Comparison of discrete Hodge star operators for surfaces
نویسندگان
چکیده
منابع مشابه
Discrete Hodge operators
Many linear boundary value problems arising in computational physics can be formulated in the calculus of differential forms. Discrete differential forms provide a natural and canonical approach to their discretization. However, much freedom remains concerning the choice of discrete Hodge operators, that is, discrete analogues of constitutive laws. A generic discrete Hodge operator is introduce...
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We define signed dual volumes at all dimensions for circumcentric dual meshes. We show that for pairwise Delaunay triangulations with mild boundary assumptions these signed dual volumes are positive. This allows the use of such Delaunay meshes for Discrete Exterior Calculus (DEC) because the discrete Hodge star operator can now be correctly defined for such meshes. This operator is crucial for ...
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We’ll start out by defining the Hodge star operator as a map from ∧k(R) to ∧n−k(R). Here ∧k(R) denotes the vector space of alternating k-tensors on R. Later on, we will extend this definition to alternating tensors on a finite dimensional vector space that is equipped with an inner product. Let I = (i1, ..., ik) be some increasing multi-index of length k. That is i1 < i2 < i3 < .... Let J = (j1...
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A fermionic analogue of the Hodge star operation is shown to have an explicit operator representation in models with fermions, in spacetimes of any dimension. This operator realizes a conjugation (pairing) not used explicitly in field-theory, and induces a metric in the space of wave-function(al)s just as in exterior calculus. If made real (Hermitian), this induced metric turns out to be identi...
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ژورنال
عنوان ژورنال: Computer-Aided Design
سال: 2016
ISSN: 0010-4485
DOI: 10.1016/j.cad.2016.05.002