English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Recently a new algorithm for model reduction of second order linear dynamicalsystems with proportional damping, the Adaptive Iterative Rational GlobalArnoldi (AIRGA) algorithm, has been proposed. The main computational cost ofthe AIRGA algorithm is in solving a sequence of linear systems. These linearsystems do change only slightly from one iteration step to the next. Here wefocus on efficiently solving these systems by iterative methods and the choiceof an appropriate preconditioner. We propose the use of relevant iterativealgorithm and the Sparse Approximate Inverse (SPAI) preconditioner. A techniqueto cheaply update the SPAI preconditioner in each iteration step of the modelorder reduction process is given. Moreover, it is shown that under certainconditions the AIRGA algorithm is stable with respect to the error introducedby iterative methods. Our theory is illustrated by experiments. It isdemonstrated that SPAI preconditioned Conjugate Gradient (CG) works well formodel reduction of a one dimensional beam model with AIRGA algorithm. Moreover,the computation time of preconditioner with update is on an average 2/3 rd ofthe computation time of preconditioner without update. With average timingsrunning into hours for very large systems, such savings are substantial.

Preconditioned Iterative Solves in Model Reduction of Second Order Linear Dynamical Systems