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We describe algorithms for finding harmonic cochains, an essential ingredient for solving elliptic partial differential equations in exterior calculus.
Elements of Algebraic Topology
Munkres, J. R · 1984
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Manifolds, Tensor Analysis, and Applications
Abraham, R., Marsden, J. E., and Ratiu, T · 1988
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Hodge Decomposition—a Method for Solving Boundary Value Problems
Schwarz, G · 1995
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Numerical methods for least squares problems
Björck, A · 1996
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Topological persistence and simplification
Edelsbrunner, H., Letscher, D., and Zomorodian, A · 2002
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Desbrun, M., Kanso, E., and Tong, Y · 2008
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Cohomology of harmonic forms on riemannian manifolds with boundary
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Computational Conformal Geometry
Gu, X. D., and Yau, S.-T · 2008
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Finite element exterior calculus: from Hodge theory to numerical stability
Arnold, D. N., Falk, R. S., and Winther, R · 2010
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PyDEC: Algorithms and software for Discretization of Exterior Calculus, March 2011
Bell, N., and Hirani, A. N · 2011
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Cohomologous harmonic cochains, 2011
Hirani, A. N., Kalyanaraman, K., Wang, H., and Watts, S · 2011
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