PyDEC: Software and algorithms for discretization of exterior calculus

Nathan Bell, Anil N. Hirani

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number3
JournalACM Transactions on Mathematical Software
Issue number1
StatePublished - Nov 2012


  • Boundary operator
  • Chain
  • Coboundary operator
  • Cochain
  • Computational topology
  • Cubical complex
  • Discrete exterior calculus
  • Finite element exterior calculus
  • Simplicial complex
  • Vietoris-Rips complex
  • Whitney form

ASJC Scopus subject areas

  • Software
  • Applied Mathematics


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