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Honshuku, Yuta; Isakari, Hiroshi

A topology optimisation of acoustic devices based on the frequency response estimation with the Padé approximation. (English) Zbl 1505.74179

Appl. Math. Modelling 110, 819-840 (2022).

MSC:

74P15 Topological methods for optimization problems in solid mechanics
49Q12 Sensitivity analysis for optimization problems on manifolds

Keywords:

topology optimisation; fast frequency sweep; Padé approximation; acoustic device; boundary element method; topological derivative
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Full Text: DOI arXiv

References:

[1] Prager, W., A note on discretized Michell structures, Computer Methods in Applied Mechanics and Engineering, 3, 3, 349-355 (1974) · Zbl 0278.73044
[2] Takahashi, T.; Sato, D.; Isakari, H.; Matsumoto, T., A shape optimisation with the isogeometric boundary element method and adjoint variable method for the three-dimensional helmholtz equation, Computer-Aided Design, 142, 103126 (2022)
[3] Bendsœ, M.; Kikuchi, N., Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, 71, 2, 197-224 (1988) · Zbl 0671.73065
[4] Amstutz, S.; Andrä, H., A new algorithm for topology optimization using a level-set method, Journal of Computational Physics, 216, 2, 573-588 (2006) · Zbl 1097.65070
[5] Isakari, H.; Takahashi, T.; Matsumoto, T., A topology optimization with level-sets of B-spline surface, Transactions of JASCOME, 17, 125-130 (2017)
[6] Wadbro, E.; Berggren, M., Topology optimization of an acoustic horn, Computer Methods in Applied Mechanics and Engineering, 196, 1-3, 420-436 (2006) · Zbl 1120.76359
[7] Kook, J.; Jensen, J. S.; Wang, S., Acoustical topology optimization of Zwicker’s loudness with Padé approximation, Computer Methods in Applied Mechanics and Engineering, 255, 40-66 (2013) · Zbl 1297.74097
[8] Sato, Y.; Izui, K.; Yamada, T.; Nishiwaki, S., Robust topology optimization of optical cloaks under uncertainties in wave number and angle of incident wave, International Journal for Numerical Methods in Engineering, 121, 17, 3926-3954 (2020) · Zbl 07863309
[9] Qin, J.; Isakari, H.; Taji, K.; Takahashi, T.; Matsumoto, T., A robust topology optimization for enlarging working bandwidth of acoustic devices, International Journal for Numerical Methods in Engineering, 122, 11, 2694-2711 (2021) · Zbl 07863771
[10] Jensen, J. S., Topology optimization of dynamics problems with Padé approximants, International Journal for Numerical Methods in Engineering, 72, 13, 1605-1630 (2007) · Zbl 1194.74270
[11] Aberth, O., Iteration methods for finding all zeros of a polynomial simultaneously, Mathematics of Computation, 27, 122, 339-344 (1973) · Zbl 0282.65037
[12] Colton, D.; Kress, R., Inverse acoustic and electromagnetic scattering theory, 2nd Edition (1998), Springer · Zbl 0893.35138
[13] Burton, A. J.; Miller, G. F., The application of integral equation methods to the numerical solution of some exterior boundary-value problems, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 323, 1553, 201-210 (1971) · Zbl 0235.65080
[14] Bebendorf, M., Hierarchical matrices (2008), Springer · Zbl 1151.65090
[15] Rokhlin, V., Rapid solution of integral equations of classical potential theory, Journal of Computational Physics, 60, 2, 187-207 (1985) · Zbl 0629.65122
[16] Greengard, L.; Rokhlin, V., A fast algorithm for particle simulations, Journal of Computational Physics, 73, 2, 325-348 (1987) · Zbl 0629.65005
[17] Otani, Y., Fast multipole methods for periodic problems in elasticity and electromagnetics (2007), PhD thesis (Kyoto University)
[18] Carpio, A.; Rapun, M. L., Solving inhomogeneous inverse problems by topological derivative methods, Inverse Problems, 24, 4, 045014 (2008) · Zbl 1153.35401
[19] Park, W. K., Performance analysis of multi-frequency topological derivative for reconstructing perfectly conducting cracks, Journal of Computational Physics, 335, 865-884 (2017) · Zbl 1375.78027
[20] Louër, F. L.; Rapún, M. L., Detection of multiple impedance obstacles by non-iterative topological gradient based methods, Journal of Computational Physics, 388, 534-560 (2019) · Zbl 1452.65041
[21] Meddahi, S.; Sayas, F. J., Analysis of a new BEM-FEM coupling for two-dimensional fluid-solid interaction, Numerical Methods for Partial Differential Equations: An International Journal, 21, 6, 1017-1042 (2005) · Zbl 1078.74054
[22] Yamada, T.; Izui, K.; Nishiwaki, S.; Takezawa, A., A topology optimization method based on the level set method incorporating a fictitious interface energy, Computer Methods in Applied Mechanics and Engineering, 199, 45-48, 2876-2891 (2010) · Zbl 1231.74365
[23] Saad, Y.; Schultz, M. H., GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM Journal on Scientific and Statistical Computing, 7, 3, 856-869 (1986) · Zbl 0599.65018
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