Least-squares approximation of affine mappings for sweep mesh generation. Functional analysis and applications

Author (s): Roca, X. and Sarrate, J.
Journal: Engineering with Computers

Volume: 29, Issue 1
Pages: 1 – 15
Date: 2013

Sweep methods are one of the most robust techniques to generate hexahedral meshes in extrusion volumes.
The main issue in sweep algorithms is the projection of cap surface meshes along the sweep path. The most competitive technique to determine this projection is to find a leastsquares approximation of an affine mapping. Several functional
formulations have been defined to carry out this leastsquares approximation. However, these functionals generate
unacceptable meshes for several common geometries in CAD models. In this paper we present a new comparative
analysis between these classical functional formulations and a new functional presented by the authors. In particular, we
prove under which conditions the minimization of the analyzed functionals leads to a full rank linear system. Moreover,
we also prove the equivalences between these formulations. These allow us to point out the advantages of the
proposed functional. Finally, from this analysis we outline an automatic algorithm to compute the nodes location in the
inner layers.

Keywords Finite element method, mesh generation, hexahedral elements, sweep, affine mapping



  author={Roca, Xevi and Sarrate, Josep},
  title={Least-squares approximation of affine mappings for sweep mesh generation: functional analysis and applications},
  journal={Engineering with Computers},