Adaptive Solution Space Projection for Fast and Robust Wideband Finite-Element Simulation of Microwave Components

Lee, Shih-Hao; Jin, Jian‐Ming

doi:10.1109/lmwc.2007.899290

Cited by 19 publications

(13 citation statements)

References 7 publications

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“…Reduction of the large generalized eigenvalue problem to the subspace spanned by modal eigenvectors at evenly spaced frequency points and its derivates is considered. A similar strategy is taken into account for fast frequency sweep of microwave circuits in [23,40]. These works propose to adaptively select the number of sample points by explicitly computing the residual error at specific frequency points.…”

Section: Introductionmentioning

confidence: 99%

Reliable Fast Frequency Sweep for Microwave Devices via the Reduced-Basis Method

Rubia

Razafison

Maday

2009

IEEE Trans. Microwave Theory Techn.

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In this paper, a reduced basis approximation-based model order reduction for fast and reliable frequency sweep in the 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 measure for each frequency in the band of interest. This certifies the accurate response of the reduced order model. The same scheme allows us, in an 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.

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Section: Introductionmentioning

confidence: 99%

Reliable Fast Frequency Sweep for Microwave Devices via the Reduced-Basis Method

Rubia

Razafison

Maday

2009

IEEE Trans. Microwave Theory Techn.

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“…When there exist wave ports in a circuit structure, we need to solve the modal fields of each port and use them to excite the structure or to construct boundary conditions for truncating the computational domain [3]. In this case a correct tree-cotree splitting should be guaranteed in both the 3D structure as well as on each port plane.…”

Section: Wave Portmentioning

confidence: 99%

“…Fortunately, we can extend a simulation to even lower frequencies by applying model order reduction techniques. In this study, a multipoint model order reduction method, called the solution space projection (SSP) [3], is applied to generate a reduced-order model for a fast broadband analysis. As the name suggests, the original finite-element matrix equation is projected to the subspace spanned by a set of solution vectors to yield a reduced-order model that can be solved very rapidly over the frequency band.…”

Section: Model Order Reductionmentioning

confidence: 99%

“…is solved at m frequency samples, which are automatically determined by an adaptive mechanism [3], we obtain a set of m solution vectors X, which is then orthonormalized to form an orthonormal basis (still denoted by X). It is expected that a solution vector at other frequencies can be approximated by the linear combination of the basis X.…”

Section: Model Order Reductionmentioning

confidence: 99%

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Application of the tree‐cotree splitting for improving matrix conditioning in the full‐wave finite‐element analysis of high‐speed circuits

Lee

Jin

2008

Micro & Optical Tech Letters

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frequency, because the typical value of PAE cannot be reached over there. In the band of 13.8 -14.8 GHz, theoretical and experimental PAE has excellent coherence, and a maximum PAE of about 22% can be achieved. CONCLUSIONWe present a maximum 45-W (CW) result for a spatial combiner circuit based on four driver amplifiers and four HPAs, integrated with the power dividers/combiners and microstrip probe transitions. A power variation less than Ϯ1 dB was achieved, and the combining efficiency was more than 87%, while the maximum PAE was 22%, within the band from 13.8 to 14.8 GHz. So high gain and high efficiency were reached. The combining structure itself was compact and has a strong potential for higher powers. APPLICATION OF THE TREE-COTREE SPLITTING FOR IMPROVING MATRIX CONDITIONING IN THE FULL-WAVE FINITE-ELEMENT ANALYSIS OF HIGH-SPEED CIRCUITS

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“…Another way to improve the efficiency of FEM in such cases is to apply model order reduction (MOR) techniques which since the end of the last century have been gaining popularity in the area of computational electromagnetics. In particular, MOR has been successfully adopted in mesh based methods such as the FEM [3][4][5][6][7][8] and the finite difference methods, both in time (FDTD) and frequency (FDFD) domain [9][10][11][12]. The main idea of MOR is to find a low-dimensional approximation (subspace) of the original large set of state-space equations which provides satisfactory accuracy of the computations as far as the input-output behavior of the circuit is concerned [13].…”

Section: Introductionmentioning

confidence: 99%

Multilevel Model Order Reduction With Generalized Compression of Boundaries for 3-D Fem Electromagnetic Analysis

Fotyga¹,

Nyka²,

Mrozowski³

2013

PIER

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Abstract-This paper presents a multilevel Model Order Reduction technique for a 3-D electromagnetic Finite Element Method analysis. The reduction process is carried out in a hierarchical way and involves several steps which are repeated at each level. This approach brings about versatility and allows one to efficiently analyze complex electromagnetic structures. In the proposed multilevel reduction the entire computational domain is covered with macro-elements which are subsequently nested, in such a way that size of the problem which has to be reduced at each level is relatively small. In order to increase the speed of the reduction at each level, the electric field at the macro-elements' boundaries is projected onto the subspace spanned by Legendre polynomials and trigonometric functions. The results of the numerical experiments confirm the validity and efficiency of the presented approach.

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Adaptive Solution Space Projection for Fast and Robust Wideband Finite-Element Simulation of Microwave Components

Cited by 19 publications

References 7 publications

Reliable Fast Frequency Sweep for Microwave Devices via the Reduced-Basis Method

Reliable Fast Frequency Sweep for Microwave Devices via the Reduced-Basis Method

Application of the tree‐cotree splitting for improving matrix conditioning in the full‐wave finite‐element analysis of high‐speed circuits

Multilevel Model Order Reduction With Generalized Compression of Boundaries for 3-D Fem Electromagnetic Analysis

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