Manifolds, tensor analysis, and applications: 2nd edition
Manifolds, tensor analysis, and applications: 2nd edition
Computational Models of Electromagnetic Resonators: Analysis of Edge Element Approximation
SIAM Journal on Numerical Analysis
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Discrete exterior calculus
Discrete & Computational Geometry
FEMSTER: An object-oriented class library of high-order discrete differential forms
ACM Transactions on Mathematical Software (TOMS)
Python for Scientific Computing
Computing in Science and Engineering
deal.II—A general-purpose object-oriented finite element library
ACM Transactions on Mathematical Software (TOMS)
An Adaptive Finite Element Method for the Laplace-Beltrami Operator on Implicitly Defined Surfaces
SIAM Journal on Numerical Analysis
Algebraic multigrid for discrete differential forms
Algebraic multigrid for discrete differential forms
DOLFIN: Automated finite element computing
ACM Transactions on Mathematical Software (TOMS)
Optimal homologous cycles, total unimodularity, and linear programming
Proceedings of the forty-second ACM symposium on Theory of computing
A generalization for stable mixed finite elements
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
The NumPy Array: A Structure for Efficient Numerical Computation
Computing in Science and Engineering
Statistical ranking and combinatorial Hodge theory
Mathematical Programming: Series A and B - Special Issue on "Optimization and Machine learning"; Alexandre d’Aspremont • Francis Bach • Inderjit S. Dhillon • Bin Yu
The least spanning area of a knot and the optimal bounding chain problem
Proceedings of the twenty-seventh annual symposium on Computational geometry
Foundations of Computational Mathematics
Dual formulations of mixed finite element methods with applications
Computer-Aided Design
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book
Technical note: Delaunay Hodge star
Computer-Aided Design
Technical note: Delaunay Hodge star
Computer-Aided Design
A programming interface to the Riemannian manifold in a finite element environment
Journal of Computational and Applied Mathematics
Computational Geometry: Theory and Applications
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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.