We investigate model reduction of large-scale linear time-invariant systems in
generalized state-space form. We consider sparse state matrix pencils, including
pencils with banded structure. The balancing-based methods employed here are
composed of well-known linear algebra operations and have been recently shown to be
applicable to large models by exploiting the structure of the matrices defining
the dynamics of the system.
In this paper we propose a modification of the LR-ADI iteration to solve
large-scale generalized Lyapunov equations together with a practical
convergence criterion, and several other implementation refinements.
Using kernels from several serial and parallel linear algebra libraries,
we have developed a parallel package for model reduction, SpaRed, extending
the applicability of balanced truncation to sparse systems with up to
$O(10^5)$ states.
Experiments on an SMP parallel architecture consisting of Intel Itanium 2 processors
illustrate the numerical performance of this approach and the potential of the
parallel algorithms for model reduction of large-scale sparse systems.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-200701947 |
| Date | 26 November 2007 |
| Creators | Badía, José M., Benner, Peter, Mayo, Rafael, Quintana-Ortí, Enrique S., Quintana-Ortí, Gregorio, Remón, Alfredo |
| Contributors | TU Chemnitz, Fakultät für Mathematik |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:preprint |
| Format | application/pdf, text/plain, application/zip |
| Source | Chemnitz Scientific Computing Preprints |
| Rights | Dokument ist für Print on Demand freigegeben |
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