Grassmann interpolation of proper orthogonal modes for robust linear and nonlinear dynamic analysis against parameter variation in structures

Article Mathematics, Interdisciplinary Applications

On the stability of POD basis interpolation on Grassmann manifolds for parametric model order reduction

Orestis Friderikos et al.

Summary: This work presents stability conditions for POD basis interpolation on Grassmann manifolds, including the definition domain of the logarithm map, local features of linearization, and issues arising from increasing the number of POD modes. The experimental results highlight the importance of these conditions for guiding the generation of parameterized ROMs.

COMPUTATIONAL MECHANICS (2022)

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Article Computer Science, Interdisciplinary Applications

Generalization of the Neville-Aitken interpolation algorithm on Grassmann manifolds: Applications to reduced order model

Rolando Mosquera et al.

Summary: This paper presents an extension of the Neville-Aitken algorithm for interpolation on the Grassmann manifold Gm(Double-struck capital Rn) in the context of parametric model order reduction. Interpolation points on Gm(Double-struck capital Rn) are generated by bases obtained from Proper Orthogonal Decomposition of available solutions, and the algorithm is recursively executed via the geodesic barycenter of two points. Three CFD applications are discussed, showing relevant numerical results and comparable asymptotic complexity to existing techniques.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS (2021)

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Article Mathematics

An efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques

Nicola Demo et al.

Summary: This contribution describes the implementation of a data-driven shape optimization pipeline in a naval architecture application. Reduced order models are adopted to improve efficiency and a dynamic mode decomposition enhancement is used to reduce computational costs. Real-time computation is achieved through proper orthogonal decomposition with Gaussian process regression technique, enabling convergence towards the optimal shape using a genetic optimization algorithm.

BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA (2021)

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Article Mathematics, Applied