Discrete Exterior Calculus

By Anil N. Hirani. 2003

723 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Graphics and Computer-Aided Design, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/88784e0d95fdb3ff31d5b817d17476257b9ceee5

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In Applied Mathematics

In Computer Graphics and Computer-Aided Design

In Mathematical Physics

Citations in the corpus

Spectral Mesh Processing (2009, methodology): “[Hir03] Anil Hirani.”
Structure-preserving discretization of incompressible fluids (2009, methodology): “gue measure will be denoted by j:j. Thus, jC ijis the volume of cell C i, jC i\C jjis the area of the face common to C iand C j, etc (see Figure2). The dual of M is the circumentric dual cell complex [28], formed by connecting the circumcenters of each cell C ibased on the connectivity of M. We will”
Combinatorial Calabi flows on surfaces (2012, background): “ual structure of circle patterns. This is why we call (A.4) discrete dual-Laplacian. There are other types of discrete Laplacians, such as cotangent-Laplacian. See more in [15], [16], [17], [21], and [22]. A.2. proof of (3.2). Lemma A.1. Consider a triangle 4ABCcoming from a conguration of circle pa”
On geometric discretization of elasticity (2008, methodology): “In this paper, for studying this problem for elasticity, we need to extend some concepts presented in [22] for discrete bundle-valued forms.”
Geometric triangulations and discrete Laplacians on manifolds (2005, methodology): “e operators, and look at the generalization of these comments to regular triangulations. 24 4.1 Laplace operator deﬁned The suggested Laplace operator on two-dimensional surfaces in [6] (also seen in [27], [35]) is the following operator on functions f : T 0 → R, (△f)i = X j:{i,j}∈T1 wij (fj −fi) (1”
Surface Matching via Currents (2005, background): “Given the recent active developments in exterior calculus [22] and current based approaches to curvature estimation [23], we expect the representations to become more sophisticated (perhaps incorporating second order geometric information), and that discretization will continue to get better.”
A combinatorial Yamabe flow in three dimensions (2005, background): “ature which we shall now describe. Combinatorial Laplacians on piecewise linear surfaces are used quite a bit in image processing, for instance [24], [30]. There is a very clear description by Hirani [17] which deﬁnes the Laplace-Beltrami operator on functions deﬁned 11 at the vertices as △fi = 1 |⋆”