Compositional maps for registration in complex geometries
| hal.structure.identifier | Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS] | |
| dc.contributor.author | TADDEI, Tommaso | |
| dc.date.accessioned | 2024-04-04T02:31:27Z | |
| dc.date.available | 2024-04-04T02:31:27Z | |
| dc.date.issued | 2023 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190310 | |
| dc.description.abstractEn | We develop and analyze a parametric registration procedure for manifolds associated with the solutions to parametric partial differential equations in two-dimensional domains. Given the domain $Ω\subset \mathbb{R}^2$ and the manifold $M=\{ u_μ : μ\in P\}$ associated with the parameter domain $P \subset \mathbb{R}^P$ and the parametric field $μ\mapsto u_μ \in L^2(Ω)$, our approach takes as input a set of snapshots from $M$ and returns a parameter-dependent mapping $Φ: Ω\times P \to Ω$, which tracks coherent features (e.g., shocks, shear layers) of the solution field and ultimately simplifies the task of model reduction. We consider mappings of the form $Φ=\texttt{N}(\mathbf{a})$ where $\texttt{N}:\mathbb{R}^M \to {\rm Lip}(Ω; \mathbb{R}^2)$ is a suitable linear or nonlinear operator; then, we state the registration problem as an unconstrained optimization statement for the coefficients $\mathbf{a}$. We identify minimal requirements for the operator $\texttt{N}$ to ensure the satisfaction of the bijectivity constraint; we propose a class of compositional maps that satisfy the desired requirements and enable non-trivial deformations over curved boundaries of $Ω$; we develop a thorough analysis of the proposed ansatz for polytopal domains and we discuss the approximation properties for general curved domains. We perform numerical experiments for a parametric inviscid transonic compressible flow past a cascade of turbine blades to illustrate the many features of the method. | |
| dc.language.iso | en | |
| dc.subject.en | parameterized partial differential equations | |
| dc.subject.en | registration in bounded domains | |
| dc.subject.en | model order reduction | |
| dc.title.en | Compositional maps for registration in complex geometries | |
| dc.type | Document de travail - Pré-publication | |
| dc.identifier.doi | 10.48550/arXiv.2308.15307 | |
| dc.subject.hal | Mathématiques [math] | |
| dc.identifier.arxiv | 2308.15307 | |
| dc.description.sponsorshipEurope | Accurate Roms for Industrial Applications | |
| 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-04382197 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04382197v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2023&rft.au=TADDEI,%20Tommaso&rft.genre=preprint |
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