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Duarte, C. Armando Duarte, C. Armando Eason, Thomas G., III Geubelle, Philippe H. Aluru, Narayana R. O'Hara, Patrick J. 2010-05-14T20:50:38Z 2010-05-14T20:50:38Z 2012-05-15T10:00:35Z 2010-05-14T20:50:38Z 2010-05 In this research, heat transfer problems exhibiting sharp thermal gradients are analyzed using the generalized finite element method. Convergence studies show that low order (linear and quadratic) elements require strongly refined meshes for acceptable accuracy. The high mesh density leads to small allowable time-step sizes, and significant increase in the computational cost. When mesh refinement and unrefinement is required between time-steps the mapping of solution vectors and state-dependent variables becomes difficult. A generalized FEM with global-local enrichments is proposed for the class of problems investigated in this research. In this procedure, a global solution space defined on a coarse mesh is enriched through the partition of unity framework of the generalized FEM with solutions of local boundary value problems. The local problems are defined using the same procedure as in the global-local FEM, where boundary conditions are provided by a coarse-scale global solution. Coarse, uniform, global meshes are acceptable even at regions with thermal spikes that are orders of magnitude smaller than the element size. Convergence on these discretizations is achieved even when no or limited convergence is observed in the local problems. The two-way information transfer provided by the proposed generalized FEM is appealing to several classes of problems, especially those involving multiple spatial scales. The proposed methodology brings the benefits of generalized FEM to problems where limited or no information about the solution is known a-priori. The proposed methodology is formulated for, and applied to transient problems, where local domains at time t^{n+1} obtain their boundary conditions from the global domain at t^{n}. No transient effects need to be considered in the local domain. The method has shown the ability to produce accurate and efficient transient simulations in situations where traditional FEM analyses would lead to difficult re-meshing, and solution mapping issues. With the proposed methodology, the enrichment functions are added hierarchically to the stiffness matrix. As such, large portions of the coarse, global meshes may be assembled and factorized only once. The factorizations can then be re-used for multiple loading scenarios, or multiple time-steps so as to significantly improve the computational efficiency of the simulations. The issue of prohibitively small time-step sizes dictated by high mesh density in traditional FEM analyses is also addressed. With the use of appropriate shape functions, sufficient accuracy is obtained without the requirement of highly refined meshes. The resulting critical time-steps are less restrictive, making transient analyses more computationally feasible. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-04-08T18:01:53Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 OHara_Patrick.pdf: 6068212 bytes, checksum: ef5a5f5a8301b519fc4d06c987fad732 (MD5) Made available in DSpace on 2010-05-14T20:50:38Z (GMT). No. of bitstreams: 3 OHara_Patrick.pdf: 6068212 bytes, checksum: ef5a5f5a8301b519fc4d06c987fad732 (MD5) ohara_patrick.pdf: 6068303 bytes, checksum: 4dd7fd66830b990452d51f3ea0467c52 (MD5) license.txt: 4062 bytes, checksum: be4409e9955c38a91122b36f85040817 (MD5) Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by William Ingram (wingram2@illinois.edu) on 2010-05-14T20:52:46Z Item is restricted until 2012-05-14T20:52:43Z Item reinstated by Sarah Shreeves (sshreeve@illinois.edu) on 2012-05-15T10:00:34Z Item was in collections: University of Illinois Dissertations and Theses (ID: 204) Dissertations and Theses - Civil and Environmental Engineering (ID: 672) No. of bitstreams: 4 ohara_patrick.pdf.txt: 324409 bytes, checksum: 2a4f98560b6b7e79610863dd83152ed7 (MD5) OHara_Patrick.pdf: 6068212 bytes, checksum: ef5a5f5a8301b519fc4d06c987fad732 (MD5) ohara_patrick.pdf: 6068303 bytes, checksum: 4dd7fd66830b990452d51f3ea0467c52 (MD5) license.txt: 4062 bytes, checksum: be4409e9955c38a91122b36f85040817 (MD5) Item released from any restrictions by Sarah Shreeves (sshreeve@illinois.edu) on 2012-05-15T10:00:35Z http://hdl.handle.net/2142/15566 en Copyright 2010 Patrick James O'Hara Generalized Finite Element Method (GFEM) Heat Transfer A multi-scale generalized finite element method for sharp, transient thermal gradients Civil & Environmental Eng 1251 Civil Engineering 0106 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Civil Engineering -UIUC 10KS0106PHD