An object-oriented framework for finite element analysis based on a compact topological data structure

• We introduce a new finite element framework (TopFEM) based on the topological data structure (TopS).
• We demonstrate the use of this framework for a variety of finite element problems in efficient, but generic fashion and compare the new software to those of the literature.
• Examples are given to show the relevance of the new framework in the context of fragmentation and topology optimization simulations.

This paper describes an ongoing work in the development of a finite element analysis system, called TopFEM, based on the compact topological data structure, TopS [1] and [2]. This new framework was written to take advantage of the topological data structure together with object-oriented programming concepts to handle a variety of finite element problems, spanning from fracture mechanics to topology optimization, in an efficient, but generic fashion. The class organization of the TopFEM system is described and discussed within the context of other frameworks in the literature that share similar ideas, such as GetFEM++, deal.II, FEMOOP and OpenSees. Numerical examples are given to illustrate the capabilities of TopS attached to a finite element framework in the context of fracture mechanics and to establish a benchmark with other implementations that do not make use of a topological data structure.