A Pseudo-Differential Sweeping Method for the Helmholtz Equation

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dc.contributor.advisorChan, Jesse
dc.creatorJohnson, Raven Shane
dc.date.accessioned2024-05-20T19:56:57Z
dc.date.available2024-05-20T19:56:57Z
dc.date.created2024-05
dc.date.issued2024-04-02
dc.date.submittedMay 2024
dc.date.updated2024-05-20T19:56:57Z
dc.description.abstractUltrasound-guided medical procedures often experience complications when imaging heterogeneous tissue. Computer simulations of the ultrasound field offer a workable solution to this heterogeneity problem, but the computational methods required for these simulations tend to be either highly accurate and computationally slow or computationally quick and inaccurate. We propose a sweeping numerical method for solving the Helmholtz equation which is built from a truncated pseudo-differential expansion. We discretize this expansion using high order spectral element methods in space and an explicit time-stepping method in time. Numerical experiments examine the behavior of the proposed method in 1D and 2D under different numerical parameters. We demonstrate that the proposed sweeping method is not only accurate but increases in accuracy as the angular frequency increases.
dc.format.mimetypeapplication/pdf
dc.identifier.citationJohnson, Raven Shane. A Pseudo-Differential Sweeping Method for the Helmholtz Equation. (2024). Masters thesis, Rice University. https://hdl.handle.net/1911/115914
dc.identifier.urihttps://hdl.handle.net/1911/115914
dc.language.isoeng
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.
dc.subjectHelmholtz equation
dc.subjectpseudodifferential operator
dc.titleA Pseudo-Differential Sweeping Method for the Helmholtz Equation
dc.typeThesis
dc.type.materialText
thesis.degree.departmentComputational and Applied Mathematics
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Arts
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