Least-squares approximation of affine mappings for sweep mesh generation: functional analysis and applications

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 least-squares approximatio...

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Bibliographic Details
Published in:Engineering with computers Vol. 29; no. 1; pp. 1 - 15
Main Authors: Roca, Xevi, Sarrate, Josep
Format: Journal Article Publication
Language:English
Published: London Springer-Verlag 01.01.2013
Springer Nature B.V
Subjects:
65 Numerical analysis
65Y Computer aspects of numerical algorithms
Algorithms
Anàlisi numèrica
CAE) and Design
Calculus of Variations and Optimal Control; Optimization
Classical Mechanics
Classificació AMS
Computer Science
Computer-Aided Engineering (CAD
Control
Finite element method Mesh generation Hexahedral elements Sweep Affine mapping
Matemàtiques i estadística
Math. Applications in Chemistry
Mathematical and Computational Engineering
Mètodes en elements finits
Numerical analysis
Original Article
Systems Theory
Àrees temàtiques de la UPC
Finite element method
Hexahedral elements
Sweep
Mesh generation
Affine mapping
ISSN:0177-0667, 1435-5663
Online Access:Get full text
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Summary: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 least-squares approximation of an affine mapping. Several functional formulations have been defined to carry out this least-squares 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.
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ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-012-0260-3