Learning based numerical methods for acoustic frequency-domain simulation with high frequency. (English) Zbl 07855374
Keywords:
learning based methods; Helmholtz equations; high frequency; fundamental solution; Tikhonov regularizationReferences:
| [1] | Karageorghis, A.; Lesnic, D.; Marin, L., The MFS for the identification of a sound-soft interior acoustic scatterer, Eng Anal Bound Elem, 83, 107-112, 2017 · Zbl 1403.76152 |
| [2] | Ihlenburg, F.; Babuška, I., Finite element solution of the Helmholtz equation with high wave number part I: The h-version of the FEM, Comput Math Appl, 30, 9, 9-37, 1995 · Zbl 0838.65108 |
| [3] | Ihlenburg, F.; Babuska, I., Finite element solution of the Helmholtz equation with high wave number part II: the hp version of the FEM, SIAM J Numer Anal, 34, 1, 315-358, 1997 · Zbl 0884.65104 |
| [4] | Duan, S.; Wu, H., Adaptive FEM for Helmholtz equation with large wavenumber, J Sci Comput, 94, 1, 21, 2023 · Zbl 1504.65253 |
| [5] | Dastour, H.; Liao, W., A fourth-order optimal finite difference scheme for the Helmholtz equation with PML, Comput Math Appl, 78, 6, 2147-2165, 2019 · Zbl 1442.65323 |
| [6] | Grigoriev, M.; Dargush, G., A fast multi-level boundary element method for the Helmholtz equation, Comput Methods Appl Mech Eng, 193, 3-5, 165-203, 2004 · Zbl 1075.76587 |
| [7] | Keuchel, S.; Vater, K.; Estorff, O.v., Hp fast multipole boundary element method for 3D acoustics, Internat J Numer Methods Engrg, 110, 9, 842-861, 2017 · Zbl 07866635 |
| [8] | Steinbach, O.; Windisch, M., Stable boundary element domain decomposition methods for the Helmholtz equation, Numer Math, 118, 171-195, 2011 · Zbl 1222.65130 |
| [9] | Qu, W.; Chen, W.; Zheng, C., Diagonal form fast multipole singular boundary method applied to the solution of high-frequency acoustic radiation and scattering, Int J Numer Methods Eng, 111, 9, 803-815, 2017 · Zbl 07867125 |
| [10] | Liu, H.; Wang, F.; Qiu, L.; Chi, C., Acoustic simulation using singular boundary method based on loop subdivision surfaces: a seamless integration of CAD and CAE, Eng Anal Bound Elem, 158, 97-106, 2024 · Zbl 07875801 |
| [11] | Wei, X.; Luo, W., 2.5D singular boundary method for acoustic wave propagation, Appl Math Lett, 112, Article 106760 pp., 2021 · Zbl 1462.76149 |
| [12] | Wei, X.; Cheng, X.; Chen, D.; Chen, S.; Zheng, H.; Sun, L., Acoustic sensitivity analysis for 3D structure with constant cross-section using 2.5D singular boundary method, Eng Anal Bound Elem, 155, 948-955, 2023 · Zbl 1537.76148 |
| [13] | Evans, L. C., Partial differential equations, 2016, American Math Society |
| [14] | Liu, Z., Multi-scale deep neural network (MscaleDNN) for solving Poisson-Boltzmann equation in complex domains, Commun Comput Phys, 28, 1970-2001, 2020 · Zbl 1473.65348 |
| [15] | Raissi, M.; Perdikaris, P.; Karniadakis, G., Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, J Comput Phys, 378, 686-707, 2019 · Zbl 1415.68175 |
| [16] | Sirignano, J.; Spiliopoulos, K., DGM: A deep learning algorithm for solving partial differential equations, J Comput Phys, 375, 1339-1364, 2018 · Zbl 1416.65394 |
| [17] | Weinan, E.; Yu, B., The deep ritz method: a deep larning-based numerical algorithm for solving variational problems, Commun Math Stat, 6, 1, 1-12, 2018 · Zbl 1392.35306 |
| [18] | Zang, Y.; Bao, G.; Ye, X.; Zhou, H., Weak adversarial networks for high-dimensional partial differential equations, J Comput Phys, 411, Article 109409 pp., 2020 · Zbl 1436.65156 |
| [19] | Aldirany, Z.; Cottereau, R.; Laforest, M.; Prudhomme, S., Operator approximation of the wave equation based on deep learning of Green’s function, 2023, arXiv:2307.13902 |
| [20] | Bar-Sinai, Y.; Hoyer, S.; Hickey, J.; Brenner, M. P., Learning data-driven discretizations for partial differential equations, Proc Natl Acad Sci USA, 116, 31, 15344-15349, 2019 · Zbl 1431.65195 |
| [21] | Ray, D.; Hesthaven, J. S., An artificial neural network as a troubled-cell indicator, J Comput Phys, 367, 166-191, 2018 · Zbl 1415.65229 |
| [22] | Wang, Y.; Shen, Z.; Long, Z.; Dong, B., Learning to discretize: solving 1D scalar conservation laws via deep reinforcement learning, Commun Comput Phys, 28, 5, 2158-2179, 2020 · Zbl 1473.65124 |
| [23] | Cheng, A. H.; Hong, Y. X., An overview of the method of fundamental solutions-solvability, uniqueness, convergence, and stability, Eng Anal Bound Elem, 120, 118-152, 2020 · Zbl 1464.65264 |
| [24] | Barnett, A.; Betcke, T., Stability and convergence of the method of fundamental solutions for Helmholtz problems on analytic domains, J Comput Phys, 227, 14, 7003-7026, 2008 · Zbl 1170.65082 |
| [25] | Gin, C. R.; Shea, D. E.; Brunton, S. L.; Kutz, J. N., DeepGreen: deep learning of Green’s functions for nonlinear boundary value problems, Sci Rep, 11, 21614, 2021 |
| [26] | Zhang, L.; Luo, T.; Zhang, Y.; Xu, Z.-Q. J.; Ma, Z., MOD-Net: a machine learning approach via model-operator-data network for solving PDEs, 2021, arXiv:2107.03673 |
| [27] | Lin, G.; Chen, F.; Hu, P.; Chen, X.; Chen, J.; Wang, J.; Shi, Z., BI-GreenNet: learning Green’s functions by boundary integral network, Commun Math Stat, 11, 103-129, 2023 · Zbl 1512.35172 |
| [28] | Cheng, J.; Yamamoto, M., One new strategy for a priori choice of regularizing parameters in Tikhonov’s regularization, Inverse Probl, 16, 4, L31, 2000 · Zbl 0957.65052 |
| [29] | Tikhonov, A. N.; Arsenin, V., Solutions of ill-posed problems, 1977, Wiley: Wiley New York · Zbl 0354.65028 |
| [30] | Chen, Y.; Cheng, J.; Li, T.; Miao, Y., Learning based numerical methods for Helmholtz equation with high frequency, 2024, arXiv:2401.09118 |
| [31] | Gopal, A.; Trefethen, L. N., New Laplace and Helmholtz solvers, Proc Natl Acad Sci USA, 116, 21, 10223-10225, 2019 · Zbl 1431.65224 |
| [32] | Brubeck, P. D.; Trefethen, L. N., Lightning Stokes solver, SIAM J Sci Comput, 44, 3, A1205-A1226, 2022 · Zbl 1509.41008 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
