A Subspace-Splitting Moment-Matching Model-Order Reduction Technique for Fast Wideband FEM Simulations of Microwave Structures

Szypulski, Damian; Fotyga, Grzegorz; Rubia, Valentín de la; Mrozowski, Michał

doi:10.1109/tmtt.2020.3001627

Cited by 17 publications

(7 citation statements)

References 40 publications

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“…A paper by Sankaran [68] presents quite well the advantages and disadvantages of various methods with an extensive discussion of flexibility, accuracy, and computational loads. To deal with computational expenses, many fast algorithms have been developed; they accelerate solution processes for modeling electrically large and complex problems [69]; they include multilevel fast multipole algorithm (MLFMA) [70]- [72], fast direct solution methods [73], [74], graphics processing unit (GPU) accelerated methods [75], [76], discontinuous Galerkin (DG) methods [57], [77], domain decomposition (DD) methods [78], and so on [79], [80]. Note that GPU acceleration is not exclusively a matter of technology but also requires a modification of the computational procedure and implementation scheme to run on specialized hardware.…”

Section: Discussionmentioning

confidence: 99%

A Unified View of Computational Electromagnetics

Chen

Wang

Hoefer

2022

IEEE Trans. Microwave Theory Techn.

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This article presents a unified description of numerical methods for solving electromagnetic field problems. Traditionally, these methods are considered to be independent and alternative ways of solving Maxwell's equations or equations derived therefrom. However, they all are projective approximations of the unknown solution by known expansion or basis functions with unknown amplitude coefficients that are determined using the so-called method of weighted residuals (MWR). This common feature forms the proposed unifying framework that may serve both as a systematic introduction to computational electromagnetics and as a way to provide insight into the nature, strengths, and limitations of the various algorithms used by present and future field solvers. For convenience, the fundamental equations and concepts of electromagnetics are summarized in order to facilitate the demonstration of the unified approach. Our aim is to provide students, designers, and researchers with a framework for developing new numerical algorithms, to guide users in the selection and application of electromagnetic design tools, and to foster informed engineering judgment. This article also serves as a review and summary of earlier theoretical works reported in different places and at different times.

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Section: Discussionmentioning

confidence: 99%

A Unified View of Computational Electromagnetics

Chen

Wang

Hoefer

2022

IEEE Trans. Microwave Theory Techn.

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“…Different MOR techniques have been proposed and applied to combat the complexity of interconnected problems [1][2][3] and finite-element equations of electromagnetic problems [4][5][6][7]. However, there are few works oriented for 3-D temperature fields.…”

Section: Introductionmentioning

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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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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“…The global FEM system of equations is constructed (line 25) and solved (line 26) at this frequency. The computed block V i is orthogonalized using the Gram-Schmidt method, and added to the projection basis V. The algorithm stops once all the expansion points in the sets have been examined (lines [13][14][15]. It is worth noting that the steps 5 and 19 can be performed extremely rapidly using the fast FEM matrix generation approach [33].…”

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confidence: 99%

A Model-Order Reduction Approach for Electromagnetic Problems With Nonaffine Frequency Dependence

Fotyga

2021

IEEE Access

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The aim of this paper is to present a novel model-order reduction (MOR) technique for the efficient frequency-domain finite-element method (FEM) simulation of microwave components. It is based on the standard reduced-basis method, but the subsequent expansion frequency points are selected following the so-called sparsified greedy strategy. This feature makes it especially useful to perform a fast-frequency sweep of problems that lead to systems of equations exhibiting a nonaffine frequency dependence. This property appears, for example, when the excitation of the problem is characterized by a frequency-dependent waveguide mode pattern, or when the computational domain includes materials with frequency-dependent permittivity or permeability tensors. Moreover, the new MOR scheme can be also used to accelerate the frequency sweep of problems with many excitations, for which the standard reduction algorithms tend to be time-consuming. Its effectiveness and accuracy is verified through analysis of three microwave structures: planar microstrip branch-line coupler, three-port waveguide junction with ferrite post, and an eighth-order dual-mode waveguide filter.

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A Subspace-Splitting Moment-Matching Model-Order Reduction Technique for Fast Wideband FEM Simulations of Microwave Structures

Cited by 17 publications

References 40 publications

A Unified View of Computational Electromagnetics

A Unified View of Computational Electromagnetics

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

A Model-Order Reduction Approach for Electromagnetic Problems With Nonaffine Frequency Dependence

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