Fast Frequency Sweep of FEM Models via the Balanced Truncation Proper Orthogonal Decomposition

Wang, Wei; Paraschos, Georgios N.; Vouvakis, Marinos N.

doi:10.1109/tap.2011.2164184

Cited by 39 publications

(2 citation statements)

References 32 publications

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“…Moreover, such a reduced model is inaccurate for simulating the transient performance of a frequency whose distance to the frequency expansion point is large. To address the locally supported approximation characteristics of a single-point moment-matching approach, the Reduced-Basis Method (RBM) [15] or Balanced Truncation Proper Orthogonal Decomposition (BT-POD) [16], based on solution snapshots [17,18] from different frequency points, is introduced. However, it involves computing snapshots on a large number of points.…”

Section: Multipoint Expansionmentioning

confidence: 99%

“…A multipoint MOR method obtains the projection basis from the moments of the transfer function at multiple frequency points, as explained in Figure 2. approach, the Reduced-Basis Method (RBM) [15] or Balanced Truncation Proper Orthogonal Decomposition (BT-POD) [16], based on solution snapshots [17,18] from different frequency points, is introduced. However, it involves computing snapshots on a large number of points.…”

Section: Multipoint Expansionmentioning

confidence: 99%

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A Block Arnoldi Algorithm Based Reduced-Order Model Applied to Large-Scale Algebraic Equations of a 3-D Field Problem

et al. 2021

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In simulations of three-dimensional transient physics filled through a numerical approach, the order of the equation set of high-fidelity models is extremely high. To eliminate the large dimension of equations, a model order reduction (MOR) technique is introduced. In the existing MOR methods, the block Arnoldi algorithm-based MOR method is numerically stable, achieving a passively reduced order model. Nevertheless, this method performs poorly when it is applied to very wide-frequency transients. To eliminate this deficiency, multipoint MOR methods are emerging. However, it is hard to directly apply an existing multipoint MOR method to a 3-D transient field equation set. The implementation issues in a reduction process (such as the selection of expansion points, the number of moments matched at a point and the error bound) have not been explored in detail. In this respect, an adaptive multipoint model reduction model based on the Arnoldi algorithm is proposed to obtain the reduced-order models of a 3-D temperature field. The originality of this study is the proposal of a novel adaptive algorithm for selecting expansion points, matching moments automatically, using a posterior-error estimator based on temperature response coupled with a network topological method (NTM). The computational efficiency and accuracy of the proposed method are evaluated by the numerical results from solving the temperature field of a prototype insulated-gate bipolar transistor (IGBT).

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Section: Multipoint Expansionmentioning

confidence: 99%

Section: Multipoint Expansionmentioning

confidence: 99%

A Block Arnoldi Algorithm Based Reduced-Order Model Applied to Large-Scale Algebraic Equations of a 3-D Field Problem

et al. 2021

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Direct synthesis of equivalent circuits from reduced FE models using proper orthogonal decomposition

Shimotani

Sato

Igarashi

2016

COMPEL

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Purpose -This paper proposes a fast synthesis method of the equivalent circuits of electromagnetic devices using model order reduction. Finite element method (FEM) has been widely used to design electromagnetic devices. For FE analysis of these devices connected to control and deriving circuits, FE equations coupled with the circuit equations have to be solved for many times in their design processes. If the FE models are replaced by equivalent circuit models, computational time could be drastically reduced. Design/methodology/approach -In the proposed method, a reduced FE model is obtained using proper orthogonal decomposition (POD) in which the size of FE equation is effectively reduced so that the computational time for FE analysis is shortened. Then, the equivalent circuits are directly synthesized from the admittance function of the reduced system. Findings -Accuracy and computational efficiency of the proposed method are compared with those of another POD-based method in which the equivalent circuits are synthesized from fitting of frequency characteristics using optimization algorithm. There are no significant differences in the accuracy of both method, while the speed-up ratio of the former method is found larger than that for the latter method for the same sampling points. Originality/value -The equivalent circuits of electric machines and devices have been synthesized on the basis of physical insight of engineers. This paper proposes a novel method by which the equivalent circuits are automatically synthesized from finite element model of the electric machines and devices using POD.

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Efficient Frequency and Time-Domain Simulations of Delayed PEEC Models With Proper Orthogonal Decomposition Techniques

Khattak,

Romano,

Antonini

et al. 2024

IEEE Access

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The Partial Element Equivalent Circuit (PEEC) method has gained signicant recognition as an electromagnetic computational technique known for its ability to represent electromagnetic phenomena using equivalent circuits. This feature makes it particularly valuable for addressing mixed EM-circuit problems. However, PEEC models often exhibit large dimensions, necessitating modeling techniques that can eectively reduce their size while preserving accuracy. Model order reduction (MOR) serves as a highly eective approach to accomplish this objective. This paper presents two MOR techniques based on proper orthogonal decomposition (POD) for PEEC models described by neutral delayed dierential equations (NDDEs). The unique characteristics of NDDEs demand specialized MOR approaches, as their formulation is inherently more complex compared to standard quasi-static PEEC models described by non-delayed dierential equations. In addition to a traditional one-shot singular value decomposition (SVD), this paper also presents an incrementally computed SVD to evaluate the orthogonal matrix needed to generate the reduced order matrices. The accuracy and eciency of the proposed PEEC-MOR methods are demonstrated through multiple relevant numerical results in both the frequency-domain and time-domain.INDEX TERMS Partial element equivalent circuit (PEEC) method, model order reduction, proper orthogonal decomposition, frequency-domain analysis, and time-domain analysis.

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Fast Frequency Sweep of FEM Models via the Balanced Truncation Proper Orthogonal Decomposition

Cited by 39 publications

References 32 publications

A Block Arnoldi Algorithm Based Reduced-Order Model Applied to Large-Scale Algebraic Equations of a 3-D Field Problem

A Block Arnoldi Algorithm Based Reduced-Order Model Applied to Large-Scale Algebraic Equations of a 3-D Field Problem

Direct synthesis of equivalent circuits from reduced FE models using proper orthogonal decomposition

Efficient Frequency and Time-Domain Simulations of Delayed PEEC Models With Proper Orthogonal Decomposition Techniques

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