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by enriquto
1158 days ago
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This is called "discrete exterior calculus" and you can find it easily. The idea is that k-forms are functions defined on the k-cliques of the graph. TFA is just the 1-dimensional case of this. The 2-dimensional case would be: 0-forms: functions defined on vertices 1-forms: functions defined on edges 2-forms: functions defined on triangles The exterior derivative is defined in a natural way, by taking differences along signed boundaries. In the case of a triangulated surface, the Hodge dual has a nice interpretation via the dual triangulation. |
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