Abstract
AbstractProjection‐based nonlinear model order reduction (MOR) often involves the computation of a truncated singular value decomposition (SVD) of a snapshot matrix A ∈ ℝm×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(mn2 ) [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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.