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Topology optimization design of 3D electrothermomechanical actuators by using GPU as a co-processor. (English) Zbl 1425.74378
Summary: The topology optimization method (TOM) requires high computational resources to be solved, especially in multiphysics problems. The high number of computational requirements is because TOM is an iterative technique, in which the iterations go from tens to thousands. Furthermore, at each TOM iteration, it is necessary to execute several routines such as the finite element method (FEM), the optimizer, the calculation of the objective function and filter, and other less intensive computations. Consequently, several topology optimization problems have been restricted in the dimensionality and/or in the complexity considered, or addressed in powerful computers of restricted access due to their cost. Hence, in order to deal with complex and large-scale problem in standard computers, a methodology based on parallel computing on graphics processing unit (GPU) has been proposed by the scientific community. However, so far, this kind of approach has been mostly investigated for the traditional mean compliance optimization problem. In this work, TOM is applied to designing three-dimensional (3D) electrothermomechanical (ETM) actuators by using GPU as a co-processor in the most intensive and intrinsic parallel tasks of the method. The TOM is based on the SIMP material model and solved by sequential linear programming. The code is programmed in Matlab and CUDA, and is tested for obtaining a 3D microactuator. Considerable speedup is gained with the GPU; the whole TOM process is achieved up to 35 times faster than that obtained with the sequential code version.
MSC:
74P15 Topological methods for optimization problems in solid mechanics
65Y05 Parallel numerical computation
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[1] Bendsøe, M. P.; Sigmund, O., Topology optimization: theory, methods, and applications, (2003), Springer Berlin · Zbl 1059.74001
[2] Challis, V. J.; Roberts, A. P.; Grotowski, J. F., High resolution topology optimization using graphics processing units (GPUs), Struct. Multidiscip. Optim., 49, 315-325, (2013), http://dx.doi.org/10.1007/s00158-013-0980-z
[3] Sigmund, O.; Maute, K., Topology optimization approaches, Struct. Multidiscip. Optim., 48, 1031-1055, (2013), http://dx.doi.org/10.1007/s00158-013-0978-6
[4] Amir, O.; Aage, N.; Lazarov, B. S., On multigrid-CG for efficient topology optimization, Struct. Multidiscip. Optim., 49, 815-829, (2014), http://dx.doi.org/10.1007/s00158-013-1015-5
[5] Aage, N.; Lazarov, B. S., Parallel framework for topology optimization using the method of moving asymptotes, Struct. Multidiscip. Optim., 47, 493-505, (2013), http://dx.doi.org/10.1007/s00158-012-0869-2 · Zbl 1274.74302
[6] Achiche, S.; Fan, Z.; Bolognini, F., Review of automated design and optimization of MEMS, (2007 IEEE International Symposium on Industrial Electronics, (2007), IEEE Vigo), 2150-2155, http://dx.doi.org/10.1109/ISIE.2007.4374941
[7] Mahdavi, A.; Balaji, R.; Frecker, M.; Mockensturm, E. M., Topology optimization of 2D continua for minimum compliance using parallel computing, Struct. Multidiscip. Optim., 32, 121-132, (2006), http://dx.doi.org/10.1007/s00158-006-0006-1
[8] Karatarakis, A.; Metsis, P.; Papadrakakis, M., GPU-acceleration of stiffness matrix calculation and efficient initialization of EFG meshless methods, Comput. Methods Appl. Mech. Engrg., 258, 63-80, (2013), http://dx.doi.org/10.1016/j.cma.2013.02.011 · Zbl 1286.65162
[9] Wang, S.; Sturler, E. D.; Paulino, G. H., Large-scale topology optimization using preconditioned Krylov subspace methods with recycling, Internat. J. Numer. Methods Engrg., 69, 2441-2468, (2007), http://dx.doi.org/10.1002/nme.1798 · Zbl 1194.74265
[10] Brodtkorb, A. R.; Dyken, C.; Hagen, T. R.; Hjelmervik, J. M.; Storaasli, O. O., State-of-the-art in heterogeneous computing, Sci. Program., 18, 1-33, (2010), http://dx.doi.org/0.3233/SPR-2009-0296
[11] Owens, J. D.; Luebke, D.; Govindaraju, N.; Harris, M.; Krüger, J.; Lefohn, A. E.; Purcell, T. J., A survey of general-purpose computation on graphics hardware, Comput. Graph. Forum, 26, 80-113, (2007), http://dx.doi.org/10.1111/j.1467-8659.2007.01012.x
[12] Kirk, D. B.; Hwu, W., Programming massively parallel processors: A hands-on approach, (2012), Morgan Kaufmann Burlington, MA, USA
[13] Wadbro, E.; Berggren, M., Megapixel topology optimization on a graphics processing unit, SIAM Rev., 51, 707-721, (2009), http://dx.doi.org/10.1137/070699822 · Zbl 1179.65079
[14] Borrvall, T.; Petersson, J., Large-scale topology optimization in 3D using parallel computing, Comput. Methods Appl. Mech. Engrg., 190, 6201-6229, (2001), http://dx.doi.org/10.1016/S0045-7825(01)00216-X · Zbl 1022.74036
[15] Vemaganti, K.; Lawrence, W. E., Parallel methods for optimality criteria-based topology optimization, Comput. Methods Appl. Mech. Engrg., 194, 3637-3667, (2005), http://dx.doi.org/10.1016/j.cma.2004.08.008 · Zbl 1176.74145
[16] Kim, T. S.; Kim, J. E.; Kim, Y. Y., Parallelized structural topology optimization for eigenvalue problems, Int. J. Solids Struct., 41, 2623-2641, (2004), http://dx.doi.org/10.1016/j.ijsolstr.2003.11.027 · Zbl 1086.74030
[17] Evgrafov, A.; Rupp, C. J.; Maute, K.; Dunn, M. L., Large-scale parallel topology optimization using a dual-primal substructuring solver, Struct. Multidiscip. Optim., 36, 329-345, (2007), http://dx.doi.org/10.1007/s00158-007-0190-7 · Zbl 1273.74375
[18] Schmidt, S.; Schulz, V., A 2589 line topology optimization code written for the graphics card, Comput. Vis. Sci., 14, 249-256, (2012), http://dx.doi.org/10.1007/s00791-012-0180-1 · Zbl 1380.74100
[19] Zegard, T.; Paulino, G. H., Toward GPU accelerated topology optimization on unstructured meshes, Struct. Multidiscip. Optim., 48, 473-485, (2013), http://dx.doi.org/10.1007/s00158-013-0920-y
[20] D. Herrero, J. Martínez, P. Martí, An implementation of level set based topology optimization using GPU, in: 10th World Congress on Structural and Multidisciplinary Optimization, Orlando, Florida, USA, 2013, pp. 1-10.
[21] Suresh, K., Efficient generation of large-scale Pareto-optimal topologies, Struct. Multidiscip. Optim., 47, 49-61, (2012), http://dx.doi.org/10.1007/s00158-012-0807-3 · Zbl 1274.74399
[22] Lau, J.; Lee, C.; Premachandran, C.; Aibin, Y., Advanced MEMS packaging, (2009), McGraw-Hill Professional New York
[23] El-Hak, M., The MEMS handbook, (2002), CRC Press Boca Raton FL · Zbl 1060.74001
[24] Rubio, W. M.; Silva, E. C.; Bordatchev, E. V.; Zeman, M. J., Topology optimized design, microfabrication and characterization of electro-thermally driven microgripper, J. Intell. Mater. Syst. Struct., 20, 669-681, (2008), http://dx.doi.org/10.1177/1045389X08093548
[25] Jonsmann, J.; Sigmund, O.; Bouwstra, S., Compliant electro-thermal microactuators, (Technical Digest. IEEE International MEMS 99 Conference. Twelfth IEEE International Conference on Micro Electro Mechanical Systems (Cat. No. 99CH36291), (1999), IEEE Orlando, Florida, USA), 588-593, http://dx.doi.org/10.1109/MEMSYS.1999.746894
[26] Mello, L. A.M.; Salas, R. A.; Silva, E. C.N., On response time reduction of electrothermomechanical MEMS using topology optimization, Comput. Methods Appl. Mech. Engrg., 247-248, 93-102, (2012), http://dx.doi.org/10.1016/j.cma.2012.08.008 · Zbl 1352.74191
[27] Mankame, N. D.; Ananthasuresh, G. K., Comprehensive thermal modelling and characterization of an electro-thermal-compliant microactuator, J. Micromech. Microeng., 11, 452-462, (2001), http://dx.doi.org/10.1088/0960-1317/11/5/303
[28] Fu, Z.; James Lewis, T.; Kirby, R. M.; Whitaker, R. T., Architecting the finite element method pipeline for the GPU, J. Comput. Appl. Math., 257, 195-211, (2014), http://dx.doi.org/10.1016/j.cam.2013.09.001 · Zbl 1291.65397
[29] Sigmund, O., Design of multiphysics actuators using topology optimization—part I: one-material structures, Comput. Methods Appl. Mech. Engrg., 190, 6577-6604, (2001), http://dx.doi.org/10.1016/S0045-7825(01)00251-1 · Zbl 1116.74407
[30] Montealegre, W.; Godoy, P. H.; Silva, E. C.N., Design of electrothermomechanical MEMS, (ABCM Symposium Series in Mechatronics, vol. 2, (2005), Brazilian Society of Mechanical Sciences and Engineering Ouro Preto, MG, Brazil), 469-476
[31] Zienkiewicz, O. C.; Taylor, R. L.; Zhu, J. Z., The finite element method: its basis and fundamentals, (2005), Elsevier Amsterdam · Zbl 1307.74005
[32] Haftka, R.; Gürdal, Z., (Elements of Structural Optimization, Solid Mechanics and its Applications, vol. 11, (1992), Kluwer Academic Publishers)
[33] Andreassen, E.; Clausen, A.; Schevenels, M.; Lazarov, B. S.; Sigmund, O., Efficient topology optimization in MATLAB using 88 lines of code, Struct. Multidiscip. Optim., 43, 1-16, (2010), http://dx.doi.org/10.1007/s00158-010-0594-7 · Zbl 1274.74310
[34] Suh, J. W.; Kim, Y., Accelerating MATLAB with GPU computing: A primer with examples, (2014), Elsevier USA
[35] Altman, Y. M., Accelerating MATLAB performance: 1001 tips to speed up MATLAB programs, (2015), CRC Press USA · Zbl 1303.68001
[36] Markall, G. R.; Slemmer, A.; Ham, D. A.; Kelly, P. H.J.; Cantwell, C. D.; Sherwin, S. J., Finite element assembly strategies on multi-core and many-core architectures, Internat. J. Numer. Methods Fluids, 71, 80-97, (2013), http://dx.doi.org/10.1002/fld.3648
[37] Cecka, C.; Lew, A. J.; Darve, E., Assembly of finite element methods on graphics processors, Internat. J. Numer. Methods Engrg., 85, 640-669, (2011), http://dx.doi.org/10.1002/nme.2989 · Zbl 1217.80146
[38] Dailey, D. P., Uniqueness of colorability and colorability of planar 4-regular graphs are NP-complete, Discrete Math., 30, 289-293, (1980), http://dx.doi.org/10.1016/0012-365X(80)90236-8 · Zbl 0448.05030
[39] Komatitsch, D.; Michéa, D.; Erlebacher, G., Porting a high-order finite-element earthquake modeling application to NVIDIA graphics cards using CUDA, J. Parallel Distrib. Comput., 69, 451-460, (2009), http://dx.doi.org/10.1016/j.jpdc.2009.01.006
[40] Krotkiewski, M.; Dabrowski, M., Parallel symmetric sparse matrix-vector product on scalar multi-core cpus, Parallel Comput., 36, 181-198, (2010), http://dx.doi.org/10.1016/j.parco.2010.02.003 · Zbl 1204.68045
[41] Dabrowski, M.; Krotkiewski, M.; Schmid, D. W., MILAMIN: MATLAB-based finite element method solver for large problems, Geochem. Geophys. Geosyst., 9, 1-24, (2008), http://dx.doi.org/10.1029/2007GC001719
[42] M. Naumov, Incomplete-LU and Cholesky Preconditioned Iterative Methods Using CUSPARSE and CUBLAS. Technical Report NVIDIA, 2011.
[43] Saad, Y., Iterative methods for sparse linear systems, (2003), SIAM · Zbl 1002.65042
[44] Davis, T. A., (Direct Methods for Sparse Linear Systems, Fundamental of Algorithms, (2006), SIAM Philadelphia)
[45] Cardoso, E. L.; Fonseca, J. S.O., Complexity control in the topology optimization of continuum structures, J. Braz. Soc. Mech. Sci. Eng., 25, 293-301, (2003), http://dx.doi.org/10.1590/S1678-58782003000300012
[46] Zhang, Y., Solving large-scale linear programs by interior-point methods under the Matlab environment, Optim. Methods Softw., 10, 1-31, (1998), http://dx.doi.org/10.1080/10556789808805699 · Zbl 0916.90208
[47] Golub, G. H.; Loan, C. F.V., Matrix computations, (1996), Johns Hopkins University Press
[48] Dziekonski, A.; Sypek, P.; Lamecki, A.; Mrozowski, M., Finite element matrix generation on a GPU, Prog. Electromagn. Res., 128, 249-265, (2012), http://dx.doi.org/10.2528/PIER12040301
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