Accelerating boundary element methods in wideband frequency sweep analysis by matrix-free model order reduction

Li, Yue; Atak, Onur; Jonckheere, Stijn; Desmet, Wim

doi:10.1016/j.jsv.2022.117323

Cited by 4 publications

(2 citation statements)

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“…In [9,10], project-based model order reduction (MOR) methods were developed for conventional BEM systems, aiming to reduce the computational cost of multi-frequency acoustic wave analysis. A key step in this approach is to construct a series of frequencyindependent matrices by expanding frequency-dependent BEM kernels, which is non-trivial especially for problems with complex boundary conditions [11]. To overcome this challenge, a matrix-free MOR method was proposed [11].…”

Section: Introductionmentioning

confidence: 99%

“…A key step in this approach is to construct a series of frequencyindependent matrices by expanding frequency-dependent BEM kernels, which is non-trivial especially for problems with complex boundary conditions [11]. To overcome this challenge, a matrix-free MOR method was proposed [11]. This method operates on the transfer functions between system inputs and outputs, circumventing complications arising from complex boundary conditions and enabling integration with existing acceleration techniques.…”

Section: Introductionmentioning

confidence: 99%

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A Boundary-based Fourier Neural Operator (B-FNO) Method for Efficient Parametric Acoustic Wave Analysis

Li,

Ye,

Liu

2024

Preprint

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Repetitive wave analysis is required in various applications involving parametric analyses across different settings. However, traditional numerical methods based on domain discretization become computationally impractical due to the large number of simulations required, especially in unbounded domains. The boundary element method (BEM) is known for its effectiveness in solving wave equations, particularly in unbounded domains. Nevertheless, even with accelerated techniques, large-scale problems and those with high frequencies often necessitate numerous iterations, hampered by ill-conditioned system matrices. As a result, BEM becomes unsuitable for parametric analysis. To address these challenges, surrogate modelling techniques have been developed, and recent advancements in neural operators show promise in constructing surrogate models. However, they still face limitations when efficiently handling exterior and high-dimensional problems. In this study, we propose a novel data-driven surrogate modelling approach called B-FNO, which combines BEM and Fourier neural operator (FNO) for wave analysis in varying domains and frequencies. This approach formulates wave equations as integral formulations and utilizes FNO to map problem boundaries and other parameters to boundary solutions. Compared to existing surrogate modelling techniques, the B-FNO approach offers several advantages. These include reduced problem dimensionality and computational complexity, the ability to handle exterior problems without domain truncation, and significantly improved efficiency and accuracy compared to well-known neural network surrogate models. Moreover, compared to accelerated BEM, the B-FNO approach is better behaved and requires a much smaller number of iterations. We validate the effectiveness of our method through numerical experiments on a series of 2D and 3D benchmark problems, demonstrating its potential for broad application.

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