1,911 research outputs found
Efficient wideband electromagnetic scattering computation for frequency dependent lossy dielectrics using WCAWE
This paper presents a model order reduction algorithm for the volume electric field integral equation (EFIE) formulation, that achieves fast and accurate frequency sweep calculations of electromagnetic wave scattering. An inhomogeneous, two-dimensional, lossy dielectric object whose material is characterized by a complex permittivity which varies with frequency is considered. The variation in the dielectric properties of the ceramic BaxLa4Ti 2+xO 12+3x in the <1 GHz frequency range is investigated for various values of x in a frequency sweep analysis. We apply the well-conditioned asymptotic waveform evaluation (WCAWE) method to circumvent the computational complexity associated with the numerical solution of such formulations. A multipoint automatic WCAWE method is also demonstrated which can produce an accurate solution over a much broader bandwidth. Several numerical examples are given on order to illustrate the accuracy and robustness of the proposed methods
Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification
Stochastic spectral methods are efficient techniques for uncertainty
quantification. Recently they have shown excellent performance in the
statistical analysis of integrated circuits. In stochastic spectral methods,
one needs to determine a set of orthonormal polynomials and a proper numerical
quadrature rule. The former are used as the basis functions in a generalized
polynomial chaos expansion. The latter is used to compute the integrals
involved in stochastic spectral methods. Obtaining such information requires
knowing the density function of the random input {\it a-priori}. However,
individual system components are often described by surrogate models rather
than density functions. In order to apply stochastic spectral methods in
hierarchical uncertainty quantification, we first propose to construct
physically consistent closed-form density functions by two monotone
interpolation schemes. Then, by exploiting the special forms of the obtained
density functions, we determine the generalized polynomial-chaos basis
functions and the Gauss quadrature rules that are required by a stochastic
spectral simulator. The effectiveness of our proposed algorithm is verified by
both synthetic and practical circuit examples.Comment: Published by IEEE Trans CAD in May 201
Characteristic Evolution and Matching
I review the development of numerical evolution codes for general relativity
based upon the characteristic initial value problem. Progress in characteristic
evolution is traced from the early stage of 1D feasibility studies to 2D
axisymmetric codes that accurately simulate the oscillations and gravitational
collapse of relativistic stars and to current 3D codes that provide pieces of a
binary black hole spacetime. Cauchy codes have now been successful at
simulating all aspects of the binary black hole problem inside an artificially
constructed outer boundary. A prime application of characteristic evolution is
to extend such simulations to null infinity where the waveform from the binary
inspiral and merger can be unambiguously computed. This has now been
accomplished by Cauchy-characteristic extraction, where data for the
characteristic evolution is supplied by Cauchy data on an extraction worldtube
inside the artificial outer boundary. The ultimate application of
characteristic evolution is to eliminate the role of this outer boundary by
constructing a global solution via Cauchy-characteristic matching. Progress in
this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note:
updated version of arXiv:gr-qc/050809
Pole-Zero Computation in Microwave Circuits Using Multipoint Padé Approximation
A new method is proposed for dominant pole- zero (or pole-residue) analysis of large linear microwave circuits containing both lumped and distributed elements. The method is based on a multipoint Padé approximation. It finds a reduced-order rational s-domain transfer function using a data set obtained by solving the circuit at only a few frequency points. We propose two techniques in order to obtain the coefficients of the transfer function from the data set. The proposed method provides a more efficient computation of both transient and frequency domain responses than conventional simulators and more accurate results than the techniques based on single-point Padé approximation such as asymptotic waveform evaluation. © 1995 IEE
A simulation program for efficient analysis of linear circuits
Ankara : Department of Electrical and Electronics Engineering and Institute of Engineering and Sciences, Bilkent University, 1996.Thesis (Master's) -- Bilkent University, 1996.Includes bibliographical references leaves 45-46.circuit simulation program using generalized asymptotic waveform evaluation
technique is introduced. The program analyzes circuits with lumped a.nd
distributed components. It computes the moments ci.t a few Irecjuency points
and extracts the coefficients of an approximating rational by employing one
of t,he two different methods. One of the examined methods is proposed to
compare the accuracy of results and the execution times with conventional
simulators and seveiâcil examples are demonstrated, indicating that our sirnulcv
tor provides a. speed improvement without a significant loss of accuracy.Sungur, MustafaM.S
Model order reduction of time-delay systems using a laguerre expansion technique
The demands for miniature sized circuits with higher operating speeds have increased the complexity of the circuit, while at high frequencies it is known that effects such as crosstalk, attenuation and delay can have adverse effects on signal integrity. To capture these high speed effects a very large number of system equations is normally required and hence model order reduction techniques are required to make the simulation of the circuits computationally feasible. This paper proposes a higher order Krylov subspace algorithm for model order reduction of time-delay systems based on a Laguerre expansion technique. The proposed technique consists of three sections i.e., first the delays are approximated using the recursive relation of Laguerre polynomials, then in the second part, the reduced order is estimated for the time-delay system using a delay truncation in the Laguerre domain and in the third part, a higher order Krylov technique using Laguerre expansion is computed for obtaining the reduced order time-delay system. The proposed technique is validated by means of real world numerical examples
Gauge and motion in perturbation theory
Through second order in perturbative general relativity, a small compact
object in an external vacuum spacetime obeys a generalized equivalence
principle: although it is accelerated with respect to the external background
geometry, it is in free fall with respect to a certain \emph{effective} vacuum
geometry. However, this single principle takes very different mathematical
forms, with very different behaviors, depending on how one treats perturbed
motion. Furthermore, any description of perturbed motion can be altered by a
gauge transformation. In this paper, I clarify the relationship between two
treatments of perturbed motion and the gauge freedom in each. I first show
explicitly how one common treatment, called the Gralla-Wald approximation, can
be derived from a second, called the self-consistent approximation. I next
present a general treatment of smooth gauge transformations in both
approximations, in which I emphasise that the approximations' governing
equations can be formulated in an invariant manner. All of these analyses are
carried through second perturbative order, but the methods are general enough
to go to any order. Furthermore, the tools I develop, and many of the results,
should have broad applicability to any description of perturbed motion,
including osculating-geodesic and two-timescale descriptions.Comment: 26 pages, 3 figures. Minor corrections. Equations (120) and (126) are
more general than in PRD versio
Passivity-preserving parameterized model order reduction using singular values and matrix interpolation
We present a parameterized model order reduction method based on singular values and matrix interpolation. First, a fast technique using grammians is utilized to estimate the reduced order, and then common projection matrices are used to build parameterized reduced order models (ROMs). The design space is divided into cells, and a Krylov subspace is computed for each cell vertex model. The truncation of the singular values of the merged Krylov subspaces from the models located at the vertices of each cell yields a common projection matrix per design space cell. Finally, the reduced system matrices are interpolated using positive interpolation schemes to obtain a guaranteed passive parameterized ROM. Pertinent numerical results validate the proposed technique
Reliable Fast Frequency Sweep for Microwave Devices via the Reduced Basis Method
International audienceIn this paper, a reduced basis approximation-based model order reduction for fast and reliable sweep in time-harmonic Maxwell's equations is detailed. Contrary to what one may expect by observing the frequency response of different microwave circuits, the electromagnetic field within these devices does not drastically vary as frequency changes in a band of interest. Thus, instead of using computationally inefficient, large dimension, numerical approximations such as finite element or boundary element methods for each frequency in the band, the point in here is to approximate the dynamics of the electromagnetic field itself as frequency changes. A much lower dimension, reduced basis approximation sorts this problem out. Not only rapid frequency evaluation of the reduced order model is carried out within this approach, but also special emphasis is placed on a fast determination of the error mesure for each frequency in the band of interest. This certifies the accurate response of the reduced order model. The same scheme allows us, in a offline stage, to adaptively select the basis functions in the reduced basis approximation and automatically select the model order reduction process whenever a preestablished accuracy is required throughout the band of interest. Finally, real-life applications will illustrate the capabilities of this approach
- âŠ