• Corpus ID: 23205268

Discrete Topology-Revealing Vector Fields on Simplicial Surfaces with Boundary

@inproceedings{Poelke2017DiscreteTV,
  title={Discrete Topology-Revealing Vector Fields on Simplicial Surfaces with Boundary},
  author={Konstantin Poelke and Konrad Polthier},
  year={2017}
}
We present a discrete Hodge-Morrey-Friedrichs decomposition for piecewise constant vector fields on simplicial surfaces with boundary which is structurally consistent with the smooth theory. In particular, it preserves a deep linkage between metric properties of the spaces of harmonic Dirichlet and Neumann fields and the topology of the underlying geometry, which reveals itself as a discrete de Rham theorem and a certain angle between Dirichlet and Neumann fields. We illustrate and discuss this… 

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