Low-Rank Alternating Direction Implicit Iteration in pyMOR

Keywords: model order reduction, matrix equations, balanced truncation, alternating direction implicit iteration, pyMOR

Abstract

The low-rank alternating direction implicit (LR-ADI) iteration is an effective method for solving large-scale Lyapunov equations. In the software library pyMOR, solutions to Lyapunov equations play an important role when reducing a model using the balanced truncation method. In this article we introduce the LR-ADI iteration as well as pyMOR, while focusing on its features which are relevant for integrating the iteration into the library. We compare the run time of the iteration's pure pyMOR implementation with those achieved by external libraries available within the pyMOR framework.

Author Biography

Linus Balicki, Otto von Guericke University Magdeburg

M.Sc. Mathematics student at Otto von Guericke University Magdeburg
Research interests are numerical linear algebra, model order reduction, and matrix equations.

Published
2020-02-14
How to Cite
Balicki, L. (2020). Low-Rank Alternating Direction Implicit Iteration in pyMOR. GAMM Archive for Students, 2(1), 1-13. https://doi.org/10.14464/gammas.v2i1.420
Section
Research Articles