A simple and efficient mesh cutting algorithm and software library based on many-to-many relations

Abstract

In this paper, we introduce a new open-source self-contained software library to carry out edge cut based remeshing on a simplicial 3-complex. The result is very concise, highly performant (more than $130\times 10^6$ tetrahedra are cut in less than one minute) and can be used for most remeshing tasks. Tasks performed by the algorithm are (i) mesh carving by means of implicit surfaces, (ii) mesh cutting to form a crack and (iii) mesh cutting/carving by a facet mesh and (iv) adaptive remeshing. Source code for algorithms and examples is made available. In the context of a framework based on generalized elements, where all boundary conditions, constraints and traditional finite elements are treated as one, adaptive capabilities are essential in such a framework. This paper presents a lightweight and robust approach to solve a classical problem. Technical intricacies related to robust remeshing (coarsening and refining) can be especially daunting and are here decoupled from the mesh operations. Extraneous themes to be addressed are the mapping of essential and natural conditions, degrees-of-freedom at nodes and internal to the elements, mapping of history variables, etc. We therefore propose and describe in detail a new approach, which is both general and flexible. Six verification examples are presented, that illustrate the use of the library. In addition, a worked example describing the library usage is presented.