PGD-Based Computational Vademecum for Efficient Design, Optimization and Control

Author (s): Chinesta, F.; Leygue, A.; Bordeu, F.; Aguado, J.V.; Cueto, E.; González, D.; Alfaro, I.; Ammar, A. and Huerta, A.
Journal: Archives of Computational Methods in Engineering

Volume: 20, Issue 1
Pages: 31 – 59
Date: 2013

In this paper we are addressing a new paradigm in the field of simulation-based engineering sciences (SBES) to face the challenges posed by current ICT technologies. Despite the impressive progress attained by simulation ca- pabilities and techniques, some challenging problems re- main today intractable. These problems, that are common to many branches of science and engineering, are of differ- ent nature. Among them, we can cite those related to high- dimensional problems, which do not admit mesh-based ap- proaches due to the exponential increase of degrees of free- dom. We developed in recent years a novel technique, called Proper Generalized Decomposition (PGD). It is based on the assumption of a separated form of the unknown field and it has demonstrated its capabilities in dealing with high- dimensional problems overcoming the strong limitations of classical approaches. But the main opportunity given by this technique is that it allows for a completely new approach for classic problems, not necessarily high dimensional. Many challenging problems can be efficiently cast into a multi- dimensional framework and this opens new possibilities to solve old and new problems with strategies not envisioned until now. For instance, parameters in a model can be set as additional extra-coordinates of the model. In a PGD frame- work, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort of computational vademecum. Under this rationale, opti- mization of complex problems, uncertainty quantification, simulation-based control and real-time simulation are now at hand, even in highly complex scenarios, by combining an off-line stage in which the general PGD solution, the vademecum, is computed, and an on-line phase in which, even on deployed, handheld, platforms such as smartphones or tablets, real-time response is obtained as a result of our queries.



@article {Chinesta-CLBACGAAH:13,
Author   = {Francisco Chinesta and Adrien Leygue and Felipe Bordeu and José Vicente Aguado and El\'{\i}as Cueto and David Gonz\'alez and Ic\'{\i}ar Alfaro and Amine Ammar and Antonio Huerta},
Title    = {{PGD-B}ased {C}omputational {V}ademecum for Efficient Design, Optimization and Control},
Fjournal = {Archives of Computational Methods in Engineering},
Journal  = {Arch. Comput. Method Eng.},
Volume   = {20},
Issue    = {1},
Pages    = {31-59},
Year     = {2013},
Url      = {dx.doi.org/10.1007/s11831-013-9080-x}}