Energy-Conserving Composite Staggered-Grid Finite-Difference Time-Domain Scheme for First-Order Wave Equation System

dc.contributor.advisorSymes, William Wen_US
dc.creatorZhou, Muhongen_US
dc.date.accessioned2017-08-01T17:54:02Zen_US
dc.date.available2018-05-01T05:01:09Zen_US
dc.date.created2017-05en_US
dc.date.issued2017-04-20en_US
dc.date.submittedMay 2017en_US
dc.date.updated2017-08-01T17:54:02Zen_US
dc.description.abstractFinite-difference time-domain (FDTD) scheme has been widely used for seismic wave simulations in hydrocarbon exploration and earthquake modeling. To reduce the grid dispersion numerical artifact, FDTD scheme needs to use finer grids on low-velocity regions than on high-velocity regions. Therefore, if the simulation region presents strong velocity variations, then using a composite-grid FDTD scheme is computationally more efficient than using a uniform-grid FDTD scheme. The challenge, however, is to construct a composite-grid FDTD scheme that is numerically stable. In this work, I propose an energy-conserving composite staggered-grid FDTD scheme (EC-CGS) for the first-order wave equation system. The composite-grid configuration allows EC-CGS to use a fine grid on the low-velocity region and a coarse grid on the high-velocity region. Meanwhile, the energy-conserving property ensures numerical stability for EC-CGS provided that the time step meets a constraint of CFL type. In addition, EC-CGS is also consistent with the transmission condition across the grid refinement interface, because one key step in EC-CGS is to update the data near the grid refinement interface by solving linear equation system(s) derived from the energy-conserving property and the transmission condition. Numerical results of 1-D/3-D wave simulations confirmed the energy-conserving property, stability and convergence of EC-CGS. In particular, EC-CGS solutions agree well with UGS solutions even when strong heterogeneity is present across the grid interface, despite the fact that EC-CGS uses a coarser grid on part of the computational domain and thereby takes less run time and needs less memory.en_US
dc.embargo.terms2018-05-01en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationZhou, Muhong. "Energy-Conserving Composite Staggered-Grid Finite-Difference Time-Domain Scheme for First-Order Wave Equation System." (2017) Diss., Rice University. <a href="https://hdl.handle.net/1911/96077">https://hdl.handle.net/1911/96077</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/96077en_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.subjectEnergy Methoden_US
dc.subjectEnergy Stabilityen_US
dc.subjectComposite Grid Schemeen_US
dc.subjectStaggered-Grid FDTD Schemeen_US
dc.subjectElastic Wave Equationen_US
dc.subjectAnisotropyen_US
dc.subjectTransmission Conditionen_US
dc.titleEnergy-Conserving Composite Staggered-Grid Finite-Difference Time-Domain Scheme for First-Order Wave Equation Systemen_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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