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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Drum, Chelsea"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Masters Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Dr. James Lambers","Dr. Tian","Dr. Zhu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-12-01T08:00:00Z","date_published":"2021-12-01T08:00:00Z","updated_at":"2026-07-24T05:45:33Z","subjects":["heat equation","eigenvalues","differential operators","inverse iteration"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/861","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dr. James Lambers","Dr. Tian","Dr. Zhu"]},{"key":"dc:creator","label":"Author","values":["Drum, Chelsea"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2021-10-01T07:00:00Z"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["heat equation","eigenvalues","differential operators","inverse iteration"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/861"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["A Multigrid Homotopy Method For Computing Eigenfunctions of Differential Operators With Two-Dimensional Heterogeneity"]}]}],"canonical_facts":{"dc:contributor":["Dr. James Lambers","Dr. Tian","Dr. Zhu"],"dc:creator":["Drum, Chelsea"],"dc:date.available":["2021-10-01T07:00:00Z"],"dc:description.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.
"],"dc:identifier":["https://aquila.usm.edu/masters_theses/861"],"dc:subject":["heat equation","eigenvalues","differential operators","inverse iteration"],"dc:title":["A Multigrid Homotopy Method For Computing Eigenfunctions of Differential Operators With Two-Dimensional Heterogeneity"],"thesis:degree_level":["Masters Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:45:33Z"}