Chan, Jesse2024-05-202024-05-202024-052024-04-02May 2024Johnson, Raven Shane. A Pseudo-Differential Sweeping Method for the Helmholtz Equation. (2024). Masters thesis, Rice University. https://hdl.handle.net/1911/115914https://hdl.handle.net/1911/115914Ultrasound-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.application/pdfengCopyright 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.Helmholtz equationpseudodifferential operatorThesis2024-05-20