A new algorithm for continuation and bifurcation analysis of large scale free surface flows

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dc.contributor.advisorSorensen, Danny C.en_US
dc.creatorCastillo, Zenaidaen_US
dc.date.accessioned2009-06-04T06:30:39Zen_US
dc.date.available2009-06-04T06:30:39Zen_US
dc.date.issued2005en_US
dc.description.abstractThis thesis presents a new algorithm to find and follow particular solutions of parameterized nonlinear systems. Important applications often arise after spatial discretization of time dependent PDEs. We embed a block eigenvalue solver in a continuation framework for the computation of some specific eigenvalues of large Jacobian matrices that depend on one or more parameters. The new approach is then employed to study the behavior of an industrial process referred to as coating. Stability analysis of the discretized system that models this process is important because it provides alternatives for changing parameters in order to improve the quality of the final product or to increase productivity. Experiments on several problems show the reliability of the new approach in the accurate detection of critical points. Further analysis of two-dimensional coating flow problems reveals that computational results are competitive with those of previous continuation approaches. As a byproduct, one obtains information about the stability of the process with no additional cost. Due to the size and structure of the matrices generated in three-dimensional free surface flow applications, it is necessary to use a general iterative linear solver, such as GMRES. However, GMRES displays a very slow rate of convergence as a consequence of the poor conditioning in the coefficient matrices. To speed up GMRES convergence, we developed and implemented a scalable approximate sparse inverse preconditioner. Numerical experiments demonstrate that this preconditioner greatly improves the convergence of the method. Results illustrate the effectiveness of the preconditioner on very large free surface flow problems with more than million unknowns.en_US
dc.format.extent162 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH.SCI. 2005 CASTILLOen_US
dc.identifier.citationCastillo, Zenaida. "A new algorithm for continuation and bifurcation analysis of large scale free surface flows." (2005) Diss., Rice University. <a href="https://hdl.handle.net/1911/18743">https://hdl.handle.net/1911/18743</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/18743en_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.titleA new algorithm for continuation and bifurcation analysis of large scale free surface flowsen_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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