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

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    Author
    Bencomo, Mario Javier
    Date
    2015-04-20
    Advisor
    Symes, William W.
    Degree
    Master of Arts
    Abstract
    This 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.
    Keyword
    staggered finite difference; discontinuous Galerkin; Acoustic equations; smooth coefficients
    Citation
    Bencomo, Mario Javier. "Discontinuous Galerkin and Finite Difference Methods for the Acoustic Equations with Smooth Coefficients." (2015) Master’s Thesis, Rice University. https://hdl.handle.net/1911/87708.
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    Home | FAQ | Contact Us | Privacy Notice | Accessibility Statement
    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map