A new least-squares approximation of affine mappings for sweep algorithms

Abstract

This paper presents a new algorithm to generate hexahedral meshes in extrusion geometries. Several algorithms have been devised to generate hexahedral meshes by projecting the cap surfaces along a sweep path. In all of these algorithms the crucial step is the placement of the inner layer of nodes. That is, the projection of the source surface mesh along the sweep path. From the computational point of view, sweep methods based on a least-squares approximation of an affine mapping are the fastest alternative to compute these projections. Several functionals have been introduced to perform the least-squares approximation. However, for very simple and typical geometrical configurations they may generate low-quality projected meshes. For instance, they may induce skewness and flattening effects on the projected discretizations. In addition, for these configurations the minimization of these functionals may lead to a set of normal equations with singular system matrix. In this work we analyze previously defined functionals. Based on this analysis we propose a new functional and show that its minimization overcomes these drawbacks. Finally, we present several examples to assess the properties of the proposed functional.