Efficient time-domain and frequency-domain finite-element solution of Maxwell's equations using spectral Lanczos decomposition method

Zunoubi, Mohammad R.; Donepudi, K.C.; Jin, Jian‐Ming; Chew, Weng Cho

doi:10.1109/22.704957

Cited by 32 publications

(14 citation statements)

References 35 publications

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“…An LU decomposition of the FEM matrix was performed at each one of these frequencies, followed by the application of the AWE process for the generation of the associated PadeH approximations. As can be seen from the generated plots in Reference [6], the frequency response obtained through the aforementioned FEM/AWE/CFH process exhibits good agreement with the measured response only within the 12}18 GHz frequency range. In contrast, the algorithm proposed in this paper achieves excellent accuracy over the entire bandwidth, at (roughly) the cost of only one LU decomposition of the FEM matrix.…”

Section: Numerical Resultssupporting

confidence: 66%

“…In an attempt to overcome this di$culty, Zunoubi et al [6] and Rubio et al [7] applied Krylov-based model order reduction to electromagnetic structures that were bounded and lossless. For such structures the matrix Z is zero.…”

Section: Traditional Fem Model Of the Generalized Impedance Matrixmentioning

confidence: 99%

“…The matrices Z, P C and B have already been de"ned in (6). Finally, the elements of the two new matrices D and P @ are…”

Section: The Fem Model For Maxwell's Curl Equationsmentioning

confidence: 99%

“…Its matrix form for the general case of lossy media and unbounded domains exhibits both linear and quadratic dependence on frequency; however, Krylov-based model order reduction requires linear frequency dependency in the matrix form of the discrete electromagnetic problem. This limits the direct application of Krylov-based model order reduction of electromagnetic FEM models to bounded, lossless domains where the quadratic dependence on frequency is absent [6,7].…”

Section: Introductionmentioning

confidence: 99%

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Finite element‐based model order reduction of electromagnetic devices

Zhu¹,

Cangellaris²

2002

Int J Numerical Modelling

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SUMMARYIn this paper an e$cient algorithm is presented for the development of compact and passive macro-models of electromagnetic devices through the systematic reduction of the order of discrete models for these devices obtained through the use of "nite elements. The proposed methodology is founded on a new "nite element formulation that casts Maxwell's curl equations in a state-space form. Such state-space representations are very compatible with a class of robust model order reduction techniques based on Krylov subspaces. However, the advantage of this compatibility appears to be hindered by the fact that the state matrix of the discretized Maxwellian system is of dimension almost twice that obtained from the "nite element approximation of the electromagnetic vector wave equation. It is shown in this paper that the apparent penalty in both memory and computation e$ciency can be avoided by a proper selection of the "nite element expansion functions used for the discretization of the electromagnetic "elds. More speci"cally, it is shown that the proper selection of expansion functions renders the state-space form of the Maxwellian system equivalent to the discrete problem obtained from the approximation of the vector wave equation using tangentially continuous vector "nite elements. This equivalence is then used to e!ect Krylov-based model order reduction directly from the "nite element approximation of the vector wave equation. In particular, a passive model order reduction algorithm is used for this purpose. The proposed reduced order macromodelling algorithm is demonstrated through its application to a variety of microwave passive components.

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Section: Numerical Resultssupporting

confidence: 66%

Section: Traditional Fem Model Of the Generalized Impedance Matrixmentioning

confidence: 99%

“…The matrices Z, P C and B have already been de"ned in (6). Finally, the elements of the two new matrices D and P @ are…”

Section: The Fem Model For Maxwell's Curl Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finite element‐based model order reduction of electromagnetic devices

Zhu¹,

Cangellaris²

2002

Int J Numerical Modelling

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show abstract

“…We can remove these higher frequency components in the FDTD output by passing it through a low pass filter. This is suggested in [32], although details are not provided there. A digital low pass filter (to be specific, a Butterworth infinite impulse response realization, due to its maximally-flat property) was designed to exclude frequencies higher than 100 GHz.…”

Section: Time (Ns) Instantaneous Frequency (Ghz)mentioning

confidence: 94%