research-article

PyDEC: Software and Algorithms for Discretization of Exterior Calculus

Authors:

Anil N. HiraniAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 39, Issue 1

Article No.: 3, Pages 1 - 41

https://doi.org/10.1145/2382585.2382588

Published: 01 November 2012 Publication History

Abstract

This article describes the algorithms, features, and implementation of PyDEC, a Python library for computations related to the discretization of exterior calculus. PyDEC facilitates inquiry into both physical problems on manifolds as well as purely topological problems on abstract complexes. We describe efficient algorithms for constructing the operators and objects that arise in discrete exterior calculus, lowest-order finite element exterior calculus, and in related topological problems. Our algorithms are formulated in terms of high-level matrix operations which extend to arbitrary dimension. As a result, our implementations map well to the facilities of numerical libraries such as NumPy and SciPy. The availability of such libraries makes Python suitable for prototyping numerical methods. We demonstrate how PyDEC is used to solve physical and topological problems through several concise examples.

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Mönkölä SRäbinä JSaksa TRossi T(2025) -dimensional discrete exterior discretization of a general wave model in Minkowski spacetime Results in Applied Mathematics10.1016/j.rinam.2024.10052825(100528)Online publication date: Mar-2025
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Saksa T(2025)Comparison of finite element and discrete exterior calculus in computation of time-harmonic wave propagation with controllabilityJournal of Computational and Applied Mathematics10.1016/j.cam.2024.116154457(116154)Online publication date: Mar-2025
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PyDEC: Software and Algorithms for Discretization of Exterior Calculus

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cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 39, Issue 1

November 2012

162 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/2382585

Issue’s Table of Contents

Copyright © 2012 ACM.

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Publication History

Published: 01 November 2012

Accepted: 01 February 2012

Revised: 01 February 2012

Received: 01 March 2011

Published in TOMS Volume 39, Issue 1

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Cited By

Mönkölä SRäbinä JSaksa TRossi T(2025) -dimensional discrete exterior discretization of a general wave model in Minkowski spacetime Results in Applied Mathematics10.1016/j.rinam.2024.10052825(100528)Online publication date: Mar-2025
https://doi.org/10.1016/j.rinam.2024.100528
Saksa T(2025)Comparison of finite element and discrete exterior calculus in computation of time-harmonic wave propagation with controllabilityJournal of Computational and Applied Mathematics10.1016/j.cam.2024.116154457(116154)Online publication date: Mar-2025
https://doi.org/10.1016/j.cam.2024.116154
Wang MJagad PHirani ASamtaney R(2023)Discrete exterior calculus discretization of two-phase incompressible Navier-Stokes equations with a conservative phase field methodJournal of Computational Physics10.1016/j.jcp.2023.112245488(112245)Online publication date: Sep-2023
https://doi.org/10.1016/j.jcp.2023.112245
Hirani AKalyanaraman KWang HWatts S(2023)Computing discrete harmonic differential forms in a given cohomology class using finite element exterior calculusComputational Geometry: Theory and Applications10.1016/j.comgeo.2022.101937109:COnline publication date: 1-Feb-2023
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Boom PSeepujak AKosmas OMargetts LJivkov A(2022)Parallelized Discrete Exterior Calculus for Three-Dimensional Elliptic ProblemsComputer Physics Communications10.1016/j.cpc.2022.108456(108456)Online publication date: Jul-2022
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Mönkölä SRäty J(2022)Discrete exterior calculus for photonic crystal waveguidesInternational Journal for Numerical Methods in Engineering10.1002/nme.7144124:5(1035-1054)Online publication date: 21-Nov-2022
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