A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
Calibrated reduced-order POD-Galerkin system for fluid flow modelling
Journal of Computational Physics
Goal-oriented, model-constrained optimization for reduction of large-scale systems
Journal of Computational Physics
An Algorithm for Finding Intrinsic Dimensionality of Data
IEEE Transactions on Computers
Moving least squares response surface approximation: Formulation and metal forming applications
Computers and Structures
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Shape optimization frequently works with geometries involving several dozen design variables. The high dimensionality itself can be an impediment to efficient optimization. Moreover, a possibly high number of explicit/implicit constraints restrict the design space. Traditional CAD geometric parameterization methods present serious difficulties in expressing these constraints leading to a high failure rate of generating admissible shapes. In this paper, we discuss shape interpolation between admissible instances of finite element/CFD meshes. We present an original approach to automatically generate a hyper-surface locally tangent to the manifold of admissible shapes in a properly chosen linearized space. This permits us to reduce the size of the optimization problem while allowing us to morph exclusively between feasible shapes. To this end, we present a two-level a posteriori mesh parameterization approach for the design domain geometry. We use Principal Component Analysis and Diffuse Approximation to replace the geometry-based variables with the smallest set of variables needed to represent an admissible shape for a chosen precision. We demonstrate this approach in two typical shape optimization problems.