A Multigrid Homotopy Method For Computing Eigenfunctions of Differential Operators With Two-Dimensional Heterogeneity

<p>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.</p>

Name thesis:degree_name

Master of Science (MS)

Level thesis:degree_level

Masters Thesis

Year dc:date.available

2021

Author dc:creator

• Drum, Chelsea

Contributors dc:contributor

• Dr. James Lambers
• Dr. Tian
• Dr. Zhu

• heat equation
• eigenvalues
• differential operators
• inverse iteration

Repository record dc:identifier

https://aquila.usm.edu/masters_theses/861

OAI identifier oai:identifier

oai:aquila.usm.edu:masters_theses-1924