166652
Meep: A flexible free-software package for electromagnetic simulations by the FDTD method
This paper describes Meep, a popular free implementation of the finite-difference time-domain (FDTD) method for simulating electromagnetism. In particular, we focus on aspects of implementing a full-featured FDTD package that go beyond standard textbook descriptions of the algorithm, or ways in which Meep differs from typical FDTD implementations. These include pervasive interpolation and accurate modeling of subpixel features, advanced signal processing, support for nonlinear materials via Pade approximants, and flexible scripting capabilities.
63470895
Numerical Techniques in Electromagnetics
Numerical Techniques in Electromagnetics is designed to show the reader how to pose, numerically analyze, and solve electromagnetic (EM) problems. It gives them the ability to expand their problem-solving skills using a variety of available numerical methods. Topics covered include fundamental concepts in EM; numerical methods; finite difference methods; variational methods, including moment methods and finite element methods; transmission-line matrix or modeling (TLM); and Monte Carlo methods. The simplicity of presentation of topics throughout the book makes this an ideal text for teaching or self-study by senior undergraduates, graduate students, and practicing engineers.
124875203
Electromagnetic Theory and Applications for Photonic Crystals
Provides comprehensive theoretical treatment of periodic structures based on general electro -magnetic theory Presents the original work of the authors, all recognized experts in their fields Builds a theoretical basis for periodic structures applicable to photonic crystals in optical to microwave regions Progresses smoothly and logically from analytical to numerical to computational approaches Illustrates the discussion with more than 250 figures and 1000 equations
121500906
Electromagnetic scattering by surfaces of arbitrary shape
The electric field integral equation (EFIE) is used with the moment method to develop a simple and efficient numerical procedure for treating problems of scattering by arbitrarily shaped objects. For numerical purposes, the objects are modeled using planar triangular surfaces patches. Because the EFIE formulation is used, the procedure is applicable to both open and closed surfaces. Crucial to the numerical formulation is the development of a set of special subdomain-type basis functions which are defined on pairs of adjacent triangular patches and yield a current representation free of line or point charges at subdomain boundaries. The method is applied to the scattering problems of a plane wave illuminated flat square plate, bent square plate, circular disk, and sphere. Excellent correspondence between the surface current computed via the present method and that obtained via earlier approaches or exact formulations is demonstrated in each case.
11306419
Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects
The recent development and extension of the method of moments technique for analyzing electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects is presented based on the combined field integral equations. The surfaces of the homogeneous three-dimensional arbitrary geometrical shapes are modeled using surface triangular patches, similar to the case of arbitrary shaped conducting objects. Further, the development and extensions required to treat efficiently three-dimensional lossy dielectric objects are reported. Numerical results and their comparisons are also presented for two canonical dielectric scatterers-a sphere and a finite circular cylinder.
117939049
Boundary Integral Equation Methods for Solids and Fluids
Note: Includes index and bibliography Reference Record created on 2004-09-07, modified on 2016-08-08
57268963
Fast and Efficient Algorithms in Computational Electromagnetics
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.
18284413
Perturbation theory for Maxwell's equations with shifting material boundaries.
Perturbation theory permits the analytic study of small changes on known solutions, and is especially useful in electromagnetism for understanding weak interactions and imperfections. Standard perturbation-theory techniques, however, have difficulties when applied to Maxwell's equations for small shifts in dielectric interfaces (especially in high-index-contrast, three-dimensional systems) due to the discontinuous field boundary conditions--in fact, the usual methods fail even to predict the lowest-order behavior. By considering a sharp boundary as a limit of anisotropically smoothed systems, we are able to derive a correct first-order perturbation theory and mode-coupling constants, involving only surface integrals of the unperturbed fields over the perturbed interface. In addition, we discuss further considerations that arise for higher-order perturbative methods in electromagnetism.
15039755
Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis.
We describe a fully-vectorial, three-dimensional algorithm to compute the definite-frequency eigenstates of Maxwell's equations in arbitrary periodic dielectric structures, including systems with anisotropy (birefringence) or magnetic materials, using preconditioned block-iterative eigensolvers in a planewave basis. Favorable scaling with the system size and the number of computed bands is exhibited. We propose a new effective dielectric tensor for anisotropic structures, and demonstrate that O Delta x;2 convergence can be achieved even in systems with sharp material discontinuities. We show how it is possible to solve for interior eigenvalues, such as localized defect modes, without computing the many underlying eigenstates. Preconditioned conjugate-gradient Rayleigh-quotient minimization is compared with the Davidson method for eigensolution, and a number of iteration variants and preconditioners are characterized. Our implementation is freely available on the Web.
27567922
FDTD analysis of wave propagation in nonlinear absorbing and gain media
An explicit finite-difference time-domain (FDTD) scheme for wave propagation in certain kinds of nonlinear media such as saturable absorbers and gain layers in lasers is proposed here. This scheme is an extension of the auxiliary differential equation FDTD approach and incorporates rate equations that govern the time-domain dynamics of the atomic populations in the medium. For small signal intensities and slowly varying pulses, this method gives the same results as frequency-domain methods using the linear susceptibility function. Population dynamics for large signal intensities and the transient response for rapidly varying pulses in two-level (absorber) and four-level (gain) atomic media are calculated to demonstrate the advantages of this approach.
18541390
Finite-difference time-domain model of lasing action in a four-level two-electron atomic system.
We report a new finite-difference time-domain (FDTD) computational model of the lasing dynamics of a four-level two-electron atomic system. Transitions between the energy levels are governed by coupled rate equations and the Pauli Exclusion Principle. This approach is an advance relative to earlier FDTD models that did not include the pumping dynamics, or the Pauli Exclusion Principle. Further, the method proposed in this paper is more versatile than the conventional modal expansion of the electromagnetic field for complex inhomogeneous laser geometries constructed in photonic crystals or light-localizing random media. For such complex geometries, the lasing modes are either difficult or impossible to calculate. The present work aims at the self-consistent treatment of the dynamics of the 4-level atomic system and the instantaneous ambient optical electromagnetic field. This permits in principle a much more robust treatment of the overall lasing dynamics of four-level gain systems integrated into virtually arbitrary electromagnetic field confinement geometries.
38452318
Computational model of solid-state, molecular, or atomic media for FDTD simulation based on a multi-level multi-electron system governed by Pauli exclusion and Fermi-Dirac thermalization with application to semiconductor photonics.
We report a general computational model of complex material media for electrodynamics simulation using the Finite-Difference Time-Domain (FDTD) method. It is based on a multi-level multi-electron quantum system with electron dynamics governed by Pauli Exclusion Principle, state filling, and dynamical Fermi-Dirac Thermalization, enabling it to treat various solid-state, molecular, or atomic media. The formulation is valid at near or far off resonance as well as at high intensity. We show its FDTD application to a semiconductor in which the carriers' intraband and interband dynamics, energy band filling, and thermal processes were all incorporated for the first time. The FDTD model is sufficiently complex and yet computationally efficient, enabling it to simulate nanophotonic devices with complex electromagnetic structures requiring simultaneous solution of the mediumfield dynamics in space and time. Applications to direct-gap semiconductors, ultrafast optical phenomena, and multimode microdisk lasers are illustrated.
15177490
Active materials embedded in photonic crystals and coupled to electromagnetic radiation
A calculational scheme is presented to model the interaction of light with active dielectric media, represented by four-level atomic materials, surrounded by photonic crystals. Optically pumped lasing is studied in three model systems: a Fabry-Perot cavity, a line of defects in a two-dimensional square lattice of rods, and a cylindrical photonic crystal. Field profiles and conversion efficiencies are calculated for these systems. It is shown that high conversion efficiency can be achieved for large regions of active material in the cavity, as well as for a single fluorescent atom in a hollow-core cylindrical photonic crystal, suggesting designs for ultralowthreshold lasers and ultrasensitive biological sensors.
53869495
Adaptive mesh refinement for hyperbolic partial differential equations
We present an adaptive method based on the idea of multiple, component grids for the solution of hyperbolic partial differential equations using finite difference techniques. Based upon Richardson-type estimates of the truncation error, refined grids are created or existing ones removed to attain a given accuracy for a minimum amount of work. Our approach is recursive in that fine grids can themselves contain even finer grids. The grids with finer mesh width in space also have a smaller mesh width in time, making this a mesh refinement algorithm in time and space. We present the algorithm, data structures and grid generation procedure, and conclude with numerical examples in one and two space dimensions.
120941554
A local mesh refinement algorithm for the time domain-finite difference method using Maxwell's curl equations
An efficient local mesh refinement algorithm, subdividing a computational domain to resolve fine dimensions in a time-domain-finite-difference (TD-FD) space-time grid structure, is discussed. At a discontinuous coarse-fine mesh interface, the boundary conditions for the tangential and normal field components are enforced for a smooth transition of highly nonuniform held quantities. >
124031375
A subgridding method for the time-domain finite-difference method to solve Maxwell's equations
A modification to the time-domain finite-difference method (TDFDM) that uses a variable step size is investigated. The entire computational volume is divided into a coarse grid with a large step size. A fine grid with a small step size is introduced only around discontinuities. The corresponding time increments are related to the spatial increments with the same ratio in order to minimize the numerical dispersion. The fields within the coarse and fine grids are found using the TDFDM, while an interpolation in space and time is utilized to calculate the tangential electric field on the coarse-fine grid boundary. This subgridding decreases the required computer memory and therefore expands the capability of the TDFDM. The technique is shown to be numerically stable and does not entail any extra numerical error. The method is applied to the calculation of waveguides and microstrips. >
62364608
Three-dimensional subgridding algorithm for FDTD
In many computational problems solved using the finite-difference time-domain (FDTD) technique, there is a need to model selected volumes with higher resolution than the whole computational space. An efficient algorithm has been developed for this purpose that provides the mesh refinement by the factor of two in each direction. The algorithm can be used in two-dimensional (2-D) and three-dimensional (3-D) problems and provides for subgridding in both space and time. Performance of the 3-D algorithm was tested in waveguides and resonators. A high accuracy and efficiency were observed in all test cases with insignificant (of an order of -60 dB) reflections from mesh interfaces. Practical applications of the algorithm in the analyses of a resonator with a dielectric rod and of a cellular phone behavior in the vicinity of the operator head are also reported.
60957569
Principles of Parallel Programming
With the rise of multi-core architecture, parallel programming is an increasingly important topic for software engineers and computer system designers. Written by well-known researchers Larry Snyder and Calvin Lin, this highly anticipated first edition emphasizes the principles underlying parallel computation, explains the various phenomena, and clarifies why these phenomena represent opportunities or barriers to successful parallel programming. Ideal for an advanced upper-level undergraduate course, Parallel Programming supplies enduring knowledge that will outlive the current hardware and software, aiming to inspire future researchers to build tomorrow's solutions. "...the first basic book on the subject that I've ever seen that seems to have the pulse on the true issues of parallelism that are relevant for students." --Alan Edelman, MIT "Principles of Parallel Programming is a wonderful book and I plan to use it in our new parallel programming course..."---Peiyi Tang, University of Arkansas, Little Rock "I like [Principles of Parallel Programming] very much for a few specific reasons: it's concise, covers the most relevant topics but does not take thousand pages to do it, it is hands on and it covers. ..recent developments with multi-core and GPGPU." --Edin Hodzic, Santa Clara University
117130101
Photonic Crystals: Molding the Flow of Light
Since it was first published in 1995, Photonic Crystals has remained the definitive text for both undergraduates and researchers on photonic band-gap materials and their use in controlling the propagation of light. This newly expanded and revised edition covers the latest developments in the field, providing the most up-to-date, concise, and comprehensive book available on these novel materials and their applications. Starting from Maxwell's equations and Fourier analysis, the authors develop the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory. They then investigate the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions. This new edition includes entirely new chapters describing important hybrid structures that use band gaps or periodicity only in some directions: periodic waveguides, photonic-crystal slabs, and photonic-crystal fibers. The authors demonstrate how the capabilities of photonic crystals to localize light can be put to work in devices such as filters and splitters. A new appendix provides an overview of computational methods for electromagnetism. Existing chapters have been considerably updated and expanded to include many new three-dimensional photonic crystals, an extensive tutorial on device design using temporal coupled-mode theory, discussions of diffraction and refraction at crystal interfaces, and more. Richly illustrated and accessibly written, Photonic Crystals is an indispensable resource for students and researchers.Extensively revised and expanded Features improved graphics throughout Includes new chapters on photonic-crystal fibers and combined index-and band-gap-guiding Provides an introduction to coupled-mode theory as a powerful tool for device design Covers many new topics, including omnidirectional reflection, anomalous refraction and diffraction, computational photonics, and much more.
122262112
Electrodynamics of continuous media
Electrostatics of conductors Static magnetic field Superconductivity The propagation of electromagnetic waves Spatial dispersion Diffraction of X rays in crystals.
31514933
Improving accuracy by subpixel smoothing in the finite-difference time domain.
Finite-difference time-domain (FDTD) methods suffer from reduced accuracy when modeling discontinuous dielectric materials, due to the inhererent discretization (pixelization). We show that accuracy can be significantly improved by using a subpixel smoothing of the dielectric function, but only if the smoothing scheme is properly designed. We develop such a scheme based on a simple criterion taken from perturbation theory and compare it with other published FDTD smoothing methods. In addition to consistently achieving the smallest errors, our scheme is the only one that attains quadratic convergence with resolution for arbitrarily sloped interfaces. Finally, we discuss additional difficulties that arise for sharp dielectric corners.
37630110
Convergent Cartesian Grid Methods for Maxwell's Equations in Complex Geometries
A convergent second-order Cartesian grid finite difference scheme for the solution of Maxwell's equations is presented. The scheme employs a staggered grid in space and represents the physical location of the material and metallic boundaries correctly, hence eliminating problems caused by staircasing, and, contrary to the popular Yee scheme, enforces the correct jump-conditions on the field components across material interfaces. A detailed analysis of the accuracy of the new embedding scheme is presented, confirming its second-order global accuracy. Furthermore, the scheme is proven to be a bounded error scheme and thus convergent. Conditions for fully discrete stability is furthermore established. This enables the derivation of bounds for fully discrete stability with CFL-restrictions being almost identical to those of the much simpler Yee scheme. The analysis exposes that the effects of staircasing as well as a lack of properly enforced jump-conditions on the field components have significant consequences for the global accuracy. It is, among other things, shown that for cases in which a field component is discontinuous along a grid line, as happens at general two- and three-dimensional material interfaces, the Yee scheme may exhibit local divergence and loss of global convergence, To validate the analysis several one- and two-dimensional test cases are presented, showing an improvement of typically 1 to 2 orders of accuracy at little or no additional computational cost over the Yee scheme, which in most cases exhibits First order accuracy. (C) 2001 Academic Press.
7085577
Accurate finite-difference time-domain simulation of anisotropic media by subpixel smoothing.
Finite-difference time-domain methods suffer from reduced accuracy when discretizing discontinuous materials. We previously showed that accuracy can be significantly improved by using subpixel smoothing of the isotropic dielectric function, but only if the smoothing scheme is properly designed. Using recent developments in perturbation theory that were applied to spectral methods, we extend this idea to anisotropic media and demonstrate that the generalized smoothing consistently reduces the errors and even attains second-order convergence with resolution.
2268286
Perturbation theory for anisotropic dielectric interfaces, and application to subpixel smoothing of discretized numerical methods.
We derive a correct first-order perturbation theory in electromagnetism for cases where an interface between two anisotropic dielectric materials is slightly shifted. Most previous perturbative methods give incorrect results for this case, even to lowest order, because of the complicated discontinuous boundary conditions on the electric field at such an interface. Our final expression is simply a surface integral, over the material interface, of the continuous field components from the unperturbed structure. The derivation is based on a "localized" coordinate-transformation technique, which avoids both the problem of field discontinuities and the challenge of constructing an explicit coordinate transformation by taking the limit in which the coordinate perturbation is infinitesimally localized around the boundary. Not only is our result potentially useful in evaluating boundary perturbations, e.g., from fabrication imperfections, in highly anisotropic media such as many metamaterials, but it also has a direct application in numerical electromagnetism. In particular, we show how it leads to a subpixel smoothing scheme to ameliorate staircasing effects in discretized simulations of anisotropic media, in such a way as to greatly reduce the numerical errors compared to other proposed smoothing schemes.
108635967
A conformal finite-difference time-domain technique for modeling cylindrical dielectric resonators
In this paper, we present a generalization of the conformal finite-difference time-domain technique, which we introduced earlier for analyzing curved metallic objects. The new scheme enables us to model arbitrarily shaped metallic as well as dielectric objects, and is based on the concept of weighted-volume effective dielectric constant. Its accuracy and usefulness are shown by modeling both open- and closed-type dielectric resonators.
31012269
Accurate theoretical analysis of photonic band-gap materials.
Two improvements for the solution of Maxwell's equations in periodic dielectric media are introduced, abandoning the plane-wave cutoff and interpolating the dielectric function. These improvements permit the accurate study of previously inaccessible systems. Example calculations are discussed, employing a basis of ∼10 6 plane waves for which these two improvements reduce both the memory and central processing unit requirements by ∼10 4
1983075
A stable FDTD algorithm for non-diagonal, anisotropic dielectrics
A stable FDTD algorithm is developed for simulating Maxwell’s equations in anisotropic dielectric materials with principal axes not aligned with the grid. The algorithm is stable because the finite-difference operator that converts D to E is symmetric and positive semidefinite; for contrast, a previously developed asymmetric algorithm is shown to suffer from late-time instabilities. The presented algorithm has second-order error for continuous dielectric materials, and the error can be reduced to third-order by Richardson extrapolation. Applied to dielectrics with sharp interfaces, the algorithm has first-order error, even when averaging the dielectric within partially filled grid cells. However, averaging the dielectric permits Richardson extrapolation to obtain second-order error.
122966116
A simple way to model curved metal boundaries in FDTD algorithm avoiding staircase approximation
The conventional FDTD algorithm in Cartesian coordinates uses staircase approximation to treat curvilinear surfaces. This approximation causes loss of accuracy often unacceptable. An extremely simple and more accurate polygonal approximation of curved surfaces is proposed in this paper. The method improves significantly the accuracy of the original FDTD algorithm, without increasing its complexity. >
110400811
Practical 3-D contour/staircase treatment of metals in FDTD
The standard finite-difference time-domain (FDTD) method incorporates an inaccurate staircase representation of perfect electric conductors. More accurate, contour-type update formulas have been proposed. These approaches suffer from bookkeeping complexity, difficulties in mesh generation, and stability problems. Only simplified special cases have been implemented in three dimensions. A new contour-like FDTD algorithm is presented. Subcell formulas and staircase logic are combined to produce a three-dimensional (3-D) algorithm that is simple, robust, and fully automatic.
20326797
Subpixel smoothing for conductive and dispersive media in the finite-difference time-domain method.
Staircasing of media properties is one of the intrinsic problems of the finite-difference time-domain method, which reduces its accuracy. There are different approaches for solving this problem, and the most successful of them are based on correct approximation of inverse permittivity tensor epsilon(-1) at the material interface. We report an application of this tensor method for conductive and dispersive media. For validation, comparisons with analytical solutions and various other subpixel smoothing methods are performed for the Mie scattering from a small sphere.
13205982
Roughness losses and volume-current methods in photonic-crystal waveguides
We present predicted relative scattering losses from sidewall roughness in a strip waveguide compared to an identical waveguide surrounded by a photonic crystal with a complete or incomplete gap in both 2d and 3d. To do so, we develop a new semi-analytical extension of the classic “volume-current method” (Green’s functions with a Born approximation), correcting a longstanding limitation of such methods to low-index contrast systems (the classic method may be off by an order of magnitude in high-contrast systems). The resulting loss predictions show that even incomplete gap structures such as photonic-crystal slabs should, with proper design, be able to reduce losses by a factor of two compared to an identical strip waveguide; however, incautious design can lead to increased losses in the photonic-crystal system, a phenomena that we explain in terms of the band structure of the unperturbed crystal.
34613748
The failure of perfectly matched layers, and towards their redemption by adiabatic absorbers.
Although perfectly matched layers (PMLs) have been widely used to truncate numerical simulations of electromagnetism and other wave equations, we point out important cases in which a PML fails to be reflectionless even in the limit of infinite resolution. In particular, the underlying coordinate-stretching idea behind PML breaks down in photonic crystals and in other structures where the material is not an analytic function in the direction perpendicular to the boundary, leading to substantial reflections. The alternative is an adiabatic absorber, in which reflections are made negligible by gradually increasing the material absorption at the boundaries, similar to a common strategy to combat discretization reflections in PMLs. We demonstrate the fundamental connection between such reflections and the smoothness of the absorption profile via coupled-mode theory, and show how to obtain higher-order and even exponential vanishing of the reflection with absorber thickness (although further work remains in optimizing the constant factor).
11780701
Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates
A simple and systematic derivation of anisotropic perfectly matched layers (PMLs) in cylindrical and spherical coordinates is presented. The derivation is based on the analytic continuation of Maxwell's equations to complex space. Through field transformations, results for Cartesian anisotropic PML media are recovered and, more importantly, a generalization of the anisotropic PML to cylindrical and spherical systems is obtained, providing further clarification on the PML concept. As expected, these new PML media are cylindrically and spherically layered, respectively.
31763498
A nonuniform cylindrical FDTD algorithm with improved PML and quasi-PML absorbing boundary conditions
Many applications require time-domain solutions of Maxwell's equations in inhomogeneous, conductive media involving cylindrical geometries with both electrically small and large structures. The conventional finite-difference time-domain (FDTD) method with a uniform Cartesian grid will result in a staircasing error, and wastes many unnecessary cells in regions with large structures in order to accommodate the accurate geometrical representation in regions with small structures. In this work, an explicit FDTD method with a nonuniform cylindrical grid is developed for time-domain Maxwell's equations. A refined lattice is used near sharp edges and within fine geometrical details, while a larger lattice is used outside these regions. This provides an efficient use of limited computer memory and computation time. The authors use two absorbing boundary conditions to a nonuniform cylindrical grid: (1) the straightforward extension of Berenger's perfectly matched layer (PML) which is no longer perfectly matched for cylindrical interfaces, thus the name quasi-PML, (QPML); (2) the improved true PML based on complex coordinates. In practice, both PML schemes can provide a satisfactory absorbing boundary condition. Numerical results are shown to compare the two absorbing boundary conditions (ABCs) and to demonstrate the effectiveness of the nonuniform grid and the absorbing boundary conditions.
63180999
Discrete-Time Signal Pro-cessing
For senior/graduate-level courses in Discrete-Time Signal Processing. THE definitive, authoritative text on DSP -- ideal for those with an introductory-level knowledge of signals and systems. Written by prominent, DSP pioneers, it provides thorough treatment of the fundamental theorems and properties of discrete-time linear systems, filtering, sampling, and discrete-time Fourier Analysis. By focusing on the general and universal concepts in discrete-time signal processing, it remains vital and relevant to the new challenges arising in the field --without limiting itself to specific technologies with relatively short life spans.
55729064
Computation of resonant frequencies and quality factors of cavities by FDTD technique and Pade approximation
The finite-difference time domain (FDTD) technique and the Pade approximation with Baker's algorithm are used to calculate the mode frequencies and quality factors of cavities. Comparing with the fast Fourier transformation/Pade method, we find that the Pade approximation and the Baker's algorithm can obtain exact resonant frequencies and quality factors based on a much shorter time record of the FDTD output.
41518782
Algebraic Computations of Scaled Padé Fractions
Two companion algorithms are developed for constructing Pade fractions along an off-diagonal path of the Pade table for a function ${{ - A(z)} / {B(z)}}$, where $A(z)$ and $B(z)$ are formal power series over a field.One of the algorithms computes the first n Pade fractions along the off-diagonal in time $O(n^2 )$. When $A(z)$ and $B(z)$ are finite power series (i.e., polynomials), it is shown that the algorithm is equivalent to Euclid’s extended algorithm for computing greatest common divisors.The other algorithm, a generalization of the first, proceeds along the off-diagonal in quadratic steps, and is of complexity $O(n\log ^2 n)$. When $A(z)$ and $B(z)$ are polynomials, the second algorithm becomes a fast Euclid’s extended algorithm for computing greatest common divisors. The algorithm is of the same complexity as other fast greatest common divisor methods, but its iterative nature provides a practical advantage during implementation.The algorithms may also be used for computing Pade fractions along an ...
20409193
Disorder-immune confinement of light in photonic-crystal cavities.
We demonstrate by finite-difference time-domain simulations in 2D and 3D that optical cavities in realistic finite photonic crystals have lifetimes and modal volumes that are essentially insensitive to disorder (of various types, including surface disorder and randomized positions), even with unphysically large disorder. A lifetime Q = 10(8) is demonstrated in a 3D single-mode cavity with a half-wavelength mode diameter using only eight vertical periods of a disordered crystal.
95591224
Harmonic inversion of time signals and its applications
New methods of high resolution spectral analysis of short time signals are presented. These methods utilize the filter-diagonalization approach of Wall and Neuhauser [J. Chem. Phys. 102, 8011 (1995)] that extracts the complex frequencies ωk and amplitudes dk from a signal C(t)=∑kdke−itωk in a small frequency interval by recasting the harmonic inversion problem as the one of a small matrix diagonalization. The present methods are rigorously adapted to the conventional case of the signal available on a sparse equidistant time grid and use a more efficient boxlike filter. Various applications are discussed, such as iterative diagonalization of large Hamiltonian matrices for calculating bound and resonance states, scattering calculations in the presence of narrow resonances, etc. For the scattering problem the harmonic inversion is directly applied to the signal cn=(χf,Tn(Ĥ)χi), generated by the dynamical system governed by a modified Chebyshev recursion, avoiding the usual recasting the problem to the time d...
110599569
Efficient computation of resonant frequencies and quality factors of cavities via a combination of the finite-difference time-domain technique and the Pade approximation
An efficient method for analyzing cavity structures by using the fast Fourier transform (FFT)/Pade technique, in combination with the finite-difference time-domain (FDTD) method, is presented. Without sacrificing the accuracy of the results, this new method significantly reduces the computational time compared to that needed where the conventional FFT algorithm is used. The usefulness of this approach is demonstrated by modeling a lossy cavity and computing its resonant frequencies as well as Q.
109511460
Three-Dimensional Finite-Difference Method for the Analysis of Microwave-Device Embedding
The embedding of microwave devices is treated by applying the finite-difference method to three-dimensional shielded structures. A program package was developed to evaluate electromagnetic fields inside arbitrary transmission-line connecting structures and to compute the scattering matrix. The air bridge, the transition through a wall, and the bond wire are examined as interconnecting structures. Detailed results are given and discussed regarding the fundamental behavior of embedding.
15815197
Templates for the solution of linear systems: building blocks for iterative methods
In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist. Templates, a description of a general algorithm rather than the executable object or source code more commonly found in a conventional software library, offer whatever degree of customization the user may desire.
2208787
BiCGstab(ell) for Linear Equations involving Unsymmetric Matrices with Complex Spectrum
For a number of linear systems of equations arising from realistic problems, using the Bi-CGSTAB algorithm of van der Vorst [17] to solve these equations is very attractive. Unfortunately, for a large class of equations, where, for instance, Bi-CG performs well, the convergence of BiCGSTAB stagnates. This was observed specifically in case of discretized advection dominated PDE’s. The stagnation is due to the fact that for this type of equations the matrix has almost pure imaginary eigenvalues. With his BiCGStab2 algorithm Gutknecht [5] attempted to avoid this stagnation. Here, we generalize the Bi-CGSTAB algorithm further, and overcome some shortcomings of BiCGStab2. In some sense, the new algorithm combines GMRES(l) and Bi-CG and profits from both.
45251313
A quarter century of UNIX
No wonder you activities are, reading will be always needed. It is not only to fulfil the duties that you need to finish in deadline time. Reading will encourage your mind and thoughts. Of course, reading will greatly develop your experiences about everything. Reading quarter century of unix is also a way as one of the collective books that gives many advantages. The advantages are not only for you, but for the other peoples with those meaningful benefits.
61087118
HDF: an update and future directions
HDF (Hierarchical Data Format) is a scientific data management project providing basic tools for managing scientific data, and support for scientists who use HDF software (http://hdf.ncsa.uiuc.edu/). HDF products include two distinct data formats, HDF4 and HDF5, supporting libraries for reading and writing HDF data, and utilities for working with HDF. Available since 1988, HDF has become a standard for scientific data archiving and data sharing. The range of users of HDF is illustrated in tabular form. HDF is the underlying format for the HDF-EOS standard (http://hdfeos.gsfc.nasa.govn/) and consequently is the target format for a large amount of remotely sensed data. HDF5 is a completely new version of HDF that provides an improved format and more general data model, supports efficient storage of very large datasets, and is supported by an I/O library that runs on both serial and parallel platforms. The home of the HDF project is the National Center for Supercomputing Applications (NCSA) at the University of Illinois at Urbana-Champaign (www.ncsa.uiuc.edu.).
207507499
H. Abelson and G. J. Sussman with J. Sussman, Structure and Interpretation of Computer Programs
a good philosophical survey of the type/schema problem; a daring psychological synthesis, if a bit broad, of the reasoning process and the nature of concepts. Sowa's insights are clear, but their application is complicated and not worked out. Nevertheless, my recommendat ion is definite: Every AI and cognitive science researcher should study the conceptual graph notation and understand its foundation in logic, database, and knowledge representat ion research. Specialists in knowledge representat ion and inference will profit by relating the conceptual graph notation to their own schemes. This book could have its greatest impact on specialists in fields such as cognitive anthropology, who might get a new perspective on knowledge and reasoning, and who could use conceptual graphs for constructing models. As a course texL the book is appropriate for a graduate seminar taught by someone who is familiar with mainstream AI of the past decade, or who intends to relate the book to some other field, such as philosophy. Given the historical bias and lack of development of current research, the experienced A1 researcher can use this book mosl confidently and to the greatest advan tage-as a source of new ideas and perspectives, and as a synthesis of research he has heard about, but previously couldn't relatc to his own work.
60693966
Computer Architecture: A Quantitative Approach
This best-selling title, considered for over a decade to be essential reading for every serious student and practitioner of computer design, has been updated throughout to address the most important trends facing computer designers today. In this edition, the authors bring their trademark method of quantitative analysis not only to high-performance desktop machine design, but also to the design of embedded and server systems. They have illustrated their principles with designs from all three of these domains, including examples from consumer electronics, multimedia and Web technologies, and high-performance computing.
8802364
The memory behavior of cache oblivious stencil computations
Abstract
We present and evaluate a cache oblivious algorithm for stencil computations, which arise for example in finite-difference methods. Our algorithm applies to arbitrary stencils in n-dimensional spaces. On an “ideal cache” of size Z, our algorithm saves a factor of Θ(Z1/n) cache misses compared to a naive algorithm, and it exploits temporal locality optimally throughout the entire memory hierarchy. We evaluate our algorithm in terms of the number of cache misses, and demonstrate that the memory behavior agrees with our theoretical predictions. Our experimental evaluation is based on a finite-difference solution of a heat diffusion problem, as well as a Gauss-Seidel iteration and a 2-dimensional LBMHD program, both reformulated as cache oblivious stencil computations.

213765
Reflection-free one-way edge modes in a gyromagnetic photonic crystal.
We point out that electromagnetic one-way edge modes analogous to quantum Hall edge states, originally predicted by Raghu and Haldane in 2D photonic crystals possessing Dirac point-derived band gaps, can appear in more general settings. We show that the TM modes in a gyromagnetic photonic crystal can be formally mapped to electronic wave functions in a periodic electromagnetic field, so that the only requirement for the existence of one-way edge modes is that the Chern number for all bands below a gap is nonzero. In a square-lattice yttrium-iron-garnet crystal operating at microwave frequencies, which lacks Dirac points, time-reversal breaking is strong enough that the effect should be easily observable. For realistic material parameters, the edge modes occupy a 10% band gap. Numerical simulations of a one-way waveguide incorporating this crystal show 100% transmission across strong defects.
6245199
Casimir forces in the time domain: Theory
We present a method to compute Casimir forces in arbitrary geometries and for arbitrary materials based on the finite-difference time-domain (FDTD) scheme. The method involves the time evolution of electric and magnetic fields in response to a set of current sources, in a modified medium with frequency-independent conductivity. The advantage of this approach is that it allows one to exploit existing FDTD software, without modification, to compute Casimir forces. In this paper, we focus on the derivation, implementation choices, and essential properties of the time-domain algorithm, both considered analytically and illustrated in the simplest parallel-plate geometry.