An optimization-based registration approach to geometry reduction
| hal.structure.identifier | Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS] | |
| dc.contributor.author | TADDEI, Tommaso | |
| dc.date.accessioned | 2024-04-04T02:33:31Z | |
| dc.date.available | 2024-04-04T02:33:31Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190488 | |
| dc.description.abstractEn | We develop and assess an optimization-based approach to parametric geometry reduction. Given a family of parametric domains, we aim to determine a parametric diffeomorphism Φ that maps a fixed reference domain Ω into each element of the family, for different values of the parameter; the ultimate goal of our study is to determine an effective tool for parametric projection-based model order reduction of partial differential equations in parametric geometries. For practical problems in engineering, explicit parameterizations of the geometry are likely unavailable: for this reason, our approach takes as inputs a reference mesh of Ω and a point cloud {y raw i } Q i=1 that belongs to the boundary of the target domain V and returns a bijection Φ that approximately maps Ω in V. We propose a two-step procedure: given the point clouds {xj} N j=1 ⊂ ∂Ω and {y raw i } Q i=1 ⊂ ∂V , we first resort to a point-set registration algorithm to determine the displacements {vj} N j=1 such that the deformed point cloud {yj := xj + vj} N j=1 approximates ∂V ; then, we solve a nonlinear non-convex optimization problem to build a mapping Φ that is bijective from Ω in R d and (approximately) satisfies Φ(xj) = yj for j = 1,. .. , N. We present a rigorous mathematical analysis to justify our approach; we further present thorough numerical experiments to show the effectiveness of the proposed method. | |
| dc.language.iso | en | |
| dc.rights.uri | http://creativecommons.org/licenses/by/ | |
| dc.title.en | An optimization-based registration approach to geometry reduction | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math] | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-04173723 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04173723v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=TADDEI,%20Tommaso&rft.genre=preprint |
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