Andrew Gillette
Finite Element Exterior Calculus for Evolution Problems.
Thu, 02/09/2012 - 15:01 — SomNambulAuthors: Andrew Gillette, Michael Holst
Subjects: Numerical Analysis
AbstractArnold, Falk, and Winther [Bull. Amer. Math. Soc. 47 (2010), 281--354]
recently showed that mixed variational problems, and their numerical
approximation by mixed methods, could be most completely understood using the
ideas and tools of Hilbert complexes.Complementary Space for Enhanced Uncertainty and Dynamics Visualization.
Fri, 10/23/2009 - 04:10 — SomNambulAuthors: Chandrajit Bajaj, Andrew Gillette, Samrat Goswami, Bong June Kwon, Jose Rivera
Subjects: Computational Geometry
AbstractGiven a computer model of a physical object, it is often quite difficult to
visualize and quantify any global effects on the shape representation caused by
local uncertainty and local errors in the data. This problem is further
amplified when dealing with hierarchical representations containing varying
levels of detail and / or shapes undergoing dynamic deformations. In this
paper, we compute, quantify and visualize the complementary topological and
geometrical features of 3D shape models, namely, the tunnels, pockets and
internal voids of the object.Stable Mesh Decimation.
Fri, 10/09/2009 - 18:27 — SomNambulAuthors: Chandrajit Bajaj, Andrew Gillette, Qin Zhang
Subjects: Analysis of PDEs
AbstractCurrent mesh reduction techniques, while numerous, all primarily reduce mesh
size by successive element deletion (e.g. edge collapses) with the goal of
geometric and topological feature preservation. The choice of geometric error
used to guide the reduction process is chosen independent of the function the
end user aims to calculate, analyze, or adaptively refine. In this paper, we
argue that such a decoupling of structure from function modeling is often
unwise as small changes in geometry may cause large changes in the associated
function.
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