Structured matrix algorithms for solving Helmholtz equation

Simple item page
dc.contributor.advisorde Hoop, Maarten V
dc.creatorLiu, Xiao
dc.date.accessioned2019-05-16T18:52:49Z
dc.date.available2019-05-16T18:52:49Z
dc.date.created2019-05
dc.date.issued2019-04-12
dc.date.submittedMay 2019
dc.date.updated2019-05-16T18:52:49Z
dc.description.abstractIn this dissertation, novel solution algorithms are developed for large structured linear systems such as the discretized Helmholtz equation. Firstly, we develop two parallel randomized algorithms for constructing hierarchically semiseparable (HSS) matrices. Randomized sampling reduces the computational complexity and the communication cost simultaneously, and the resulting method is suitable for solving dense systems arising from multiple scattering problems. Secondly, a direct factorization update algorithm is proposed for solving the Helmholtz equation with changing wavespeed. The data dependency among a set of interior and exterior sub-problems is exploited to maximize the data reuse and to minimize the propagation of changes. Thirdly, interconnected HSS structures are designed to improve the efficiency of rank-structured factorization of PDE problems. Intermediate Schur complements at different levels share the same set of HSS bases during the factorization. Finally, we propose a contour integration preconditioner for solving 3D high-frequency Helmholtz equation. By solving systems with complex shifts, the problem is projected in subspaces with faster GMRES convergence. The shifted problems are solved by a polynomial fixed-point iteration, which is robust when the shift changes.
dc.format.mimetypeapplication/pdf
dc.identifier.citationLiu, Xiao. "Structured matrix algorithms for solving Helmholtz equation." (2019) Diss., Rice University. <a href="https://hdl.handle.net/1911/105384">https://hdl.handle.net/1911/105384</a>.
dc.identifier.urihttps://hdl.handle.net/1911/105384
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.subjecthierarchically semiseparable matrix
dc.subjectrandomized sampling
dc.subjectfactorization update
dc.subjectexterior boundary value problem
dc.subjectcontour integration
dc.subjectmatrix exponential
dc.titleStructured matrix algorithms for solving Helmholtz equation
dc.typeThesis
dc.type.materialText
thesis.degree.departmentComputational and Applied Mathematics
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
LIU-DOCUMENT-2019.pdf
Size:
2.22 MB
Format:
Adobe Portable Document Format
Download
License bundle
Now showing 1 - 2 of 2
No Thumbnail Available
Name:
PROQUEST_LICENSE.txt
Size:
5.84 KB
Format:
Plain Text
Description:
Download
No Thumbnail Available
Name:
LICENSE.txt
Size:
2.6 KB
Format:
Plain Text
Description:
Download
Collections
Rice University Electronic Theses and Dissertations