Abstract: We study the stability of an interpolatory model order reduction (MOR) algorithm for first-order and second-order parametric linear dynamical systems, with respect to inexact linear solves. This analysis is easily extendible to other MOR algorithms for such systems. Besides deriving the two conditions for stability, and subsequent experimentation, our most novel contribution here is achieving a backward stable algorithm.
To achieve this, we first categorize the involved orthogonality conditions into different classes. Second, we adapt the underlying linear solver (here Conjugate Gradient or CG) to satisfy these orthogonalities. Finally, and third, we implement Recycling CG in such a way that these orthogonalities can be achieved with no code changes to the linear solver (for an end user or a model reducer here) as well as cheaply (extra orthogonality cost offset by savings because of recycling).
Speaker’s Bio: After completing a double Master’s plus a Ph.D. in Computer Science and Mathematics from the Virginia Polytechnic Institute and State University (USA), Prof. Kapil Ahuja did a postdoc from the Max Planck Institute in Magdeburg (Germany). Subsequently, he worked as an Assistant Professor and an Associate Professor in Computer Science and Engineering at the Indian Institute of Technology Indore (Indore), where he is currently holding a Full Professor position. Recently, he has also been a Visiting Professor at the University of Texas at Austin (USA) École Nationale Supérieure Mines-Télécom Atlantique Bretagne-Pays de la Loire or École des Mines Télécom Atlantique), (France), Technische Universität Dresden (Germany), Sandia National Laboratories (USA), and the Technical University of Braunschweig (Germany).
Last Updated: May 28, 2024 - 10:23 am