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

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dc.contributor.advisorSymes, William W.en_US
dc.contributor.committeeMemberWarburton, Timothy Cen_US
dc.contributor.committeeMemberRiviere, Beatrice Men_US
dc.creatorBencomo, Mario Javieren_US
dc.date.accessioned2016-01-06T20:25:31Zen_US
dc.date.available2016-01-06T20:25:31Zen_US
dc.date.created2015-05en_US
dc.date.issued2015-04-20en_US
dc.date.submittedMay 2015en_US
dc.date.updated2016-01-06T20:25:31Zen_US
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.en_US
dc.format.mimetypeapplication/pdfen_US
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>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/87708en_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.subjectstaggered finite differenceen_US
dc.subjectdiscontinuous Galerkinen_US
dc.subjectAcoustic equationsen_US
dc.subjectsmooth coefficientsen_US
dc.titleDiscontinuous Galerkin and Finite Difference Methods for the Acoustic Equations with Smooth Coefficientsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentComputational and Applied Mathematicsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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