Parametric solutions involving geometry: A step towards efficient shape optimization

Navarrina, 1991, A general methodological analysis for optimum design, Int. J. Numer. Methods Eng., 31, 85, 10.1002/nme.1620310106 Belytschko, 2003, Topology optimization with implicit functions and regularization, Int. J. Numer. Methods Eng., 57, 1177, 10.1002/nme.824 Olesen, 2006, A high-level programming-language implementation of topology optimization applied to steady-state Navier–Stokes flow, Int. J. Numer. Methods Eng., 65, 975, 10.1002/nme.1468 Yoon, 2008, A monolithic approach for topology optimization of electrostatically actuated devices, Comput. Methods Appl. Mech. Eng., 197, 4062, 10.1016/j.cma.2008.04.004 C. Ghnatios, A. Ammar, A. Cimetiere, A. Hamdouni, A. Leygue, F. Chinesta, First steps in the space separated representation of models defined in complex domains, in: 11th Biennial Conference on Engineering Systems Design and Analysis, ASME, Nantes, 2012, ESDA2012-82489. van Keulen, 2005, Review of options for structural design sensitivity analysis. I. Linear systems, Comput. Methods Appl. Mech. Eng., 194, 3213, 10.1016/j.cma.2005.02.002 Wang, 2012, Sensitivity analysis and shape optimization of a hole in a vibrating rectangular plate for eigenfrequency maximization, J. Eng. Mech. – ASCE, 138, 662, 10.1061/(ASCE)EM.1943-7889.0000376 Ammar, 2006, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids, J. Non-Newtonian Fluid Mech., 139, 153, 10.1016/j.jnnfm.2006.07.007 Ammar, 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-Newtonian Fluid Mech., 144, 98, 10.1016/j.jnnfm.2007.03.009 Chinesta, 2010, Recent advances and new challenges in the use of the Proper Generalized Decomposition for solving multidimensional models, Arch. Comput. Methods Eng., 17, 327, 10.1007/s11831-010-9049-y Chinesta, 2011, A short review on model order reduction based on Proper Generalized Decomposition, Arch. Comput. Methods Eng., 18, 395, 10.1007/s11831-011-9064-7 Pruliere, 2010, On the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition, Math. Comput. Simul., 81, 791, 10.1016/j.matcom.2010.07.015 Ghnatios, 2011, Methodological approach to efficient modeling and optimization of thermal processes taking place in a die: application to pultrusion, Compos. Pt. A – Appl. Sci. Manuf., 42, 1169, 10.1016/j.compositesa.2011.05.001 Ghnatios, 2012, Proper Generalized Decomposition based dynamic data-driven control of thermal processes, Comput. Methods Appl. Mech. Eng., 213–216, 29, 10.1016/j.cma.2011.11.018 Bognet, 2012, Advanced simulation of models defined in plate geometries: 3D solutions with 2D computational complexity, Comput. Methods Appl. Mech. Eng., 201–204, 1, 10.1016/j.cma.2011.08.025 González, 2012, Proper Generalized Decomposition based dynamic data driven inverse identification, Math. Comput. Simul., 82, 1677, 10.1016/j.matcom.2012.04.001 Heyberger, 2012, Multiparametric analysis within the Proper Generalized Decomposition framework, Comput. Mech., 49, 277, 10.1007/s00466-011-0646-x Ladevèze, 1999 Passieux, 2010, A scalable time–space multiscale domain decomposition method: adaptive time scale separation, Comput. Mech., 46, 621, 10.1007/s00466-010-0504-2 Ladevèze, 2010, The LATIN multiscale computational method and the proper generalized decomposition, Comput. Methods Appl. Mech. Eng., 199, 1287, 10.1016/j.cma.2009.06.023 Néron, 2010, Proper Generalized Decomposition for multiscale and multiphysics problems, Arch. Comput. Methods Eng., 17, 351, 10.1007/s11831-010-9053-2 Halabi, 2013, Multiparametric response surface construction by means of proper generalized decomposition: an extension of the parafac procedure, Comput. Methods Appl. Mech. Eng., 253, 543, 10.1016/j.cma.2012.08.005 Nouy, 2010, A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations, Comput. Methods Appl. Mech. Eng., 199, 1603, 10.1016/j.cma.2010.01.009 Ammar, 2010, An error estimator for separated representations of highly multidimensional models, Comput. Methods Appl. Mech. Eng., 199, 1872, 10.1016/j.cma.2010.02.012 Babuška, 1970, The finite element method for elliptic equations with discontinuous coefficients, Computing (Arch. Elektron. Rechnen), 5, 207