Component Mapping Automation for Parametric Component Reduced Basis Techniques (RB-Component)

Rachida Chakir (1) , Charles Dapogny (2) , Caroline Japhet (3) , Yvon Maday (4) , Jean-Baptiste Montavon (3) , Olivier Pantz (5) , Anthony T. Patera (6)

1 IFSTTAR/COSYS/LISIS - Laboratoire Instrumentation, Simulation et Informatique Scientifique
2 CVGI - Calcul des Variations, Géométrie, Image
3 LAGA - Laboratoire Analyse, Géométrie et Applications
4 LJLL - Laboratoire Jacques-Louis Lions
5 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
6 MIT-MECHE - Department of Mechanical Engineering [Massachusetts Institute of Technology]

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.

Domaines: Analyse numérique [math.NA]

Rachida Chakir, Charles Dapogny, Caroline Japhet, Yvon Maday, Jean-Baptiste Montavon, et al.. Component Mapping Automation for Parametric Component Reduced Basis Techniques (RB-Component). ESAIM: Proceedings and Surveys, 2018, 63, pp.208-227. ⟨10.1051/proc/201863208⟩. ⟨hal-01736669⟩