Discontinuous Galerkin and Finite Difference Methods for the Acoustic Equations with Smooth Coefficients

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dc.contributor.advisorSymes, William W.
dc.contributor.committeeMemberWarburton, Timothy C
dc.contributor.committeeMemberRiviere, Beatrice M
dc.creatorBencomo, Mario Javier
dc.date.accessioned2016-01-06T20:25:31Z
dc.date.available2016-01-06T20:25:31Z
dc.date.created2015-05
dc.date.issued2015-04-20
dc.date.submittedMay 2015
dc.date.updated2016-01-06T20:25:31Z
dc.description.abstractThis thesis analyzes the computational efficiency of two types of numerical methods: finite difference (FD) and discontinuous Galerkin (DG) methods, in the context of 2D acoustic equations in pressure-velocity form with smooth coefficients. The acoustic equations model propagation of sound waves in elastic fluids, and are of particular interest to the field of seismic imaging. The ubiquity of smooth trends in real data, and thus in the acoustic coefficients, validates the importance of this novel study. Previous work, from the discontinuous coefficient case of a two-layered media, demonstrates the efficiency of DG over FD methods but does not provide insight for the smooth coefficient case. Floating point operation (FLOPs) counts are compared, relative to a prescribed accuracy, for standard 2-2 and 2-4 staggered grid FD methods, and a myriad of standard DG implementations. This comparison is done in a serial framework, where FD code is implemented in C while DG code is written in Matlab. Results show FD methods considerably outperform DG methods in FLOP count. More interestingly, implementations of quadrature based DG with mesh refinement (for lower velocity zones) yield the best results in the case of highly variable media, relative to other DG methods.
dc.format.mimetypeapplication/pdf
dc.identifier.citationBencomo, Mario Javier. "Discontinuous Galerkin and Finite Difference Methods for the Acoustic Equations with Smooth Coefficients." (2015) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/87708">https://hdl.handle.net/1911/87708</a>.
dc.identifier.urihttps://hdl.handle.net/1911/87708
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.subjectstaggered finite difference
dc.subjectdiscontinuous Galerkin
dc.subjectAcoustic equations
dc.subjectsmooth coefficients
dc.titleDiscontinuous Galerkin and Finite Difference Methods for the Acoustic Equations with Smooth Coefficients
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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