyzed with the well-known techniques and (commercial) software packages. This means that in this chapter the major numerical techniques and software tools used can be overviewed in a general sense, referring to standard literature. These techniques will not be derived or explained here in detail. In stead, this chapter focuses on those aspects that come into the picture when the antenna is planar. After the section on techniques and tools, this chapter will focus on the performance of these techniques and tools for planar antennas. This is done through an overview of benchmarks available in literature. 2. Modeling techniques In this section the full wave solvers are introduced and categorized on the basis of their solution method: Integral Equations (IE) solved by Method of Moments (MoM), Finite Elements (FE), Finite Differences in the Time Domain (FDTD), and Finite Integration Technique (FIT). Based on their theoretical specificities, the application of each method in

Network methods applied to the computation of stochastic electromagnetic fields

Abstract: In this paper we present a methodology for the numerical computation of noisy electromagnetic fields excited by spatially distributed noise sources with arbitrary correlation. The method uses the field transfer function computed for deterministic fields and can be combined with available electromagnetic modeling tools.

Effect of Genetic Algorithm parameters on convergence of the electromagnetic inverse method

Abstract: Nowadays, the EMC researches have been advanced. The evolution, the diversity of the calculation's method and computing resources have to emphasize the investigations dedicated to the electromagnetic modeling method. Thus, we find the electromagnetic inverse method. It attracted the attention of several research's teams. This method can use different methods of optimization and, especially, the Genetic Algorithms (GA). In this work, we apply the electromagnetic inverse method coupled with the method of GA in order to model the radiated emissions of electrical circuits with the electric and magnetic dipole from near field measurement. In this paper, we study the effect of the parameters of Genetic Algorithms on the convergence of the electromagnetic inverse method. To do it, we changed the main parameters of GA in Matlab and we study the effect of each parameter.

Schur Complement Preconditioners for Surface Integral-Equation Formulations of Dielectric Problems Solved with the Multilevel Fast Multipole Algorithm

Abstract: Surface integral-equation methods accelerated with the multilevel fast multipole algorithm (MLFMA) provide a suitable mechanism for electromagnetic analysis of real-life dielectric problems. Unlike the perfect-electric-conductor case, discretizations of surface formulations of dielectric problems yield $2 \times 2$ partitioned linear systems. Among various surface formulations, the combined tangential formulation (CTF) is the closest to the category of first-kind integral equations, and hence it yields the most accurate results, particularly when the dielectric constant is high and/or the dielectric problem involves sharp edges and corners. However, matrix equations of CTF are highly ill-conditioned, and their iterative solutions require powerful preconditioners for convergence. Second-kind surface integral-equation formulations yield better conditioned systems, but their conditionings significantly degrade when real-life problems include high dielectric constants. In this paper, for the first time in the context of surface integral-equation methods of dielectric objects, we propose Schur complement preconditioners to increase their robustness and efficiency. First, we approximate the dense system matrix by a sparse near-field matrix, which is formed naturally by MLFMA. The Schur complement preconditioning requires approximate solutions of systems involving the (1,1) partition and the Schur complement. We approximate the inverse of the (1,1) partition with a sparse approximate inverse (SAI) based on the Frobenius norm minimization. For the Schur complement, we first approximate it via incomplete sparse matrix-matrix multiplications, and then we generate its approximate inverse with the same SAI technique. Numerical experiments on sphere, lens, and photonic crystal problems demonstrate the effectiveness of the proposed preconditioners. In particular, the results for the photonic crystal problem, which has both surface singularity and a high dielectric constant, shows that accurate CTF solutions for such problems can be obtained even faster than with second-kind integral equation formulations, with the acceleration provided by the proposed Schur complement preconditioners.

Electromagnetic Modeling of Breaking Waves at Low Grazing Angles With Adaptive Higher Order Hierarchical Legendre Basis Functions

Abstract: At low grazing angles (LGA), sophisticated electromagnetic scattering of sea surfaces may give rise to complicated surface-current distribution. Therefore, for the multilevel fast multipole algorithm (MLFMA) with the Rao-Wilton-Glisson basis function, the sea scatterer must be meshed fine enough to ensure the precision of the scattering at LGA, which brings huge computational costs. The higher order hierarchical Legendre vector basis functions can bring a great reduction of the unknowns and sparsification of the impedance matrix. The MLFMA with higher order hierarchical Legendre basis functions is applied in the electromagnetic-scattering approach of 3-D breaking water wave crests at LGA for the first time. In addition, an adaptive-order technique is also introduced for the first time in describing the currents which can achieve accurate results and maximally reduce the computational costs from some case analysis. It has been investigated in analyzing the vertically (VV) and horizontally (HH) polarized scattering of profiles of the LONGTANK breaking waves. "Sea-spike" phenomenon has been demonstrated at LGA.

A fast modeling method to solve Maxwell's equations in 1D layered biaxial anisotropic medium

Abstract: A fast 1D electromagnetic modeling method has been developed and tested. It allows simulating triaxial responses of induction and propagation resistivity logging tools for both logging-while-drilling and wireline applications. An important new feature of the method is its ability to model resistivity tool responses in 1D biaxial anisotropic medium, whose anisotropy tensor has up to three different principal values. This feature is particularly useful to evaluate fractured formations. A few possible implementations of the method have been suggested. The modeling code has been extensively tested versus three other independent modeling methods. The new method demonstrates a high sensitivity of transverse and cross couplings of triaxial tensor measurement to all three principal values of the conductivity tensor.

Conformal FDTD Modeling of Imperfect Conductors at Millimeter Wave Bands

Abstract: The Dey-Mittra conformal finite difference time domain (CFDTD) algorithm for perfect electrical conductors is modified for the analysis of finite conductivity conductors at millimeter wave frequencies. Formulas are derived for CFDTD coefficients using voltage state variables and a constant surface impedance boundary condition (SIBC). The approach permits a fast implementation suitable for CUDA type GPU hardware. Accuracy and stability are investigated with respect to the stability constraints on intersection areas introduced by Dey-Mittra and Benkler as well as the distance stability constraints of Zagorodnov that permits 100% Courant temporal sampling. A relaxation of the Zagorodnov distance constraints permits increased accuracy with respect to all alternative area constraints. Analytic solutions are used to judge the performance of the proposed CFDTD modifications for millimeter wave band applications.

The WLP-FDTD Method for Periodic Structures With Oblique Incident Wave

Abstract: A new unconditionally stable finite-difference time-domain (FDTD) method for periodic structures is presented, which is based on the field transformation method and the weighted Laguerre polynomials FDTD (WLP-FDTD). The proposed method uses a field transformation to remove the time gradient across the grid, and then uses the concept of the WLP-FDTD to get the implicit relationship between the transformed field variables. It holds the advantages of the WLP-FDTD, can eliminate the restriction of the Courant-Friedrich-Levy (CFL) stability condition. Compared with other field transform methods, the new method needn't to do special treatment for the additional terms. It appears to be much more efficient than the other field transformation FDTD method for solving periodic structures with fine structures and large incident angle. To verify the accuracy and the efficiency of the proposed method, we compare the results of the Split-Field FDTD method with the proposed method.

A Mixed-Form Thin-Stratified Medium Fast-Multipole Algorithm for Both Low and Mid-Frequency Problems

Abstract: A mixed-form thin-stratified medium fast-multipole algorithm is proposed for fast simulation of general microstrip structures at both low and mid-frequencies. The newly developed matrix-friendly formula of layered medium Green's function is applied in this algorithm. For well-separated interactions, the path deformation technique is implemented to achieve a smoother and exponentially convergent integral. The two-dimensional addition theorem is then incorporated into the integrand to expedite the matrix-vector product. In our approach, multipole expansion (low-frequency fast-multiple algorithm) as well as the plane wave expansion (mid-frequency fast-multipole algorithm) of the translational addition theorem are combined into a single multilevel tree to capture quasi-static physics and wave physics simultaneously. The outgoing wave is represented first in terms of multipole expansion at leafy levels, and then switched to plane wave expansion automatically at higher levels. This seamless connection makes the algorithm applicable in simulations, where subwavelength interaction and wave physics both exist.

Efficient Time-Domain Simulations of a Helix Traveling-Wave Tube

Abstract: An efficient time-domain discrete model of the interaction of an electron beam with an electromagnetic wave propagating in a slow-wave structure has been described by Kuznetsov. Using a projection of Maxwell's equations onto the eigenmodes of the structure, the evolution of the entire electromagnetic field can be reduced to the evolution of its amplitude alone in each period of the waveguide. The number of degrees of freedom of the system is thus greatly reduced. This model has been successfully applied in the case of coupled-cavity traveling-wave tubes (TWTs) and can be applied to klystrons, where the circuit field is localized between the gaps of the cavities. In this paper, we present the results of numerical simulations performed by applying this model to a helix TWT. We show that the results obtained are in very good agreement with theory. We also compare our results with those from frequency-domain TWT simulation software.

Analysis of Dielectric Photonic-Crystal Problems With MLFMA and Schur-Complement Preconditioners

Abstract: We present rigorous solutions of electromagnetics problems involving 3-D dielectric photonic crystals (PhCs). Problems are formulated with recently developed surface integral equations and solved iteratively using the multilevel fast multipole algorithm (MLFMA). For efficient solutions, iterations are accelerated via robust Schur-complement preconditioners. We show that complicated PhC structures can be analyzed with unprecedented efficiency and accuracy by an effective solver based on the combined tangential formulation, MLFMA, and Schur-complement preconditioners.