<p>Script geometry, as a new kind of discrete geometry and calculus, has been introduced by Frank Sommen and his co-authors in recent years. The key idea of the script geometry is to generalise the classical simplicial topology to more general meshes than only simplicial complexes. This generalisation opens new possibilities to develop discrete function theories on a flexible geometrical foundation. Therefore, in this paper, we develop first ideas of using Frank Sommen’s script geometry as a foundation of the finite element exterior calculus in the Clifford setting. Moreover, we also present a categorical perspective on scripts, providing a deeper understanding of connections between the script geometry and the classical simplicial topology.</p>

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Script Geometry: Categorical Perspective and a Connection to Exterior Calculus FEM

  • Paula Cerejeiras,
  • Uwe Kähler,
  • Dmitrii Legatiuk

摘要

Script geometry, as a new kind of discrete geometry and calculus, has been introduced by Frank Sommen and his co-authors in recent years. The key idea of the script geometry is to generalise the classical simplicial topology to more general meshes than only simplicial complexes. This generalisation opens new possibilities to develop discrete function theories on a flexible geometrical foundation. Therefore, in this paper, we develop first ideas of using Frank Sommen’s script geometry as a foundation of the finite element exterior calculus in the Clifford setting. Moreover, we also present a categorical perspective on scripts, providing a deeper understanding of connections between the script geometry and the classical simplicial topology.