Date of Award
12-2021
Degree Type
Masters Thesis
Degree Name
Master of Science (MS)
School
Mathematics and Natural Sciences
Committee Chair
Dr. James Lambers
Committee Chair School
Mathematics and Natural Sciences
Committee Member 2
Dr. Tian
Committee Member 2 School
Mathematics and Natural Sciences
Committee Member 3
Dr. Zhu
Committee Member 3 School
Mathematics and Natural Sciences
Abstract
In this thesis, we develop an accurate algorithm for computing the smallest eigenvalues of the self-adjoint spatial differential operator for the two-dimensional heat equation with a piecewise constant coefficient and periodic boundary conditions. The piecewise constant coefficient is created by the discontinuity of the diffusivity coefficient across the interfaces between two or more heterogeneous materials. Our method involves the combination of the well-known Inverse Iteration with a multigrid homotopy.
Recommended Citation
Drum, Chelsea, "A Multigrid Homotopy Method For Computing Eigenfunctions of Differential Operators With Two-Dimensional Heterogeneity" (2021). Master's Theses. 861.
https://aquila.usm.edu/masters_theses/861