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Multiparametric analysis within the proper generalized decomposition framework. (English) Zbl 1246.80011
Summary: Optimization campaigns, which are being launched more and more often, require the execution of many parametric studies which can make the approach very costly in terms of computation time. Here, in order to reduce these computation times, we undertake to develop a multiparametric strategy using the LATIN method along with Proper Generalized Decomposition. This approach is compared to other common strategies, especially those based on POD.

80M25 Other numerical methods (thermodynamics) (MSC2010)
80A20 Heat and mass transfer, heat flow (MSC2010)
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[1] El-Sayed MEM, Hsiung C-K (1991) Optimum structural design with parallel finite element analysis. Comput Struct 40(6): 1469–1474 · Zbl 0850.73198
[2] Umesha PK, Venuraju MT, Leimbach KR (2005) Optimal design of truss structures using parallel computing. Struct Multidiscip Optim 29: 286–297
[3] Theocaris PS, Stravroulakis GE (1998) Multilevel optimal design of composite structures including materials with negative poisson’s ratio. Struct Optim 15: 8–15
[4] Bendsoe MP (1995) Optimization of structural topology, shape and material. Springer, Heidelberg · Zbl 0822.73001
[5] Borbaru F, Mukherjee S (2001) Shape sensitivity analysis and shape optimization in planar elasticity using the element-free galerkin method. Comput Method Appl Mech Eng 190: 4319–4337 · Zbl 1048.74051
[6] Li W, Li Q, Steven GP, Xie YM (2003) An evolutionary approach to elastic contact optimization of frame structure. Finite Elem Anal Design 40: 61–81
[7] Li W, Li Q, Steven GP, Xie YM (2005) An evolutionary shape optimization for elastic contact problems subject to multiple load cases. Comput Method Appl Mech Eng 194: 3394–3415 · Zbl 1093.74049
[8] Pàczelt I, Mròz Z (2007) Optimal shapes of contact interfaces due to the sliding wear in the steady motion. Int J Solids Struct 44: 895–925 · Zbl 1156.74035
[9] Barthelemy J, Haftka R (1993) Approximation concepts for optimum structural design. Struct Multidiscip Optim 5(3): 129–144
[10] Booker A, Dennis J, Frank P, Serafini D, Torczon V, Trosset M (1993) A rigorous framework for optimization of expensive functions by surrogates. Struct Multidiscip Optim 17(1): 1–13
[11] Queipo N, Haftka R, Shyy W, Goel T, Vaidyanathan R, Tucker P (2005) Surrogate-based analysis and optimization. Prog Aerosp Sci 41(1): 1–28
[12] Barton R, Meckesheimer M (2006) Metamodel-based simulation optimization. In: Handbooks in operations research and management science, vol 13. Elsevier, New York, pp 535–574
[13] Lumley JL (1967) Atmospheric turbulence and wave propagation. In: Yaglmo AM, Tatarski VI (eds) The structure of inhomogeneous turbulence. Nauka, Moscow, pp 166–178
[14] Chatterjee A (2000) An introduction to the proper orthogonal decomposition. Curr Sci 78(7): 808–817
[15] Maday Y, Ronquist EM (2004) The reduced-basis element method : application to a thermal fin problem. J Sci Comput 26(1): 240–258 · Zbl 1077.65120
[16] Kunish K, Xie L (2005) Pod-based feedback control of the burgers equation by solving the evolutionary hjb equation. Comput Math Appl 49(7–8): 1113–1126 · Zbl 1080.93012
[17] Lieu T, Farhat C, Lesoinne A (2006) Reduced-order fluid/structure modeling of a complete aircraft configuration. Comput Method Appl Mech Eng 195(41-43): 5730–5742 · Zbl 1124.76042
[18] Gunzburger MD, Peterson JS, Shadid JN (2007) Reduced-order modeling of time-dependent pdes with multiple parameters in the boundary data. Comput Method Appl Mech Eng 196(4–6): 1030–1047 · Zbl 1121.65354
[19] Ryckelynck D (2005) A priori hyperreduction method: an adaptive approach. J Comput Phys 202: 346–366 · Zbl 1288.65178
[20] Ryckelynck D, Chinesta F, Cueto E, Ammar A. (2006) On the a priori model reduction: overview and recent developments. Arch Comput Methods Eng 13(1): 91–128 · Zbl 1142.76462
[21] Ladevèze P (1999) Nonlinear computational structural mechanics–new approaches and non-incremental methods of calculation. Springer Verlag, New York · Zbl 0912.73003
[22] Ammar A, Mokdad B, Chinesta F, Keunings R (2006) A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. J Non-Newton Fluid Mech 139(3): 153–176 · Zbl 1195.76337
[23] Ammar A, Mokdad B, Chinesta F, Keunings R (2007) A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids : Part ii: transient simulation using space-time separated representations. J Non-Newton Fluid Mech 144(2-3): 98–121 · Zbl 1196.76047
[24] Chinesta F, Ammar A, Lemarchand F, Beauchene P, Boust F (2008) Alleviating mesh constraints: model reduction, parallel time integration and high resolution homogenization. Comput Method Appl Mech Eng 197: 400–413 · Zbl 1169.74530
[25] Nouy A (2007) A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations. Comput Method Appl Mech Eng 196(45–48): 4521–4537 · Zbl 1173.80311
[26] Nouy A (2009) Recent developments in spectral stochastic methods for the numerical solution of stochastic partial differential equations. Arch Comput Methods Eng 16(3): 251–285 · Zbl 1360.65036
[27] Neron D, Dureisseix D (2008) A computational strategy for thermo-poroelastic structures with a time-space interface coupling. Int J Numer Method Eng 75(9): 1053–1084 · Zbl 1195.74191
[28] Ladevèze P, Passieux J-C, Neron D (2010) The latin multiscale computational method and the proper generalized decomposition. Comput Method Appl Mech Eng 199(21–22): 1287–1296 · Zbl 1227.74111
[29] Boucard P-A, Ladevèze P (1999) A multiple solution method for non-linear structural mechanics. Mech Eng 50(5): 317–328
[30] Boucard P-A, Champaney L (2003) A suitable computational strategy for the parametric analysis of problems with multiple contact. Int J Numer Method Eng 57: 1259–1282 · Zbl 1062.74607
[31] Ladevèze P (1989) The large time increment method for the analyse of structures with nonlinear constitutive relation described by internal variables. Comptes Rendus Acad Sci Paris 309(II): 1095–1099
[32] Bussy P, Boisse P, Ladevèze P (1990) A new approach in non-linear mechanics: the large time increment method. Int J Numer Method Eng 29: 647–663 · Zbl 0712.73029
[33] Allix O, Vidal P (2002) A new multi-solution approach suitable for structural identification problems. Comput Method Appl Mech Eng 191(25–26): 2727–2758 · Zbl 1131.74322
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