Fast algorithms for frequency domain wave propagation

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dc.contributor.advisorYing, Lexingen
dc.contributor.committeeMemberGhattas, Omar N.en
dc.contributor.committeeMemberEngquist, Bjornen
dc.contributor.committeeMemberFomel, Sergeyen
dc.contributor.committeeMemberRen, Kuien
dc.creatorTsuji, Paul Hikaruen
dc.date.accessioned2013-02-22T15:56:27Zen
dc.date.issued2012-12en
dc.date.submittedDecember 2012en
dc.date.updated2013-02-22T15:56:27Zen
dc.descriptiontexten
dc.description.abstractHigh-frequency wave phenomena is observed in many physical settings, most notably in acoustics, electromagnetics, and elasticity. In all of these fields, numerical simulation and modeling of the forward propagation problem is important to the design and analysis of many systems; a few examples which rely on these computations are the development of metamaterial technologies and geophysical prospecting for natural resources. There are two modes of modeling the forward problem: the frequency domain and the time domain. As the title states, this work is concerned with the former regime. The difficulties of solving the high-frequency wave propagation problem accurately lies in the large number of degrees of freedom required. Conventional wisdom in the computational electromagnetics commmunity suggests that about 10 degrees of freedom per wavelength be used in each coordinate direction to resolve each oscillation. If K is the width of the domain in wavelengths, the number of unknowns N grows at least by O(K^2) for surface discretizations and O(K^3) for volume discretizations in 3D. The memory requirements and asymptotic complexity estimates of direct algorithms such as the multifrontal method are too costly for such problems. Thus, iterative solvers must be used. In this dissertation, I will present fast algorithms which, in conjunction with GMRES, allow the solution of the forward problem in O(N) or O(N log N) time.en
dc.description.departmentComputational Science, Engineering, and Mathematicsen
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/2152/19533en
dc.language.isoen_USen
dc.subjectFast algorithmsen
dc.subjectBoundary element methodsen
dc.subjectBoundary integral equationsen
dc.subjectFast multipole methodsen
dc.subjectNedelec elementsen
dc.subjectSpectral element methodsen
dc.subjectFinite element methodsen
dc.subjectPreconditionersen
dc.subjectPerfectly matched layersen
dc.subjectRadiation conditionsen
dc.subjectTime harmonicen
dc.subjectFrequency domainen
dc.subjectWave propagationen
dc.subjectMaxwell's equationsen
dc.subjectHelmholtz equationen
dc.subjectLinear elasticityen
dc.subjectElastic wave equationen
dc.subjectComputational electromagneticsen
dc.subjectComputational acousticsen
dc.subjectElectromagnetic cloakingen
dc.subjectSeismic velocity modelsen
dc.subjectOverthrusten
dc.subjectSalt domeen
dc.titleFast algorithms for frequency domain wave propagationen
thesis.degree.departmentComputational Science, Engineering, and Mathematicsen
thesis.degree.disciplineComputational and Applied Mathematicsen
thesis.degree.grantorThe University of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen

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