Automatic sizing functions for unstructured surface mesh generation

Abstract

Summary Accurate sizing functions are crucial for efficient generation of high‐quality meshes, but to define the sizing function is often the bottleneck in complicated mesh generation tasks because of the tedious user interaction involved. We present a novel algorithm to automatically create high‐quality sizing functions for surface mesh generation. First, the tessellation of a Computer Aided Design (CAD) model is taken as the background mesh, in which an initial sizing function is defined by considering geometrical factors and user‐specified parameters. Then, a convex nonlinear programming problem is formulated and solved efficiently to obtain a smoothed sizing function that corresponds to a mesh satisfying necessary gradient constraint conditions and containing a significantly reduced element number. Finally, this sizing function is applied in an advancing front mesher. With the aid of a walk‐through algorithm, an efficient sizing‐value query scheme is developed. Meshing experiments of some very complicated geometry models are presented to demonstrate that the proposed sizing‐function approach enables accurate and fully automatic surface mesh generation. Copyright © 2016 John Wiley & Sons, Ltd.

Sizing Function Based on Machine Learning for Unstructured Mesh Generation

“…The time cost of defining sources may be affordable for simple configurations, but for complicated models, the interactive process that defines these sources is time-consuming and error-prone. Recently, an automatic sizing function defined at unstructured background mesh is proposed in [2,3]. This kind of algorithm starts from an initial mesh of the geometry model, in which initial element scales are defined by considering geometrical factors at mesh boundaries and several user-specified parameters.…”

Scalable generation of large-scale unstructured meshes by a novel domain decomposition approach

“…The element sizing function considered in this study is defined by a background mesh and many grid sources [19,20]. This sizing function can be roughly coarsened by scaling up the sizing values defined on background nodes and grid sources.…”

“…This sizing function can be roughly coarsened by scaling up the sizing values defined on background nodes and grid sources. In the region where geometrical proximity features are prominent [19], the scaled sizing values may be too large so that the resulting background mesh for domain decom-position contains badly shaped elements in this region. This is not an issue in practice because proximity features only have impact on a small fraction of elements, and the proposed mesh simplification approach can tolerate a background mesh composed of a certain percentage of badly shaped elements.…”

“…The combustion model contains plenty of small geometry features (see Fig. 11), and the distributions of element scales adapted to these features are computed by a fully automatic approach proposed in [19].…”

Tree-based Control Space Structures for Discrete Metric Sources in 3D Meshing

“…A separate problem in this second approach is how to store, retrieve, and process metric information for this field. The auxiliary structures dedicated to this purpose may have the form of a Cartesian mesh (either homogeneous [21] or adapted [3]), background mesh [7,19,20,23], or quadtree/octree [18,22,23]. Recently, the application of a kd-tree was also proposed by the authors of [16].…”