Mostafa Shaaban, Ahmed; Anitescu, Cosmin; Atroshchenko, Elena; Rabczuk, Timon Shape optimization by conventional and extended isogeometric boundary element method with PSO for two-dimensional Helmholtz acoustic problems. (English) Zbl 1464.76188 Eng. Anal. Bound. Elem. 113, 156-169 (2020). Summary: In this paper, a new approach is developed for applications of shape optimization on the two-dimensional time harmonic wave propagation (Helmholtz equation) in acoustic problems. The particle swarm optimization (PSO) algorithm – a gradient-free optimization method avoiding the sensitivity analysis – is coupled with two boundary element methods (BEM) and isogeometric analysis (IGA). The first method is the conventional isogeometric boundary element method (IGABEM). The second method is the eXtended IGABEM (XIBEM) enriched with the partition-of-unity expansion using a set of plane waves. In both methods, the computational domain is parameterized and the unknown solution is approximated using non-uniform rational B-splines basis functions (NURBS).In the optimization models, the advantage of IGA is the feature of representing the three models; i.e. shape design/analysis/optimization, using a set of control points, which also represent control variables and optimization parameters, making communication between the three models easy and straightforward.A numerical example is considered for the duct problem to validate the presented techniques against the analytical solution. Furthermore, two different applications for various frequencies are studied; the vertical noise barrier and the horn problems, and the obtained results are compared against previously published numerical methods using sensitivity analysis and genetic algorithms to verify the efficiency of the proposed approaches. Cited in 9 Documents MSC: 76Q05 Hydro- and aero-acoustics 76M15 Boundary element methods applied to problems in fluid mechanics 76N25 Flow control and optimization for compressible fluids and gas dynamics 65N38 Boundary element methods for boundary value problems involving PDEs Keywords:BEM; isogeometric analysis; acoustics; partition of unity; shape optimization PDFBibTeX XMLCite \textit{A. Mostafa Shaaban} et al., Eng. Anal. Bound. Elem. 113, 156--169 (2020; Zbl 1464.76188) Full Text: DOI References: [1] Goel, G. C.; Jain, D. L., Scattering of plane waves by a penetrable elliptic cylinder, JASA, 69, 2, 371-379 (1981) · Zbl 0459.76060 [2] Su, J.; Varadan, V. V.; Varadan, V.; Flax, L., Acoustic wave scattering by a finite elastic cylinder in water, JASA, 68, 2, 686-691 (1980) · Zbl 0444.73021 [3] Duczek, S.; Willberg, C.; Schmicker, D.; Gabbert, U., Development, validation and comparison of higher order finite element approaches to compute the propagation of Lamb waves efficiently, Key Eng. Mater., 518, 95-105 (2012) [4] Willberg, C.; Duczek, S.; Vivar Perez, J. M.; Ahmad, Z. A.B., Simulation methods for guided-wave based structural health monitoring: a review, Appl. Mech. Rev., 67, 1, 1-20 (2015) [5] Harari, I.; Hughes, T., Galerkin/least-squares finite element methods for the reduced wave equation with non-reflecting boundary conditions in unbounded domains, CMAME, 98, 3, 411-454 (1992) · Zbl 0762.76053 [6] Strouboulis, T.; BabuÅ!‘ka, I.; Hidajat, R., The generalized finite element method for Helmholtz equation: theory, computation, and open problems, CMAME, 195, 37, 4711-4731 (2006) · Zbl 1120.76044 [7] Suleau, S.; Bouillard, P., One-dimensional dispersion analysis for the element-free Galerkin method for the helmholtz equation, IJNME, 47, 6, 1169-1188 (2000) · Zbl 0960.76065 [8] Wrobel, L., The boundary element method: Applications in thermo-fluids and acoustics, John Wiley & Sons, 1 (2002) [9] Hughes, T.; Cottrell, J.; Bazilevs, Y., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, CMAME, 194, 39, 4135-4195 (2005) · Zbl 1151.74419 [10] Piegl, L.; Tille, W., The NURBS book, Springer (1995) [11] Bazilevs, Y.; Calo, V.; Cottrell, J.; Evans, J.; Hughes, T.; Lipton, S., Isogeometric analysis using T-splines, CMAME, 199, 5, 229-263 (2010), Computational Geometry and Analysis · Zbl 1227.74123 [12] Auricchio, F.; da Veiga, L. B.; Huges, T. J.R.; Reali, A.; Sangalli, G., Isogeometric collocation methods, Math Model Methods Appl Sci, 20, 11, 2075-2107 (2010) · Zbl 1226.65091 [13] Chai, Y.; You, X.; Li, W.; Huang, Y.; Yue, Z.; Wang, M., Application of the edge-based gradient smoothing technique to acoustic radiation and acoustic scattering from rigid and elastic structures in two dimensions, Comput Struct, 203, 43-58 (2018) [14] Videla, J.; Anitescu, C.; Khajah, T.; Bordas, S. P.; Atroshchenko, E., h- and p-adaptivity driven by recovery and residual-based error estimators for pht-splines applied to time-harmonic acoustics, Comput Math Appl, 77, 9, 2369-2395 (2019) · Zbl 1442.65409 [15] Simpson, R.; Bordas, S.; Trevelyan, J.; Rabczuk, T., A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis, CMAME, 209-212, 87-100 (2012) · Zbl 1243.74193 [16] Peng, X.; Atroshchenko, E.; Kerfriden, P.; Bordas, S. P.A., Linear elastic fracture simulation directly from cad: 2D nurbs-based implementation and role of tip enrichment, Int J Fract, 204, 1, 55-78 (2017) [17] Peng, X.; Atroshchenko, E.; Kerfriden, P.; Bordas, S., Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth, Comput Method Appl Mech Eng, 316, 151-185 (2017), Special Issue on Isogeometric Analysis: Progress and Challenges · Zbl 1439.74370 [18] Beer, G.; Mallardo, V.; Ruocco, E.; Marussig, B.; Zechner, J.; Dünser, C., Isogeometric boundary element analysis with elasto-plastic inclusions. part 2: 3-d problems, Comput Method Appl Mech Eng, 315, 418-433 (2017) · Zbl 1439.74056 [19] Ginnis, A.; Kostas, K.; Politis, C.; Kaklis, P.; Belibassakis, K.; Gerostathis, T., Isogeometric boundary-element analysis for the wave-resistance problem using t-splines, Comput Method Appl Mech Eng, 279, 425-439 (2014) · Zbl 1423.74270 [20] Peake, M.; Trevelyan, J.; Coates, G., Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems, CMAME, 259, 93-102 (2013) · Zbl 1286.65176 [21] Simpson, R.; Scott, M.; Taus, M.; Thomas, D.; Lian, H., Acoustic isogeometric boundary element analysis, Comput Method Appl Mech Eng, 269, 265-290 (2014) · Zbl 1296.65175 [22] Chen, L.; Liu, C.; Zhao, W.; Liu, L., An isogeometric approach of two dimensional acoustic design sensitivity analysis and topology optimization analysis for absorbing material distribution, CMAME, 336, 507-532 (2018) · Zbl 1440.74286 [23] Melenk, J.; BabuÅ!‘ka, I., The partition of unity finite element method: basic theory and applications, Comput Method Appl Mech Eng, 139, 1, 289-314 (1996) · Zbl 0881.65099 [24] Perrey-Debain, E.; Trevelyan, J.; Bettess, P., Plane wave interpolation in direct collocation boundary element method for radiation and wave scattering: numerical aspects and applications, J Sound Vibrat, 261, 5, 839-858 (2003) · Zbl 1237.74107 [25] Kane, J. H.; Mao, S.; Everstine, G. C., A boundary element formulation for acoustic shape sensitivity analysis, J Acoust Soc Am, 90, 1, 561-573 (1991) [26] Bängtsson, E.; Noreland, D.; Berggren, M., Shape optimization of an acoustic horn, Comput Method Appl Mech Eng, 192, 11, 1533-1571 (2003) · Zbl 1175.76127 [27] Chen, L.; Chen, H.; Zheng, C.; Marburg, S., Structural acoustic sensitivity analysis of radiated sound power using a finite element/ discontinuous fast multipole boundary element scheme, IJNMF, 82, 12, 858-878 (2016) [28] Kennedy, J.; Eberhart, R., Particle swarm optimization, Proceedings of ICNN’95 - International Conference on Neural Networks, 4, 1942-1948 (1995), IEEE [29] Eberhart, R.; Kennedy, J., A new optimizer using particle swarm theory, Proceedings of the Sixth International Symposium on Micro Machine and Human Science, 39-42 (1995), IEEE [30] Sun, S.; Yu, T.; Nguyen, T.; Atroshchenko, E.; Bui, T., Structural shape optimization by IGABEM and particle swarm optimization algorithm, EABE, 88, 26-40 (2018) · Zbl 1403.74234 [31] Barbieri, R.; Barbieri, N.; de Lima, K. F., Some applications of the PSO for optimization of acoustic filters, Appl Acoust, 89, 62-70 (2015) [32] Li, K.; Qian, X., Isogeometric analysis and shape optimization via boundary integral, Comput-Aided Des, 43, 11, 1427-1437 (2011) [33] Blanchard, L.; Duvigneau, R.; Vuong, A.-V.; Simeon, B., Shape gradient for isogeometric structural design, J Optim Theory Appl, 161, 2, 361-367 (2014) · Zbl 1291.90236 [34] Ding, C. S.; Cui, X. Y.; Li, G. Y., Accurate analysis and thickness optimization of tailor rolled blanks based on isogeometric analysis, Struct Multidiscip Optim, 54, 4, 871-887 (2016) [35] Espath, L. F.R.; Linn, R. V.; Awruch, A. M., Shape optimization of shell structures based on NURBS description using automatic differentiation, Int J Numer Method Eng, 88, 7, 613-636 (2011) · Zbl 1242.74067 [36] Kiendl, J.; Schmidt, R.; Wüchner, R.; Bletzinger, K.-U., Isogeometric shape optimization of shells using semi-analytical sensitivity analysis and sensitivity weighting, Comput Method Appl Mech Eng, 274, 148-167 (2014) · Zbl 1296.74082 [37] Kostas, K.; Ginnis, A.; Politis, C.; Kaklis, P., Shape-optimization of 2D hydrofoils using an isogeometric BEM solver, Comput-Aided Des, 82, 79-87 (2017) [38] Park, B.-U.; Seo, Y.-D.; Sigmund, O.; Youn, S.-K., Shape optimization of the stokes flow problem based on isogeometric analysis, Struct Multidiscip Optim, 48, 5, 965-977 (2013) [39] Nørtoft, P.; Gravesen, J., Isogeometric shape optimization in fluid mechanics, Struct Multidiscip Optim, 48, 5, 909-925 (2013) [40] Nguyen, Q. M.; Dang, V.; Kilic, O.; El-Araby, E., Parallelizing fast multipole method for large-scale electromagnetic problems using GPU clusters, IEEE Antennas Wirel Propagat Lett, 12, 868-871 (2013) [41] Kostas, K.; Fyrillas, M.; Politis, C.; Ginnis, A.; Kaklis, P., Shape optimization of conductive-media interfaces using an IGA-BEM solver, Comput Method Appl Mech Eng, 340, 600-614 (2018) · Zbl 1440.74334 [42] Keller, J. B.; Givoli, D., Exact non-reflecting boundary conditions, J Comput Phys, 82, 1, 172-192 (1989) · Zbl 0671.65094 [43] M, G.; G., K.; J., R. T.; J., R. F., A general algorithm for the numerical solution of hypersingular boundary integral equations, J Appl Mech ASME, 59(3), 604-614 (1992) · Zbl 0765.73072 [44] Telles, J. C.F., A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals, Int J Numer Method Eng, 24, 5, 959-973 (1987) · Zbl 0622.65014 [45] Huttunen, T.; Gamallo, P.; Astley, R. J., Comparison of two wave element methods for the Helmholtz problem, Commun Numer Method Eng, 25, 1, 35-52 (2009) · Zbl 1158.65347 [46] Ishizuka, T.; Fujiwara, K., Performance of noise barriers with various edge shapes and acoustical conditions, Appl Acoustic, 65, 2, 125-141 (2004) [47] Barbieri, R.; Barbieri, N., Acoustic horns optimization using finite elements and genetic algorithm, Appl Acoust, 74, 3, 356-363 (2013) [48] Udawalpola, R.; Berggren, M., Optimization of an acoustic horn with respect to efficiency and directivity, IJNME, 73, 11, 1571-1606 (2008) · Zbl 1159.76043 [49] Johannessen, K. A.; Kvamsdal, T.; Dokken, T., Isogeometric analysis using LR B-splines, Comput Method Appl Mech Eng, 269, 471-514 (2014) · Zbl 1296.65021 [50] Deng, J.; Chen, F.; Li, X.; Hu, C.; Tong, W.; Yang, Z., Polynomial splines over hierarchical T-meshes, Graph Models, 70, 4, 76-86 (2008) 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.