Registration-Based Model Reduction in Complex Two-Dimensional Geometries

We present a general—i.e., independent of the underlying equation—egistration procedure for parameterized model order reduction. Given spatial domain $$\varOmega \subset \mathbb {R}^2$$ and manifold $$\mathcal {M}= \{ u_{\mu } : \mu \in \mathcal {P} \}$$ associated with parameter {R}^P$$ parametric field $$\mu \mapsto L^2(\varOmega )$$ , our approach takes as input set snapshots $$\{ u^k \}_{k=1}^{n_\mathrm{train}} {M}$$ returns parameter-dependent bijective mapping $${\varPhi }: \varOmega \times \rightarrow is designed to make mapped \circ {\varPhi }_{\mu \, more amenable linear compression methods. In this work, we extend further analyze registration proposed in [Taddei, SISC, 2020]. The contributions work are twofold. First, deal annular domains by introducing suitable transformation coordinate system. Second, discuss extension general two-dimensional geometries: towards end, introduce spectral element approximation, which relies on partition _{q} \}_{q=1} ^{N_\mathrm{dd}}$$ $$ such that _1,\ldots ,\varOmega _{N_\mathrm{dd}}$$ isomorphic unit square. show approximation can cope geometries. rigorous mathematical analysis justify proposal; furthermore, numerical results heat-transfer problem an domain, potential flow past rotating symmetric airfoil, inviscid transonic compressible non-symmetric demonstrate effectiveness method.