Approximation of the 2D complex eikonal equation : analysis and simulation

dc.contributor.advisorEngquist, Björn, 1945-en
dc.contributor.committeeMemberTsai, Yen-Hsien
dc.contributor.committeeMemberGamba, Ireneen
dc.contributor.committeeMemberVasseur, Alexisen
dc.contributor.committeeMemberGhattas, Omaren
dc.creatorLiu, Peijiaen
dc.date.accessioned2013-01-30T16:54:17Zen
dc.date.available2013-01-30T16:54:17Zen
dc.date.issued2012-12en
dc.date.submittedDecember 2012en
dc.date.updated2013-01-30T16:55:07Zen
dc.descriptiontexten
dc.description.abstractHigh frequency wave propagation is well described even at caustics by Gaussian beams and the complex eikonal equation. In contrast to the real eikonal equation, the complex eikonal equation is elliptic and not well posed as an initial value problem. We develop a new model that approximates the 2D complex eikonal equation but is well posed as an initial value problem. This model consists of a coupled system of partial and ordinary differential equations. We prove that there exists a local solution to this new system by a Picard iteration method and show uniqueness under certain constraints. Different numerical approximations are then developed based on direct finite difference approximations or the method of characteristics. Numerical simulations with a variety of velocity profiles are presented and compared with solutions to the corresponding Helmholtz equation.en
dc.description.departmentMathematicsen
dc.format.mimetypeapplication/pdfen
dc.identifier.slug2152/ETD-UT-2012-12-6790en
dc.identifier.urihttp://hdl.handle.net/2152/ETD-UT-2012-12-6790en
dc.language.isoengen
dc.subject2D complex eikonal equationen
dc.titleApproximation of the 2D complex eikonal equation : analysis and simulationen
dc.type.genrethesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorUniversity of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen

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