Abstract
Parallel Adaptive
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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
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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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