Randomized nonlinear model order reduction methods for large dynamical problems with explicit time integration. Issue 1 (17th December 2018)

• Record Type: Journal Article
• Authors: Bach, C.; Bartol, J.; Ceglia, D.; Song, L.; Duddeck, F.
• Other Names: Müller G. guestEditor.; Ulbrich M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 18:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-12-17
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201800252
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Projection‐based nonlinear model order reduction (MOR) often involves the computation of a truncated singular value decomposition (SVD) of a snapshot matrix A ∈ ℝ m × n, m ≥ n, computed from training simulations, where only the first k basis vectors are retained. A can however become very large in case of detailed models with a large number of degrees of freedom (DoFs), or when many snapshots are present. This is often the case for explicit FEM simulations of industrial problems. Computing the SVD can then become problematic, as most widely used SVD algorithms for MOR have an asymptotic complexity of 𝒪( mn 2 ) [1]. Randomized algorithms can alternatively be used to compute only the k most significant basis vectors. Such methods only scale with 𝒪( mnk ) or even 𝒪( mn log(k)) [2]. We present a modified hybrid randomized incremental algorithm for efficient reduced basis (RB) computation with low memory requirements, and apply the method to a large‐scale example problem. The results show that the hybrid algorithm is capable of efficiently computing a RB even for very large problems at a manageable computational effort.