Date of Award
Summer 8-2016
Degree Type
Masters Thesis
Degree Name
Master of Science (MS)
Department
Mathematics
Committee Chair
James Lambers
Committee Chair Department
Mathematics
Committee Member 2
Haiyan Tian
Committee Member 2 Department
Mathematics
Committee Member 3
Huiqing Zhu
Committee Member 3 Department
Mathematics
Abstract
Krylov Subspace Spectral (KSS) methods are traditionally used to solve time-dependent, variable-coefficient PDEs. They are high-order accurate, component-wise methods that are efficient with variable input sizes.
This thesis will demonstrate how one can make KSS methods even more efficient by using a Multigrid-like approach for low-frequency components. The essential ingredients of Multigrid, such as restriction, residual correction, and prolongation, are adapted to the timedependent case. Then a comparison of KSS, KSS with Multigrid, KSS-EPI and standard Krylov projection methods will be demonstrated.
ORCID ID
orcid.org/0000-0003-2852-3914
Copyright
2016, Haley Renee Dozier
Recommended Citation
Dozier, Haley Renee, "Krylov Subspace Spectral Method with Multigrid for a Time-Dependent, Variable-Coefficient Partial Differential Equation" (2016). Master's Theses. 205.
https://aquila.usm.edu/masters_theses/205