Parametrized Local Reduced-Order Models With Compressed Projection Basis for Fast Parameter-Dependent Finite-Element Analysis

Czarniewska, Martyna; Fotyga, Grzegorz; Lamęcki, Adam; Mrozowski, Michał

doi:10.1109/tmtt.2018.2842744

Cited by 14 publications

(3 citation statements)

References 42 publications

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“…However, to allow for near real-time assembly of the respective subspaces for arbitrary localised damage features, the ROM framework requires access to the full flexibility matrix of the system. To this end, our work has been inspired by contributions that employed tensor techniques and compression algorithms to approximate the system matrices, 57 remove redundancy from reduced order bases 58 or enrich the trial ROM bases without FOM solves, 59 thus effectively reducing the computational toll and the storage burden. Specifically, we employ a matrix compression technique termed as Hierarchically Off-Diagonal Low Rank (HODLR) [60][61][62] representation for the matrices involved, which enables efficient evaluations of the flexibility matrix and allows storage with reduced memory requirements.…”

Section: Introductionmentioning

confidence: 99%

Accelerating structural dynamics simulations with localised phenomena through matrix compression and projection‐based model order reduction

Agathos,

Vlachas,

Garland

et al. 2024

Numerical Meth Engineering

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In this work, a novel approach is introduced for accelerating the solution of structural dynamics problems in the presence of localised phenomena, such as cracks. For this category of problems, conventional projection‐based Model Order Reduction (MOR) methods are either limited with respect to the range of system configurations that can be represented or require frequent solutions of the Full Order Model (FOM) to update the low‐dimensional spaces, in which solutions are represented. In the proposed approach, low‐dimensional spaces, constructed for the healthy structure, are enriched with appropriately selected columns of the flexibility matrix of the system. It can be shown that these spaces contain the solution to the original problem for the static case, while their dimension is much smaller. In order to allow their online construction for arbitrary localised features, the full flexibility matrix of the system should be available. To this end, a hierarchical representation is used for the matrices involved, allowing to compute the flexibility matrix efficiently and with reduced memory requirements. The resulting method offers significant speedups, without sacrificing the flexibility and accuracy of the full order model. The performance and limitations of the approach are studied through a series of examples in structural dynamics.

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Section: Introductionmentioning

confidence: 99%

Accelerating structural dynamics simulations with localised phenomena through matrix compression and projection‐based model order reduction

Agathos,

Vlachas,

Garland

et al. 2024

Numerical Meth Engineering

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“…Since the FEM equations are formulated with respect to frequency, repetitive analysis of large FEM systems has to be performed for different frequencies. To accelerate this repetitive process, various model order reduction (MOR) techniques [2][3][4] have been introduced, such as the asymptotic waveform evaluation, 5,6 the Arnoldi method, 7 the matrix Padé via Lanczos (MPVL). [8][9][10] With MOR techniques, only the large system of EM equations at a single frequency needs to be solved.…”

Section: Introductionmentioning

confidence: 99%

Padé via Arnoldi with single‐size matrix simplification for electromagnetic fast frequency sweep

Ma,

Zhang,

Jin

et al. 2023

Micro & Optical Tech Letters

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This paper proposes a new Padé via Arnoldi algorithm with single‐size matrix simplification for electromagnetic (EM) fast frequency sweep. New equations are derived to reduce the double‐size system matrix to single‐size system matrix. We also propose a systematic algorithm to calculate S‐parameters using the simplified single‐size system matrix. Using the proposed algorithm, the EM responses can be obtained with the same accuracy while consuming much less time compared with that using the existing double‐size matrix Padé via Lanczos. The proposed algorithm is demonstrated by two microwave examples.

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“…It involves a sequence of repeated simulations preceded by some structure modifications, which are usually carried out within small subregions that may be represented by macromodels. As presented in [14,17,18], in each step, only a single macromodel that is in the subregion being currently modified needs to be re-generated, while the rest remain unchanged. Since the generation of macromodels is the most costly part of the simulations, the total optimization time can be significantly reduced.…”

Section: Introductionmentioning

confidence: 99%

Diagonalized Macromodels in Finite Element Method for Fast Electromagnetic Analysis of Waveguide Components

Nyka

2019

Electronics

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A new technique of local model-order reduction (MOR) in 3-D finite element method (FEM) for frequency-domain electromagnetic analysis of waveguide components is proposed in this paper. It resolves the problem of increasing solution time of the reduced-order system assembled from macromodels created in the subdomains, into which an analyzed structure is partitioned. This problem becomes particularly relevant for growing size and count of the macromodels, and when they are cloned in multiple locations of the structures or are used repeatedly in a tuning and optimization process. To significantly reduce the solution time, the diagonalized macromodels are created by means of the simultaneous diagonalization and subsequently assembled in the global system. For the resulting partially diagonal matrix, an efficient dedicated solver based on the Schur complement technique is proposed. The employed MOR method preserves frequency independence of the macromodels, which is essential for efficient diagonalization, as it can be performed once for the whole analysis bandwidth. The numerical validation of the proposed procedures with respect to accuracy and speed was carried out for varying size and count of macromodels. An exemplary finite periodical waveguide structure was chosen to investigate the influence of macromodel cloning on the resultant efficiency. The results show that the use of the diagonalized macromodels provided a significant solution speedup without any loss of accuracy.

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Parametrized Local Reduced-Order Models With Compressed Projection Basis for Fast Parameter-Dependent Finite-Element Analysis

Cited by 14 publications

References 42 publications

Accelerating structural dynamics simulations with localised phenomena through matrix compression and projection‐based model order reduction

Accelerating structural dynamics simulations with localised phenomena through matrix compression and projection‐based model order reduction

Padé via Arnoldi with single‐size matrix simplification for electromagnetic fast frequency sweep

Diagonalized Macromodels in Finite Element Method for Fast Electromagnetic Analysis of Waveguide Components

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