Model reduction is a common theme within the simulation, control and
optimization of complex dynamical systems. For instance, in control
problems for partial differential equations, the associated large-scale
systems have to be solved very often. To attack these problems in
reasonable time it is absolutely necessary to reduce the dimension of the
underlying system. We focus on model reduction by balanced truncation
where a system theoretical background provides some desirable properties
of the reduced-order system. The major computational task in
balanced truncation is the solution of large-scale Lyapunov equations,
thus the method is of limited use for really large-scale applications.
We develop an effective implementation of balancing-related model reduction
methods in exploiting the structure of the underlying problem.
This is done by a data-sparse approximation of the large-scale state
matrix A using the hierarchical matrix format. Furthermore, we integrate
the corresponding formatted arithmetic in the sign function method
for computing approximate solution factors of the Lyapunov equations.
This approach is well-suited for a class of practical relevant problems
and allows the application of balanced truncation and related methods
to systems coming from 2D and 3D FEM and BEM discretizations.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-200701952 |
| Date | 27 November 2007 |
| Creators | Baur, Ulrike, Benner, Peter |
| 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 |
| Rights | Dokument ist für Print on Demand freigegeben |
| Relation | dcterms:isPartOf:Chemnitz Scientific Computing Preprints ; 07-01 |
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