Fast Low‐Rank Empirical Cross Gramians. Issue 1 (15th March 2018)

• Record Type: Journal Article
• Authors: Himpe, Christian; Leibner, Tobias; Rave, Stephan; Saak, Jens
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 17:Issue 1(2017)
• Page Start: 841
• Page End: 842
• Publication Date: 2018-03-15
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201710388
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: The cross Gramian matrix encodes the input‐output coherence of linear control systems and is used in projection‐based model reduction. The empirical cross Gramian is a data‐driven variant of the cross Gramian which also extends to nonlinear systems. A drawback of the empirical cross Gramian for large‐scale systems is its full order and dense structure; yet, it may be computed column‐wise. Using the hierarchical approximate proper orthogonal decomposition (HAPOD), this partial computability can be exploited to obtain a truncated projection for model order reduction without assembling a full cross Gramian. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)