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Abstract 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.
Li et al. (Thu,) studied this question.