An efficient automatic mesh generation algorithm for planar isogeometric analysis using high-order rational Bézier triangles

Isogeometric analysis (IGA) is a numerical method that is receiving increasing attention in the last decade. The main goal of IGA is to closely couple geometric modeling with numerical analysis. To that end, in IGA both components use the same geometric representation, e.g., Bézier and NURBS curves and surfaces. However, in many cases, the geometric representation in a CAD system cannot be directly employed in numerical simulation, as only the boundary of the geometry is parametrized. In these cases, an interior parametrization must be constructed before performing isogeometric analysis. This paper presents an algorithm for generation of unstructured geometrically exact meshes composed of rational Bézier triangles of arbitrary degree, and applies it to plane models described by NURBS curves in a Boundary-Representation (B-Rep) scheme. The proposed algorithm respects input discretization and is capable of generating high quality coarse meshes even when high curvature segments are considered. An efficient high-order smoothing step is employed to avoid tangled elements and to improve element quality. The proposed algorithm attains superior performance when compared to a well-known algorithm in the literature, and performs well in the case of complex geometries. High quality meshes were obtained in all examples analyzed. Furthermore, our implementation is efficient, written in C++, and is available as an open-source software