Reference : A fast, certified and "tuning free" two-field reduced basis method for the metamodell...
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A fast, certified and "tuning free" two-field reduced basis method for the metamodelling of affinely-parametrised elasticity problems
Hoang, K. C. [> >]
Kerfriden, P. [> >]
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit]
Computer Methods in Applied Mechanics and Engineering
[en] Two-field reduced basis method (TF-RBM) ; Model order reduction ; Constitutive relation error ; Goal-oriented greedy sampling ; a posteriori error estimation
[en] 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.
EPSRC under grant EP/J01947X/1: “Towards rationalised computational expense for simulating fracture over multiple scales (RationalMSFrac)”
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FP7 ; 279578 - REALTCUT - Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery

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