Discontinuous Galerkin time domain methods for acoustics and comparison with finite difference time domain methods

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dc.contributor.advisorSymes, William W.en_US
dc.creatorWang, Xinen_US
dc.date.accessioned2011-07-25T02:04:49Zen_US
dc.date.available2011-07-25T02:04:49Zen_US
dc.date.issued2010en_US
dc.description.abstractThis thesis describes an implementation of the discontinuous Galerkin finite element time domain (DGTD) method on unstructured meshes to solve acoustic wave equations in heterogeneous media. In oil industry people use finite difference time domain (FDTD) methods to simulate seismic surveys, the first step to explore oil and gas in the earth's subsurface, conducted either in land or sea. The results in this thesis indicate that the first order time shift effect resulting from misalignment between numerical meshes and material interfaces in the DGTD method occurs in the same way as interface errors in the finite difference simulation of wave propagation. This thesis describes two approaches: interface-fitting mesh and local mesh refinement, without modifying the DGTD scheme, to decrease this troublesome effect with verifications of 2D examples. The comparison of the DGTD method on the piecewise linear interface-fitting mesh and the staggered FDTD method both applied to a square-circle model and a 2D dome model in this thesis confirms the fact that the DGTD method can achieve a suboptimal second order convergence rate while the error in the staggered FDTD method is dominated by the first order interface error when the curved material interfaces are presented. I conclude that the DGTD method is more efficient than the staggered FDTD method for the two solutions to have roughly the same accuracy when the accuracy requirement becomes more and more strict and the model becomes more and more complex.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH.SCI. 2010 WANGen_US
dc.identifier.citationWang, Xin. "Discontinuous Galerkin time domain methods for acoustics and comparison with finite difference time domain methods." (2010) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/61981">https://hdl.handle.net/1911/61981</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/61981en_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.subjectApplied mathematicsen_US
dc.subjectGeophysicsen_US
dc.titleDiscontinuous Galerkin time domain methods for acoustics and comparison with finite difference time domain methodsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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