the discrete level is another goal, overlapping with our goals for variational problems. Comments: Subjects: Differential Geometry (math. One of the objectives of this thesis is to fill this gap. 49, 022901 (2008 DOI:10.1063/1.2830977 Discrete Differential Geometry : An Applied Introduction). (advisor arvo, James. Edu/CaltechETD:etd, default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. For every ( k 1)-dimensional subcomplex of T,. Degree Grantor: California Institute of Technology, division: Engineering and Applied Science, major Option: Computer Science. Other concepts such as the discrete wedge product and the discrete Hodge star can also be defined. The derivation of these may require that the objects on the discrete mesh, but not the mesh itself, are interpolated.
(February 2009 in mathematics, the discrete exterior calculus dEC ) is the extension of the exterior calculus to discrete spaces including graphs and finite element meshes. Thesis Committee: Marsden, Jerrold. (chair arvo, James. For example, a curve would be approximated as a union of straight line segments; a surface would be approximated by a union of triangles, whose edges are straight line segments, which themselves terminate in points.
This thesis presents the beginnings of a theory of discrete exterior calculus (DEC). Our approach is to develop DEC using only discrete combinatorial and geometric operations on a simplicial complex and its geometric dual. In mathematics, the discrete exterior calculus (DEC) is the extension of the exterior calculus to discrete spaces including graphs and finite element meshes.
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DEC methods have proved to be very powerful in improving and analyzing finite element methods: for instance, DEC-based methods allow the use of highly non-uniform meshes to obtain accurate results. See also edit References edit Discrete Calculus, Grady, Leo., Polimeni, Jonathan., 2010 Discrete Exterior Calculus with Convergence to the Smooth Continuum Hirani Thesis on Discrete Exterior Calculus Convergence of discrete essays on blindness by jose saramago exterior calculus approximations for Poisson problems,. Desbrun, Mathieu, ortiz, Michael. Non-uniform meshes are advantageous because they allow the use of large elements where the process to be simulated is relatively simple, as opposed to a fine resolution where the process may be complicated (e.g., near an obstruction to a fluid flow while using less computational. Cite as: arXiv:math/0508341 math.