Elasticity-based morphing technique and application to reduced-order modeling

The aim of this article is to introduce a new methodology for constructing morphings between shapes that have identical topology. The morphings are obtained by deforming a reference shape, through the resolution of a sequence of linear elasticity equations, onto every target shape. In particular, our approach does not assume any knowledge of a boundary parametrization, and the computation of the boundary deformation is not required beforehand. Furthermore, constraints can be imposed on specific points, lines and surfaces in the reference domain to ensure alignment with their counterparts in the target domain after morphing. Additionally, we show how the proposed methodology can be integrated in an offline and online paradigm, which is useful in reduced-order modeling involving variable shapes. This framework facilitates the efficient computation of the morphings in various geometric configurations, thus improving the versatility and applicability of the approach. The robustness and computational efficiency of the methodology is illustrated on two-dimensional test cases, including the regression problem of the drag and lift coefficients of airfoils of non-parameterized variable shapes.