Solid and physical modeling with chain complexes
Antonıo DiCarlo, Franco Milicchio, Alberto Paoluzzi, Vadim Shapiro · 2007
In this paper we show that the (co)chain complex associated with a decomposition of the computational domain, commonly called a mesh in computational science and engineering, can be represented by a block-bidiagonal matrix that we call the Hasse matrix. Moreover, we show that topology-preserving mesh refinements, produced by the action of (the simplest) Euler operators, can be reduced to multi-linear transformations of the Hasse matrix representing the complex.