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

Chady  Ghnatios; Guangtao  Xu; Adrien  Leygue; Michel  Visonneau; Francisco  Chinesta; Alain  Cimetiere

doi:10.3934/dcdss.2016008

Article Contents

2016, Volume 9, Issue 2: 475-500. Doi: 10.3934/dcdss.2016008

This issue Previous Article A geological delayed response model for stratigraphic reconstructions Next Article On the equilibria and qualitative dynamics of a forced nonlinear oscillator with contact and friction

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

Received: August 31, 2014

Revised: September 30, 2015

Published: March 2016

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Abstract

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.

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Mathematics Subject Classification: Primary: 65N21, 65N85, 68U20; Secondary: 65N30.

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