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

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dc.contributor.advisorSorensen, Dannyen_US
dc.creatorSun, Kaien_US
dc.date.accessioned2018-12-03T18:31:14Zen_US
dc.date.available2018-12-03T18:31:14Zen_US
dc.date.issued2008en_US
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.en_US
dc.format.extent182 ppen_US
dc.identifier.callnoTHESIS MATH. SCI. 2009 SUN [Kai]en_US
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>.en_US
dc.identifier.digital304507831en_US
dc.identifier.urihttps://hdl.handle.net/1911/103534en_US
dc.language.isoengen_US
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.en_US
dc.subjectMathematicsen_US
dc.subjectPure sciencesen_US
dc.subjectDomain decompositionen_US
dc.subjectDynamical systemsen_US
dc.subjectModel order reductionen_US
dc.subjectNumerical algebraen_US
dc.subjectNumerical analysisen_US
dc.titleModel order reduction and domain decomposition for large-scale dynamical systemsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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