Efficient computation of Jacobian matrices for entropy stable summation by parts schemes

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dc.contributor.advisorChan, Jesse
dc.creatorTaylor, Christina Gabrielle
dc.date.accessioned2022-10-11T19:20:54Z
dc.date.available2022-10-11T19:20:54Z
dc.date.created2021-08
dc.date.issued2021-06-22
dc.date.submittedAugust 2021
dc.date.updated2022-10-11T19:20:54Z
dc.description.abstractThis work presents efficient formulas for the computation of Jacobian matrices arising from entropy stable summation-by-parts schemes. Competing methods for computing Jacobian matrices include finite difference, automatic differentiation, graph coloring, and Jacobian-free Newton-Krylov methods. In contrast to these methods the formulas proposed provide a sparsity-informed method for computing Jacobian matrices that are free of truncation error. Computational timings confirm that the proposed formulas scale very robustly with respect to the size of the system and easily outperform existing methods on denser Jacobian matrices. Two applications of Jacobian matrices, two-derivative and implicit time stepping, are also explored in numerical experiments with Burgers' and the shallow water equations.
dc.format.mimetypeapplication/pdf
dc.identifier.citationTaylor, Christina Gabrielle. "Efficient computation of Jacobian matrices for entropy stable summation by parts schemes." (2021) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/113688">https://hdl.handle.net/1911/113688</a>.
dc.identifier.urihttps://hdl.handle.net/1911/113688
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.subjectJacobian
dc.subjectEntropy stable
dc.subjectSummation by parts
dc.titleEfficient computation of Jacobian matrices for entropy stable summation by parts schemes
dc.typeThesis
dc.type.materialText
thesis.degree.departmentComputational and Applied Mathematics
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Arts
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