Geodesic
Component Mapping Automation for Parametric Component Reduced Basis Techniques (RB-COMPONENT)
Rachida Chakir1 ; Charles Dapogny2 ; Caroline Japhet3 ; Yvon Maday4 ; Jean-Baptiste Montavon5 ; Olivier Pantz6 ; Anthony Patera7
1 Universitée Paris Est, IFSTTAR, 14-20 Bd Newton, Citée Descartes Champs sur Marne, 77447 Marne-la-Valéee Cedex 2, France
2 Laboratoire Jean Kuntzmann, CNRS, Universitée Grenoble-Alpes,, BP 53,Cedex 9 38041 Grenoble France
3 Universitée Paris 13, Sorbonne Paris Cité, LAGA, CNRS UMR 7539,, 99 Avenue J-B Cléement 93430,Villetaneuse France
4 Sorbonne Universitées, UPMC Universitée Paris 06 and CNRS UMR 7598, Laboratoire Jacques-Louis Lions,Institut Universitaire de France; and Division of Applied Mathematics, Brown University, F-75005 Paris,Providence RI France,USA
5 Universitée Paris 13, Sorbonne Paris Citée, LAGA, CNRS UMR 7539, 99 Avenue J-B Cléement, 93430 Villetaneuse, France
6 Universitée de Nice Sophia-Antipolis, Laboratoire J.A. Dieudonnée, UMR CNRS 7351, Parc Valrose,, 06108 Parc Valrose,Nice Cedex 02, France
7 Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue Cambridge,77 Massachusetts Avenue USA
ESAIM. Proceedings, Tome 63 (2018), pp. 208-227.

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The aim of this paper is to develop some techniques for automation of the mappings (between working and reference domains) required by reduced basis methods: the development of geometry mappings is indeed often a substantial impediment to the implementation of reduced basis techniques, especially in the context of the reduced basis element method (RBEM) and the reduced basis component method (RBCM). In the RBCM context, the geometry mappings are applied at the level of components. The methods have been tested on various cases to understand the limits of the approach and try to foresee and overcome the possible failures.
DOI : 10.1051/proc/201863208

Rachida Chakir 1 ; Charles Dapogny 2 ; Caroline Japhet 3 ; Yvon Maday 4 ; Jean-Baptiste Montavon 5 ; Olivier Pantz 6 ; Anthony Patera 7

1 Universitée Paris Est, IFSTTAR, 14-20 Bd Newton, Citée Descartes Champs sur Marne, 77447 Marne-la-Valéee Cedex 2, France
2 Laboratoire Jean Kuntzmann, CNRS, Universitée Grenoble-Alpes,, BP 53,Cedex 9 38041 Grenoble France
3 Universitée Paris 13, Sorbonne Paris Cité, LAGA, CNRS UMR 7539,, 99 Avenue J-B Cléement 93430,Villetaneuse France
4 Sorbonne Universitées, UPMC Universitée Paris 06 and CNRS UMR 7598, Laboratoire Jacques-Louis Lions,Institut Universitaire de France; and Division of Applied Mathematics, Brown University, F-75005 Paris,Providence RI France,USA
5 Universitée Paris 13, Sorbonne Paris Citée, LAGA, CNRS UMR 7539, 99 Avenue J-B Cléement, 93430 Villetaneuse, France
6 Universitée de Nice Sophia-Antipolis, Laboratoire J.A. Dieudonnée, UMR CNRS 7351, Parc Valrose,, 06108 Parc Valrose,Nice Cedex 02, France
7 Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue Cambridge,77 Massachusetts Avenue USA 
@article{EP_2018_63_a9,
     author = {Rachida Chakir and Charles Dapogny and Caroline Japhet and Yvon Maday and Jean-Baptiste Montavon and Olivier Pantz and Anthony Patera},
     title = {Component {Mapping} {Automation} for {Parametric} {Component} {Reduced} {Basis} {Techniques} {(RB-COMPONENT)}},
     journal = {ESAIM. Proceedings},
     pages = {208--227},
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     doi = {10.1051/proc/201863208},
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Rachida Chakir; Charles Dapogny; Caroline Japhet; Yvon Maday; Jean-Baptiste Montavon; Olivier Pantz; Anthony Patera. Component Mapping Automation for Parametric Component Reduced Basis Techniques (RB-COMPONENT). ESAIM. Proceedings, Tome 63 (2018), pp. 208-227. doi : 10.1051/proc/201863208. http://geodesic.mathdoc.fr/articles/10.1051/proc/201863208/

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