2026-09-21T07:10:37Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/81795 2023-07-11 col_2142_5131 col_2142_10761 com_2142_5130 com_2142_10755 com_2142_234

http://hdl.handle.net/2142/81795 Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007. de Sturler, Eric Paulino, Glaucio H. Wang, Shun 2015-09-25T20:20:29Z 2015-09-25T20:20:29Z 10000-01-01 2007 2007 Third, we propose a multilevel sparse approximate inverse (MSPAI) preconditioner for adaptive mesh refinement. It significantly improves the conditioning of the linear systems by approximating the global modes with multilevel techniques, while remaining cheap to update and apply, especially when the mesh changes. For convection-diffusion problems, it achieves a level-independent convergence rate. We then make a few extensions in the MSPAI preconditioner for topology optimization problems, which lead to nearly level-independent convergence rate and better scalability than incomplete factorization type of preconditioners. Made available in DSpace on 2015-09-25T20:20:29Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3290423.pdf: 3584733 bytes, checksum: 6c12f61325eec5f831152270bf31fa09 (MD5) Previous issue date: 2007 Embargo set by: Seth Robbins for item 83076 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 124 p. (MiAaPQ)AAI3290423 eng Computer Science Krylov Subspace Methods for Topology Optimization on Adaptive Meshes text Computer Science Computer Science University of Illinois at Urbana-Champaign Dissertation Ph.D.