A Padé approximate linearization algorithm for solving the quadratic eigenvalue problem with low‐rank damping. (5th June 2015)

• Record Type: Journal Article
• Authors: Lu, Ding; Huang, Xin; Bai, Zhaojun; Su, Yangfeng
• Is Part Of: International journal for numerical methods in engineering. Volume 103:Number 11(2015)
• Page Start: 840
• Page End: 858
• Publication Date: 2015-06-05
• Subjects: Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.4919
• Languages: English
• ISSNs: 0029-5981

Abstract

<abstract abstract-type="main" id="nme4919-abs-0001"> <title>Summary</title> <p id="nme4919-para-0001">The low‐rank damping term appears commonly in quadratic eigenvalue problems arising from physical simulations. To exploit the low‐rank damping property, we propose a Padé approximate linearization (PAL) algorithm. The advantage of the PAL algorithm is that the dimension of the resulting linear eigenvalue problem is only <italic>n</italic> + <italic>ℓ</italic><italic>m</italic>, which is generally substantially smaller than the dimension 2<italic>n</italic> of the linear eigenvalue problem produced by a direct linearization approach, where <italic>n</italic> is the dimension of the quadratic eigenvalue problem, and <italic>ℓ</italic> and <italic>m</italic> are the rank of the damping matrix and the order of a Padé approximant, respectively. Numerical examples show that by exploiting the low‐rank damping property, the PAL algorithm runs 33–47% faster than the direct linearization approach for solving modest size quadratic eigenvalue problems. Copyright © 2015 John Wiley &amp; Sons, Ltd.</p> </abstract>