A Primal-to-Primal Discretization of Exterior Calculus on Polygonal Meshes

Ptackova, Lenka; Velho, Luiz

A Primal-to-Primal Discretization of Exterior Calculus on Polygonal Meshes

Files

007-008.pdf (473.24 KB)

Date

2017

Authors

Ptackova, Lenka
Velho, Luiz

Publisher

The Eurographics Association

Abstract

Discrete exterior calculus (DEC) offers a coordinate-free discretization of exterior calculus especially suited for computations on curved spaces. We present an extended version of DEC on surface meshes formed by general polygons that bypasses the construction of any dual mesh and the need for combinatorial subdivisions. At its core, our approach introduces a polygonal wedge product that is compatible with the discrete exterior derivative in the sense that it obeys the Leibniz rule. Based on this wedge product, we derive a novel primal-primal Hodge star operator, which then leads to a discrete version of the contraction operator. We show preliminary results indicating the numerical convergence of our discretization to each one of these operators.

        @inproceedings{10.2312:sgp.20171204
,
booktitle = {Symposium on Geometry Processing 2017- Posters
},
editor = {Jakob Andreas Bærentzen and Klaus Hildebrandt
},
title = {{A Primal-to-Primal Discretization of Exterior Calculus on Polygonal Meshes
}},
author = {Ptackova, Lenka and 
Velho, Luiz
},
year = {2017
},
publisher = {The Eurographics Association
},
ISSN = {1727-8384
},
ISBN = {978-3-03868-047-5
},
DOI = {10.2312/sgp.20171204
}
}