{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/83331"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/83331","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Stabilized Finite Elements and a Domain Decomposition Method for First-Order Transient Problems","abstract":"In the third part, a novel domain decomposition method for first-order transient nonlinear problems is presented. To the author's knowledge the proposed method is the only known robust domain decomposition method for transient problems that enables arbitrary numeric schemes to be coupled with different time steps in each subdomain, which is a highly desirable feature in the multiscale and multiphysics simulations. One of the advantages of the method is that existing software and numerical techniques can be used to solve each subdomain separately. 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The proposed coupling method provides a powerful approach not only to solve large-scale problems very efficiently, but also to solve small-scale problems wherein multiple scales in the response demand the use of different schemes in different regions.","abstract_has_math":false,"creators":["Nakshatrala, Kalyana Babu"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Civil and Environmental Engineering","degree_department":null,"school":null,"contributors":["Keith J. 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