Large-scale three-dimensional acoustic Horn optimization. (English) Zbl 1515.35030
Summary: We consider techniques that enable large-scale gradient-based shape optimization of wave-guiding devices in the context of three-dimensional time-domain simulations. The approach relies on a memory efficient boundary representation of the shape gradient together with primal and adjoint solvers semiautomatically generated by the FEniCS framework. The hyperbolic character of the governing linear wave equation, written as a first-order system, is exploited through systematic use of the characteristic decomposition both to define the objective function and to obtain stable numerical fluxes in the discontinuous Galerkin spatial discretization. The methodology is successfully used to optimize the shape of a midrange acoustic horn, described by 1,762 design variables, for maximum transmission efficiency, where the parallel computations involve a total of \(3.5\times10^9\) unknowns.
MSC:
| 35A35 | Theoretical approximation in context of PDEs |
| 35L05 | Wave equation |
| 65K10 | Numerical optimization and variational techniques |
| 65M25 | Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs |
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 68N19 | Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.) |
Keywords:
shape optimization; shape derivatives; acoustic wave equation; computational acoustics; discontinuous Galerkin method; code generationReferences:
| [1] | S. G. Amin, M. H. M. Ahmed, and H. A. Youssef, {\it Computer-aided design of acoustic horns for ultrasonic machining using finite-element analysis}, J. Materials Process. Tech., 55 (1995), pp. 254-260. |
| [2] | E. Arian and S. Ta’asan, {\it Analysis of the Hessian for Aerodynamic Optimization: Inviscid Flow}, Technical Report 96-28, Institute for Computer Applications in Science and Engineering (ICASE), 1996. · Zbl 0969.76015 |
| [3] | E. Bängtsson, D. Noreland, and M. Berggren, {\it Shape optimization of an acoustic horn}, Comput. Methods Appl. Mech. Engrg., 192 (2003), pp. 1533-1571. · Zbl 1175.76127 |
| [4] | R. Barbieri, N. Barbieri, and K. F. de Lima, {\it Some applications of the PSO for optimization of acoustic filters}, Appl. Acoustics, 80 (2015), pp. 62-70. |
| [5] | M. P. Bendsø e and O. Sigmund, {\it Topology Optimization–Theory, Methods and Applications}, 2nd ed., Springer, Berlin, Heidelberg, New York, 2004. · Zbl 1059.74001 |
| [6] | R. Berbieri and N. Barbieri, {\it Acoustic horns optimization using finite elements and genetic algorithm}, Appl. Acoustics, 74 (2013), pp. 356-363, doi:10.1016/j.apacoust.2012.09.007. |
| [7] | M. Berggren, {\it A unified discrete-continuous sensitivity analysis method for shape optimization}, in Applied and Numerical Partial Differential Equations, Comput. Methods Appl. Sci. 15, Springer, New York, 2010, pp. 25-39. · Zbl 1186.65078 |
| [8] | D. J. Brackett, I. A. Ashcroft, and R. J. M. Hague, {\it Multi-physics optimisation of “brass” instruments–A new method to include structural and acoustical interactions}, Struct. Multidiscip. Optim., 40 (2009), p. 611-624, doi:10.1007/s00158-009-0394-0. |
| [9] | L. Chen, {\it Mesh smoothing schemes based on optimal Delaunay triangulations}, in Proceedings of the 13th International Meshing Roundtable, Williamsburg, VA, 2004, Sandia National Laboratories, pp. 109-120. |
| [10] | M. Colloms, {\it High Performance Loudspeakers}, 6th ed., Wiley, New York, 2005. |
| [11] | M. C. Delfour and J.-P. Zolésio, {\it Shapes and Geometries. Metrics, Analysis, Differential Calculus, and Optimization}, 2nd ed., Adv. Des. Control 22, SIAM, Philadelphia, 2011. · Zbl 1251.49001 |
| [12] | Q. Du, V. Faber, and M. Gunzburger, {\it Centroidal Voronoi tessellations: Applications and algorithms}, SIAM Rev., 41 (1999), pp. 637-676, doi:10.1137/S0036144599352836. · Zbl 0983.65021 |
| [13] | B. Farhadinia, {\it Structural optimization of an acoustic horn}, Appl. Math. Modeling, 36 (2012), pp. 2017-2030, doi:10.1016/j.apm.2011.08.016. · Zbl 1243.74143 |
| [14] | J. S. Hesthaven and T. Warburton, {\it Nodal Discontinuous Galerkin Methods. Algorithms, Analysis, and Applications}, Texts Appl. Math. 54, Springer, New York, 2008, doi:10.1007/978-0-387-72067-8. · Zbl 1134.65068 |
| [15] | R. M. Hicks and P. A. Henne, {\it Wing design by numerical optimization}, J. Aircraft, 15 (1978), pp. 407-412. |
| [16] | F. Kasolis, E. Wadbro, and M. Berggren, {\it Fixed-mesh curvature-parameterized shape optimization of an acoustic horn}, Struct. Multidiscip. Optim., 46 (2012), pp. 727-738, doi:10.1007/s00158-012-0828-y. · Zbl 1274.74274 |
| [17] | A. Logg, K.-A. Mardal, and G. N. Wells, eds., {\it Automated Solution of Differential Equations by the Finite Element Method}, Lect. Notes Comput. Sci. Eng., Springer, New York, 2012, doi:10.1007/978-3-642-23099-8. · Zbl 1247.65105 |
| [18] | R. C. Morgans, A. C. Zander, C. H. Hansen, and D. J. Murphy, {\it EGO shape optimization of horn-loaded loudspeakers}, Optim. Engrg., 9 (2008), pp. 361-374. · Zbl 1419.76580 |
| [19] | P. M. Morse, {\it Vibration and Sound}, McGraw-Hill, New York, 1948. |
| [20] | D. Noreland, R. Udawalpola, and M. Berggren, {\it A hybrid scheme for bore design optimization of a brass instrument}, J. Acoust. Soc. Amer., 128 (2010), pp. 1391-1400, doi:10.1121/1.3466871. |
| [21] | D. Noreland, R. Udawalpola, P. Seoane, E. Wadbro, and M. Berggren, {\it An Efficient Loudspeaker Horn Design by Numerical Optimization: An Experimental Study}, Technical Report UMINF 10.01, Department of Computing Science, Ume\aa University, 2010. |
| [22] | S. W. Rienstra and A. Hirschberg, {\it An Introduction to Acoustics}, revised and updated version of reports IWDE 92-06 and IWDE 01-03, Eindhoven University of Technology, Eindhoven, The Netherlands, 2015. |
| [23] | S. Schmidt, {\it Efficient Large Scale Aerodynamic Design Based on Shape Calculus}, Ph.D. thesis, Department of Mathematics, University of Trier, Germany, 2010. |
| [24] | S. Schmidt, {\it A Two Stage CVT/Eikonal Convection Mesh Deformation Approach for Large Nodal Deformations}, preprint, arXiv:1411.7663, 2014. |
| [25] | S. Schmidt, C. Ilic, V. Schulz, and N. Gauger, {\it Three dimensional large scale aerodynamic shape optimization based on shape calculus}, AIAA J., 51 (2013), pp. 2615-2627, doi:10.2514/1.J052245. |
| [26] | S. Schmidt and V. Schulz, {\it Impulse response approximations of discrete shape Hessians with application in CFD}, SIAM J. Control Optim., 48 (2009), pp. 2562-2580, doi:10.1137/080719844. · Zbl 1387.49064 |
| [27] | S. Schmidt and V. Schulz, {\it A 2589 line topology optimization code written for the graphics card}, Comput. Vis. Sci., 14 (2011), pp. 249-256, doi:10.1007/s00791-012-0180-1. · Zbl 1380.74100 |
| [28] | J. Sokolowski and J.-P. Zolésio, {\it Introduction to Shape Optimization: Shape Sensitivity Analysis}, Springer, Berlin, Heidelberg, 1992. · Zbl 0761.73003 |
| [29] | S. Ta’asan, {\it One-shot methods for optimal control of distributed parameter systems I: Finite dimensional control}, ICASE, Technical Report 91-2, 1991. |
| [30] | R. Udawalpola and M. Berggren, {\it Optimization of an acoustic horn with respect to efficiency and directivity}, Internat. J. Numer. Methods Engrg., 73 (2008), pp. 1571-1606. · Zbl 1159.76043 |
| [31] | R. Udawalpola, E. Wadbro, and M. Berggren, {\it Optimization of a variable mouth acoustic horn}, Internat. J. Numer. Methods Engrg., 85 (2011), pp. 591-606, doi:10.1002/nme.2982. · Zbl 1217.76068 |
| [32] | E. Wadbro and M. Berggren, {\it Topology optimization of an acoustic horn}, Comput. Methods Appl. Mech. Engrg., 196 (2006), pp. 429-436. · Zbl 1120.76359 |
| [33] | E. Wadbro, R. Udawalpola, and M. Berggren, {\it Shape and topology optimization of an acoustic horn-lens combination}, J. Comput. Appl. Math., 234 (2010), pp. 1781-1787. · Zbl 1256.74020 |
| [34] | B. Webb and J. Baird, {\it Advances in line array technology for live sound}, in Proceedings of the 18th Audio Engineering Society Conference: Live Sound, 2003, 10. |
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