Generation of FDTD subcell equations by means of reduced order modeling

Denecker, Bart; Olyslager, F.; Knockaert, Luc; Zutter, D. De

doi:10.1109/tsp.2003.815439

Cited by 52 publications

(42 citation statements)

References 22 publications

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“…For each cell, an optimization procedure is used to find the scaling and frequency shifting system coefficients that make each vertex an accurate approximant of the other cell vertices. For each vertex , a set of scaling and frequency shifting real coefficients are found, such that (9) (10) This optimization problem can be solved using, for example, the Matlab [39] routines fmincon and fminsearchbnd with as an initial guess. These routines are able to impose some constraints on the optimized coefficients, which is important to guarantee the passivity of parameterized reduced order models as explained in what follows.…”

Section: B Scaling and Frequency Shifting Coefficientsmentioning

confidence: 99%

Interpolation-Based Parameterized Model Order Reduction of Delayed Systems

Ferranti

Nakhla

Antonini

et al. 2012

IEEE Trans. Microwave Theory Techn.

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Abstract-Three-dimensional electromagnetic methods are fundamental tools for the analysis and design of high-speed systems. These methods often generate large systems of equations, and model order reduction (MOR) methods are used to reduce such a high complexity. When the geometric dimensions become electrically large or signal waveform rise times decrease, time delays must be included in the modeling.Design space optimization and exploration are usually performed during a typical design process that consequently requires repeated simulations for different design parameter values. Efficient performing of these design activities calls for parameterized model order reduction (PMOR) methods, which are able to reduce large systems of equations with respect to frequency and other design parameters of the circuit, such as layout or substrate features.We propose a novel PMOR method for neutral delayed differential systems, which is based on an efficient and reliable combination of univariate model order reduction methods, a procedure to find scaling and frequency shifting coefficients and positive interpolation schemes. The proposed scaling and frequency shifting coefficients enhance and improve the modeling capability of standard positive interpolation schemes and allow accurate modeling of highly dynamic systems with a limited amount of initial univariate models in the design space. The proposed method is able to provide parameterized reduced order models passive by construction over the design space of interest. Pertinent numerical examples validate the proposed PMOR approach.Index Terms-Delayed systems, interpolation, parameterized model order reduction (PMOR), partial element equivalent circuit method (PEEC).

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Section: B Scaling and Frequency Shifting Coefficientsmentioning

confidence: 99%

Interpolation-Based Parameterized Model Order Reduction of Delayed Systems

Ferranti

Nakhla

Antonini

et al. 2012

IEEE Trans. Microwave Theory Techn.

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“…Note the change in material index from 2 to 1 when comparing this ratio to that appearing in (9). This relationship permits E s, j 1 (ρ), the amplitude of the z-directed electric field radiated jointly byJ j 1 (ρ) andK j 1 (ρ) in the defectless and unbounded EC, to be expressed solely in terms of electric unknowns as…”

Section: A Formulationmentioning

confidence: 99%

“…Unfortunately, as ECs often contain small elements, their FDTD discretization and analysis require small spatial cells and time steps. Although the ensuing computational burden can be partially alleviated by using subcell models [9], FDTD methods remain computationally expensive, especially when high accuracies are required and phase dispersion is to be controlled. The eigenmode expansion method (EME) [10], [11] constitutes another frequently used technique for analyzing EC devices.…”

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confidence: 99%

Fast analysis of 2-D electromagnetic crystal devices using a periodic Green function approach

Pissoort

Michielssen

Olyslager

et al. 2005

J. Lightwave Technol.

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Abstract-A novel integral equation-based method for simulating wave propagation in two-dimensional (2-D) electromagnetic crystal (EC) devices is presented. A small number of irregular defects aside, the targeted devices are obtained by removing cylinders from infinite, doubly periodic, and defectless electromagnetic crystals. Integral equations in terms of equivalent currents that reside on the surfaces of the voids left by the removed cylinders are constructed by using Green functions innate to the defectless electromagnetic crystal. The sparse system of equations that results upon discretizing these integral equations is solved efficiently by a multifrontal method. The scheme is ideally suited to extract electromagnetic crystal device S parameters as it permits imposing modal excitations and exact absorbing boundary conditions. The scheme is applied to the analysis of two multiplexer-demultiplexer devices, a filter, and a bended EC waveguide, thereby demonstrating its versatility and computational efficiency.

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“…If a finite expansion point is taken then, in general, the factorization of a large matrix is required. Examples of methods that follow this approach are given in [3]- [6]. The factorization needs to be computed only once, but its computational costs are high and the factorization matrices need to be stored as well.…”

Section: Introductionmentioning

confidence: 99%

Low-Frequency Model-Order Reduction of Electromagnetic Fields Without Matrix Factorization

Remis

2004

IEEE Trans. Microwave Theory Techn.

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Abstract-In this paper, we develop a reduced-order modeling technique, which is based on a low-frequency expansion of the electromagnetic field. The expansion can be written in terms of the pseudoinverse of a so-called system matrix. This pseudoinverse is given explicitly, and it is shown that it satisfies a reciprocity relation. Moreover, we show that computing matrix-vector products with this pseudoinverse essentially amounts to repeatedly solving Poisson's equation. The latter two properties allow us to efficiently compute reduced-order models via a Lanczos-type algorithm. The proposed method is illustrated by a number of numerical examples.

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Generation of FDTD subcell equations by means of reduced order modeling

Cited by 52 publications

References 22 publications

Interpolation-Based Parameterized Model Order Reduction of Delayed Systems

Interpolation-Based Parameterized Model Order Reduction of Delayed Systems

Fast analysis of 2-D electromagnetic crystal devices using a periodic Green function approach

Low-Frequency Model-Order Reduction of Electromagnetic Fields Without Matrix Factorization

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