Model order reduction and domain decomposition for large-scale dynamical systems

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dc.contributor.advisorSorensen, Danny
dc.creatorSun, Kai
dc.date.accessioned2018-12-03T18:31:14Z
dc.date.available2018-12-03T18:31:14Z
dc.date.issued2008
dc.description.abstractDomain decomposition and model order reduction are both very important techniques for scientific and engineering computing. Their goals are both trying to speed up computations, however by different approaches. Domain decomposition is based on the general concept of divide-and-conquer which partitions a large-scale problem into a sequence of smaller and easy-to-solve problems. Model order reduction tries to relieve the simulation loads of dynamical systems by reducing the size of the systems dramatically. In this thesis, I investigate some problems arising from these two areas and propose some potential applications of them. At first, I give a sensitivity analysis of Smith method via iterative solvers. Smith method is a very important for balance truncation model order reduction. Secondly, we introduce a new effective approach to compute the reduced order model based on balanced truncation for a class of descriptor systems. Computational results were presented which indicate this new approach is promising and very efficient computationally. Thirdly, by combining balanced truncation model order reduction and domain decomposition techniques together, the reduced order models for systems of discretized partial differential equations with a spatially localized nonlinearities is derived. Finally, I present fully parallel domain decomposition techniques for another kind of problems, fast simulations of large-scale linear circuits such as power grids.
dc.format.extent182 pp
dc.identifier.callnoTHESIS MATH. SCI. 2009 SUN [Kai]
dc.identifier.citationSun, Kai. "Model order reduction and domain decomposition for large-scale dynamical systems." (2008) Diss., Rice University. <a href="https://hdl.handle.net/1911/103534">https://hdl.handle.net/1911/103534</a>.
dc.identifier.digital304507831
dc.identifier.urihttps://hdl.handle.net/1911/103534
dc.language.isoeng
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.subjectMathematics
dc.subjectPure sciences
dc.subjectDomain decomposition
dc.subjectDynamical systems
dc.subjectModel order reduction
dc.subjectNumerical algebra
dc.subjectNumerical analysis
dc.titleModel order reduction and domain decomposition for large-scale dynamical systems
dc.typeThesis
dc.type.materialText
thesis.degree.departmentMathematical Sciences
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
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