A fast, certified and " tuning free " two-field reduced basis method for the metamodelling of affinely-parametrised elasticity problems

Chi Hoang 1 Pierre Kerfriden 1 Stephane Pierre-Alain Bordas 1
1 Cardiff University School of Engineering
Abstract : This paper proposes a new reduced basis algorithm for the metamodelling of parametrised elliptic problems. The developments rely on the Constitutive Relation Error (CRE), and the construction of separate reduced order models for the primal variable (displacement) and flux (stress) fields. A two-field greedy sampling strategy is proposed to construct these two fields simultaneously and in an efficient manner: at each iteration, one of the two fields is enriched by increasing the dimension of its reduced space in such a way that the CRE is minimised. This sampling strategy is then used as a basis to construct goal-oriented reduced order modelling. The resulting algorithm is certified and " tuning-free " : the only requirement from the engineer is the level of accuracy that is desired for each of the outputs of the surrogate. It is also shown to be significantly more efficient in terms of computational expense than competing methodologies.
Keywords : two-field reduced basis method (TF-RBM) model order reduction constitutive relation error goal-oriented greedy sampling a posteriori error estimation
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Article dans une revue
Computer Methods in Applied Mechanics and Engineering, Elsevier, 2015, 10.1016/j.cma.2015.08.016, pp.48
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Chi Hoang, Pierre Kerfriden, Stephane Pierre-Alain Bordas. A fast, certified and " tuning free " two-field reduced basis method for the metamodelling of affinely-parametrised elasticity problems. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2015, 10.1016/j.cma.2015.08.016, pp.48. 〈hal-01189017〉

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