190 research outputs found
Parametric Model Order Reduction using pyMOR
pyMOR is a free software library for model order reduction that includes both
reduced basis and system-theoretic methods. All methods are implemented in
terms of abstract vector and operator interfaces, which allows direct
integration of pyMOR's algorithms with a wide array of external PDE solvers. In
this contribution, we give a brief overview of the available methods and
experimentally compare them for the parametric instationary thermal-block
benchmark defined in arXiv:2003.00846.Comment: 9 pages, 6 figure
On an integrated Krylov-ADI solver for large-scale Lyapunov equations
One of the most computationally expensive steps of the low-rank ADI method for large-scale Lyapunov equations is the solution of a shifted linear system at each iteration. We propose the use of the extended Krylov subspace method for this task. In particular, we illustrate how a single approximation space can be constructed to
solve all the shifted linear systems needed to achieve a prescribed accuracy in terms of Lyapunov residual norm. Moreover, we show how to fully merge the two iterative procedures in order to obtain a novel, efcient implementation of the low-rank ADI method, for an important class of equations. Many state-of-the-art algorithms for the shift computation can be easily incorporated into our new scheme, as well. Several numerical results illustrate the potential of our novel procedure when compared to an implementation of the low-rank ADI method based on sparse direct solvers for the shifted linear systems
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