Quadrilateral Mesh Generation with Deferred Constraint Insertion

Abstract

In this paper, we present a new method for quadrilateral mesh generation in complex 2D domains, based on deferred constraint insertion. Our method is especially designed to handle complex geological cross-sections and multi-fractured media. We first introduce a new algorithm for triangular mesh generation: starting with a initial mesh, in general simple and regular, we adaptively modify it in order to accommodate each constraint, despite its complexity. We then propose a set of heuristics to convert the achieved triangular mesh into a quadrilateral one, pursuing the alignment of elements along constraints. As a result, we achieve a very stable, efficient, good-quality, and automated mesh generator. We demonstrate the robustness of our proposal by showing resulting triangular and quadrilateral meshes for a set of geological domains with complex line constraints.