An adaptive SVD–Krylov reduced order model for surrogate based structural shape optimization through isogeometric boundary element method

Li, S.; Trevelyan, J.; Wu, Zhenyu; Lian, Haojie; Wang, D.; Zhang, W.

doi:10.1016/j.cma.2019.02.023

Cited by 36 publications

(14 citation statements)

References 72 publications

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“…Moreover, the surrogate model and model order reduction techniques can be employed to improve the efficiency of shape optimization. [31,30]. The application of shape optimization in electromagnetics is also a direction to pursue and a natural extension of this work.…”

Section: Vasementioning

confidence: 93%

Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods

Chen

Lian

Liu

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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133

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The boundary element method (BEM) is a powerful tool in computational acoustics, because the analysis is conducted only on structural surfaces, compared to the finite element method (FEM) which resorts to special techniques to truncate infinite domains. The isogeometric boundary element method (IGABEM) is a recent progress in the category of boundary element approaches, which is inspired by the concept of isogeometric analysis (IGA) and employs the spline functions of CAD as basis functions to discretize unknown physical fields. As a boundary representation approach, IGABEM is naturally compatible with CAD and thus can directly perform numerical analysis on CAD models, avoiding the cumbersome meshing procedure in conventional FEM/BEM and eliminating the difficulty of volume parameterization in isogeometric finite element methods. The advantage of tight integration of CAD and numerical analysis in IGABEM renders it particularly attractive in the application of structural shape optimization because (1) the geometry and the analysis can be interacted, (2) remeshing with shape morphing can be avoided, and (3) an optimized solution returns a CAD

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Section: Vasementioning

confidence: 93%

Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods

Chen

Lian

Liu

et al. 2019

Computer Methods in Applied Mechanics and Engineering

Self Cite

133

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“…where { } =1 and { } =1 are the interpolation points and tangential direction respectively. The left projector is computed by the observability Gramian utilizing the singular value decomposition-based techniques discussed in [17]- [19] as…”

Section: Preliminariesmentioning

confidence: 99%

“…System (3) can be written in a reduced-order form as ( 8) by exerting the reduced-order matrices defined in (19) and corresponding CARE can be attained as…”

Section: Computing the Optimal Feedback Matrix From Rommentioning

confidence: 99%

SVD-Krylov based Sparsity-preserving Techniques for Riccati-based Feedback Stabilization of Unstable Power System Models

2021

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We propose an efficient sparsity-preserving reduced-order modelling approach for index-1 descriptor systems extracted from large-scale power system models through two-sided projection techniques. The projectors are configured by utilizing Gramian based singular value decomposition (SVD) and Krylov subspace-based reduced-order modelling. The left projector is attained from the observability Gramian of the system by the low-rank alternating direction implicit (LR-ADI) technique and the right projector is attained by the iterative rational Krylov algorithm (IRKA). The classical LR-ADI technique is not suitable for solving Riccati equations and it demands high computation time for convergence. Besides, in most of the cases, reduced-order models achieved by the basic IRKA are not stable and the Riccati equations connected to them have no finite solution. Moreover, the conventional LR-ADI and IRKA approach not preserves the sparse form of the index-1 descriptor systems, which is an essential requirement for feasible simulations. To overcome those drawbacks, the fitting of LR-ADI and IRKA based projectors from left and right sides, respectively, desired reduced-order systems attained. So that, finite solution of low-rank Riccati equations, and corresponding feedback matrix can be executed. Using the mechanism of inverse projection, the Riccati-based optimal feedback matrix can be computed to stabilize the unstable power system models. The proposed approach will maintain minimized ℌ2 -norm of the error system for reduced-order models of the target models.

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“…Ding et al [42][43][44] coupled POD and MCs to conduct multidimensional uncertainty analysis and verified the effectiveness and efficiency of the method. RBF is used for continuous approximation of the system response that enables fast evaluation of the coefficients of the interpolation in the reduced space [45].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Fracture Analysis Using Scaled Boundary Finite Element Methods Accelerated by Proper Orthogonal Decomposition and Radial Basis Functions

Shen

Wang

et al. 2021

Geofluids

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This paper presents a stochastic analysis method for linear elastic fracture mechanics using the Monte Carlo simulations (MCs) and the scaled boundary finite element method (SBFEM) based on proper orthogonal decomposition (POD) and radial basis functions (RBF). The semianalytical solutions obtained by the SBFEM enable us to capture the stress intensity factors (SIFs) easily and accurately. The adoption of POD and RBF significantly reduces the model order and increases computation efficiency, while maintaining the versatility and accuracy of MCs. Numerical examples of cracks in homogeneous and bimaterial plates are provided to demonstrate the effectiveness and reliability of the proposed method, where the crack inclination angles are set as uncertain variables. It is also found that the larger the scale of the problem, the more advantageous the proposed method is.

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An adaptive SVD–Krylov reduced order model for surrogate based structural shape optimization through isogeometric boundary element method

Abstract: W. (2019) 'An adaptive SVD-Krylov reduced order model for surrogate based structural shape optimization through isogeometric boundary element method.', Computer methods in applied mechanics and engineering., 349. pp. 312-338.

Cited by 36 publications

References 72 publications

Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods

Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods

SVD-Krylov based Sparsity-preserving Techniques for Riccati-based Feedback Stabilization of Unstable Power System Models

Stochastic Fracture Analysis Using Scaled Boundary Finite Element Methods Accelerated by Proper Orthogonal Decomposition and Radial Basis Functions

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