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Olson, Luke N. Bell, William N. 2015-09-25T20:20:35Z 2015-09-25T20:20:35Z 10000-01-01 2008 2008 Discrete differential forms arise in scientific disciplines ranging from computational electromagnetics to computer graphics. Examples include stable discretizations of the eddy-current problem, topological methods for sensor network coverage, visualization of complex flows, surface parameterization, and the design of vector fields on meshes. In this thesis we describe efficient and scalable numerical solvers for discrete k-form problems. Our approach is based on the principles of algebraic multigrid (AMG) which is designed to solve large-scale linear systems with optimal, or near-optimal efficiency. Since the k-form problems to be solved are arbitrarily large, the need for scalable numerical solvers is clear. Made available in DSpace on 2015-09-25T20:20:35Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3337696.pdf: 1728341 bytes, checksum: 095d07d06c81490214c73c32f24bf2e9 (MD5) Previous issue date: 2008 Embargo set by: Seth Robbins for item 83101 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 92 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008. http://hdl.handle.net/2142/81820 (MiAaPQ)AAI3337696 eng Computer Science Algebraic Multigrid for Discrete Differential Forms text Computer Science Computer Science University of Illinois at Urbana-Champaign Dissertation Ph.D.