Andrew Gillette

  1. Finite Element Exterior Calculus for Evolution Problems.

    Authors: Andrew Gillette, Michael Holst
    Subjects: Numerical Analysis
    Abstract

    Arnold, 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.

  2. Complementary Space for Enhanced Uncertainty and Dynamics Visualization.

    Authors: Chandrajit Bajaj, Andrew Gillette, Samrat Goswami, Bong June Kwon, Jose Rivera
    Subjects: Computational Geometry
    Abstract

    Given 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.

  3. Stable Mesh Decimation.

    Authors: Chandrajit Bajaj, Andrew Gillette, Qin Zhang
    Subjects: Analysis of PDEs
    Abstract

    Current 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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