PhD thesis,

Parallel Adaptive C1 Macro-Elements for Nonlinear Thin Film and Non-Newtonian Flow Problems

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The University of Texas at Austin, (2008)

Abstract

Parallel Adaptive C 1 Macro-Elements for Nonlinear Thin Film and Non-Newtonian Flow Problems Publication No. Roy Hulen Stogner, Ph.D. The University of Texas at Austin, 2008 Supervisor: Graham F. Carey This research deals with several novel aspects of finite elem ent for- mulations and methodology in parallel adaptive simulation of flow problems. Composite macroelement schemes are developed for problems of thin fluid lay- ers with deforming free surfaces or decomposing material ph ases; experiments are also run on divergence-free formulations that can be der ived from the same element classes. The constrained composite nature and C 1 continuity require- ments of these elements raises new issues, especially with r espect to adaptive refinement patterns and the treatment of hanging node constr aints, which are more complex than encountered with standard element types. This work com- bines such complex elements with these applications and wit h parallel adaptive mesh refinement and coarsening (AMR/C) techniques for the fir st time. The use of adaptive macroelement spaces also requires appro priate pro- gramming interfaces and data structures to enable easy and e fficient imple- mentation in parallel software. The algorithms developed f or this work are implemented using object-oriented designs described here in.

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