Geometric Computing with Chain Complexes: Design and Features of a Julia Package (1710.07819v2)

Abstract: Geometric computing with chain complexes allows for the computation of the whole chain of linear spaces and (co)boundary operators generated by a space decomposition into a cell complex. The space decomposition is stored and handled with LAR (Linear Algebraic Representation), i.e. with sparse integer arrays, and allows for using cells of a very general type, even non convex and with internal holes. In this paper we discuss the features and the merits of this approach, and describe the goals and the implementation of a software package aiming at providing for simple and efficient computational support of geometric computing with any kind of meshes, using linear algebra tools with sparse matrices. The library is being written in Julia, the novel efficient and parallel language for scientific computing. This software, that is being ported on hybrid architectures (CPU+GPU) of last generation, is yet under development.