A Time-Domain, Finite-Volume Treatment for the Maxwell Equations
TL;DR: In this paper, the differential form of the time-domain Maxwell's equations are first cast in a conservation form and then solved using a finite-volume discretization procedure derived from proven Computational Fluid Dynamics (CFD) methods.
Abstract: For computation of electromagnetic scattering from layered objects, the differential form of the time-domain Maxwell's equations are first cast in a conservation form and then solved using a finite-volume discretization procedure derived from proven Computational Fluid Dynamics (CFD) methods 1 . The formulation accounts for any variations in the material properties (time, space, and frequency dependent), and can handle thin resistive sheets and lossy coatings by positioning them at finite-volume cell boundaries. The time-domain approach handles both continuous wave (single frequency) and pulse (broadband frequency) incident excitation. Arbitrarily shaped objects are modeled by using a body-fitted coordinate transformation. For treatment of complex internal/external structures with many material layers, a multizone framework with ability to handle any type of zonal boundary conditions (perfectly conducting, flux through, zero flux, periodic, nonreflecting outer boundary, resistive card, and lossy ...
Citations
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01 Dec 2005
TL;DR: The principal computational approaches for Maxwell's equations included the high-frequency asymptotic methods of Keller (1962) as well as Kouyoumjian and Pathak (1974) and the integral equation techniques of Harrington (1968) .
Abstract: Prior to abour 1990, the modeling of electromagnetic engineering systems was primarily implemented using solution techniques for the sinusoidal steady-state Maxwell's equations. Before about 1960, the principal approaches in this area involved closed-form and infinite-series analytical solutions, with numerical results from these analyses obtained using mechanical calculators. After 1960, the increasing availability of programmable electronic digital computers permitted such frequency-domain approaches to rise markedly in sophistication. Researchers were able to take advantage of the capabilities afforded by powerful new high-level programming languages such as Fortran, rapid random-access storage of large arrags of numbers, and computational speeds that were orders of magnitude faster than possible with mechanical calculators. In this period, the principal computational approaches for Maxwell's equations included the high-frequency asymptotic methods of Keller (1962) as well as Kouyoumjian and Pathak (1974) and the integral equation techniques of Harrington (1968) .
941 citations
15 Apr 2005
TL;DR: The finite-difference time-domain (FDTD) solution of the Maxwell's equations is a robust and popular computational technique in science and engineering for modeling electromagnetic wave interactions with complex material structures as mentioned in this paper.
Abstract: The finite-difference time-domain (FDTD ) solution of Maxwell's equations is a robust and popular computational technique in science and engineering for modeling electromagnetic wave interactions with complex material structures. This article reviews key elements of the foundation of FDTD analysis as well as selected recent and emerging FDTD application areas.
Keywords:
finite-difference time domain;
FDTD, Maxwell's equations;
numerical methods;
computations;
electromagnetic waves;
computational electrodynamics
294 citations
Book•
25 Jan 2011TL;DR: This book 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.
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
288 citations
01 Jan 2001
TL;DR: 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.
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.
211 citations
01 Feb 2013
TL;DR: This paper provides a comprehensive review of different DGTD schemes, highlighting the fundamental issues arising in each step of constructing a D GTD system, as well as the implementation of different time-stepping schemes.
Abstract: Efficient multiscale electromagnetic simulations require several major challenges that need to be addressed, such as flexible and robust geometric modeling schemes, efficient and stable time-stepping methods, etc. Due to the versatile choices of spatial discretization and temporal integration, discontinuous Galerkin time-domain (DGTD) methods can be very promising in simulating transient multiscale problems. This paper provides a comprehensive review of different DGTD schemes, highlighting the fundamental issues arising in each step of constructing a DGTD system. The issues discussed include the selection of governing equations for transient electromagnetic analysis, different basis functions for spatial discretization, as well as the implementation of different time-stepping schemes. Numerical examples demonstrate the advantages of DGTD for multiscale electromagnetic simulations.
163 citations
Cites background or methods from "A Time-Domain, Finite-Volume Treatm..."
...One commonly used numerical flux is the Riemann solver [31], [32], which is a type of upwind numerical flux and is derived from the physical process of wave propagation and reflection across an interface between two different media...
[...]
...Moreover, the implementation of numerical fluxes [31]–[33], a critical step in building a DGTD system, is based on both E and H variables....
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References
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TL;DR: In this article, it is shown that these features can be obtained by constructing a matrix with a certain property U, i.e., property U is a property of the solution of the Riemann problem.
8,174 citations
TL;DR: This work develops a systematic method for obtaining a hierarchy of local boundary conditions at these artifical boundaries that not only guarantee stable difference approximations, but also minimize the (unphysical) artificial reflections that occur at the boundaries.
Abstract: In practical calculations, it is often essential to introduce artificial boundaries to limit the area of computation. Here we develop a systematic method for obtaining a hierarchy of local boundary conditions at these artifical boundaries. These boundary conditions not only guarantee stable difference approximations, but also minimize the (unphysical) artificial reflections that occur at the boundaries.
2,648 citations
Book•
01 Jan 1987
TL;DR: Quasi-linear Hyperbolic Equations Conservation Laws Single Conservation Laws The Decay of Solutions as t Tends to infinity Hypothesis of conservation laws Pairs of Conservation Laws as mentioned in this paper.
Abstract: Quasi-linear Hyperbolic Equations Conservation Laws Single Conservation Laws The Decay of Solutions as t Tends to Infinity Hyperbolic Systems of Conservation Laws Pairs of Conservation Laws Notes References.
1,919 citations
TL;DR: In this article, the authors consider the application of explicit Isecond-order, one-sided or "upwind," difference schemes for the numerical solution of hyperbolic systems in conservation-law form.
Abstract: Explicit second-order upwind difference schemes in combination with spatially symmetric schemes can produce larger stability bounds and better numerical resolution than symmetric schemes alone. However, if conservation form is essential, a special operator is required for transition between schemes. An operational approach has been devised for deriving transition operators so that strict conservation and local consistency are maintained. Various aspects of hybrid schemes are studied numerically for model linear and nonlinear equations. To demonstrate the utility of combining two different algorithms, MacCormack's explicit, noncentered, second-order method is combined with a completely upwind version, and numerical solutions of the Euler equations are obtained for two-dimensional, transonic flows with embedded supersonic regions and shock I. Introduction "1T4 this paper we consider the application of explicit Isecond-order, one-sided or "upwind," difference schemes for the numerical solution of hyperbolic systems in conservation-law form = 0
386 citations
TL;DR: In this article, a systematic procedure for constructing semidiscrete, second order accurate, variation diminishing, five-point band width, approximations to scalar conservation laws is presented.
Abstract: A systematic procedure for constructing semidiscrete, second order accurate, variation diminishing, five-point band width, approximations to scalar conservation laws, is presented. These schemes are constructed to also satisfy a single discrete entropy inequality. Thus, in the convex flux case, we prove convergence to the unique physically correct solution. For hyperbolic systems of conservation laws, we formally use this construction to extend the first author’s first order accurate scheme, and show (under some minor technical hypotheses) that limit solutions satisfy an entropy inequality. Results concerning discrete shocks, a maximum principle, and maximal order of accuracy are obtained. Numerical applications are also presented.
317 citations