# American Institute of Mathematical Sciences

April  2016, 9(2): 475-500. doi: 10.3934/dcdss.2016008

## On the space separated representation when addressing the solution of PDE in complex domains

 1 Notre Dame University-Louaize, Zouk Mosbeh P.O. Box 72, Lebanon 2 GeM Institute, UMR CNRS - Ecole Centrale de Nantes, 1 rue de la Noe, BP 92101, F-44321 Nantes cedex 3, France, France 3 LHEEA, UMR CNRS - Ecole Centrale de Nantes, 1 rue de la Noe, BP 92101, F-44321 Nantes cedex 3, France 4 High Performance Computing Institute - Ecole Centrale de Nantes, 1 rue de la Noe, BP 92101, F-44321 Nantes cedex 3, France 5 P' Institute, UPR CNRS - University of Poitiers & ENSMA, 11 Boulevard Marie et Pierre Curie, BP 30179, F-86962 Futuroscope Chasseneuil cedex, France

Received  September 2014 Revised  October 2015 Published  March 2016

Separated representations allow impressive computational CPU time savings when applied in different fields of computational mechanics. They have been extensively used for solving models defined in multidimensional spaces coming from (i) its proper physics, (ii) model parameters that were introduced as extra-coordinates and (iii) 3D models when the solution can be separated as a finite sum of functional products involving lower dimensional spaces. The last route is especially suitable when models are defined in hexahedral domains. When it is not the case, different possibilities exist and were considered in our former works. In the present work, we are analyzing two alternative routes. The first one consists of immersing the real non-separable domain into a fully separable hexahedral domain. The second procedure consists in applying a geometrical transformation able to transform the real domain into a hexahedra in which the model is solved by using a fully separated representation of the unknown field.
Citation: Chady Ghnatios, Guangtao Xu, Adrien Leygue, Michel Visonneau, Francisco Chinesta, Alain Cimetiere. On the space separated representation when addressing the solution of PDE in complex domains. Discrete and Continuous Dynamical Systems - S, 2016, 9 (2) : 475-500. doi: 10.3934/dcdss.2016008
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