Matching interior and exterior all-quadrilateral meshes with guaranteed angle bounds

Abstract

This paper presents an extension of our earlier work on quadtree-based all-quadrilateral mesh generation, which generates guaranteed-quality meshes for the interior or exterior domain of any given planar curve. In this paper, we develop an algorithm to match the generated interior and exterior meshes with conformal boundary, preserving the guaranteed angle bounds. In addition, we introduce another automatic and robust approach to preserve sharp features. All the elements in the final mesh are within $$[45^{\circ} - \varepsilon, 135^{\circ} + \varepsilon] (\varepsilon \leq 5^{\circ}),$$ except small sharp angles present in the input geometry. Here, $$\varepsilon$$ is an input parameter. The smaller $$\varepsilon$$ is, the better angle bounds we can get. Finally, we group all the elements into six types, and most elements only need a few flops to construct the element stiffness matrix. This will significantly reduce the computational time during the finite element analysis.