Transfer-of-approximation Approaches for Subgrid Modeling

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dc.contributor.advisorSymes, William W.en_US
dc.contributor.committeeMemberWarburton, Timen_US
dc.contributor.committeeMemberRiviere, Beatrice M.en_US
dc.contributor.committeeMemberZelt, Colin A.en_US
dc.creatorWang, Xinen_US
dc.date.accessioned2013-07-24T19:50:18Zen_US
dc.date.accessioned2013-07-24T19:50:21Zen_US
dc.date.available2013-07-24T19:50:18Zen_US
dc.date.available2013-07-24T19:50:21Zen_US
dc.date.created2012-12en_US
dc.date.issued2013-07-24en_US
dc.date.submittedDecember 2012en_US
dc.date.updated2013-07-24T19:50:21Zen_US
dc.description.abstractI propose two Galerkin methods based on the transfer-of-approximation property for static and dynamic acoustic boundary value problems in seismic applications. For problems with heterogeneous coefficients, the polynomial finite element spaces are no longer optimal unless special meshing techniques are employed. The transfer-of-approximation property provides a general framework to construct the optimal approximation subspace on regular grids. The transfer-of-approximation finite element method is theoretically attractive for that it works for both scalar and vectorial elliptic problems. However the numerical cost is prohibitive. To compute each transfer-of-approximation finite element basis, a problem as hard as the original one has to be solved. Furthermore due to the difficulty of basis localization, the resulting stiffness and mass matrices are dense. The 2D harmonic coordinate finite element method (HCFEM) achieves optimal second-order convergence for static and dynamic acoustic boundary value problems with variable coefficients at the cost of solving two auxiliary elliptic boundary value problems. Unlike the conventional FEM, no special domain partitions, adapted to discontinuity surfaces in coe cients, are required in HCFEM to obtain the optimal convergence rate. The resulting sti ness and mass matrices are constructed in a systematic procedure, and have the same sparsity pattern as those in the standard finite element method. Mass-lumping in HCFEM maintains the optimal order of convergence, due to the smoothness property of acoustic solutions in harmonic coordinates, and overcomes the numerical obstacle of inverting the mass matrix every time update, results in an efficient, explicit time step.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationWang, Xin. "Transfer-of-approximation Approaches for Subgrid Modeling." (2013) Diss., Rice University. <a href="https://hdl.handle.net/1911/71700">https://hdl.handle.net/1911/71700</a>.en_US
dc.identifier.slug123456789/ETD-2012-12-288en_US
dc.identifier.urihttps://hdl.handle.net/1911/71700en_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.subjectFinite element methoden_US
dc.subjectTransfer-of-approximationen_US
dc.subjectElliptic problemen_US
dc.subjectAcoustic wave equationen_US
dc.subjectHarmonic coordinatesen_US
dc.titleTransfer-of-approximation Approaches for Subgrid Modelingen_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.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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