Affordable Access

Publisher Website

Variational method for untangling and optimization of spatial meshes

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Volume
269
Identifiers
DOI: 10.1016/j.cam.2014.03.006
Keywords
  • Variational Mesh Generation
  • Mesh Untangling
  • Barrier Functional
  • Quasi-Isometric Mapping
  • Polyconvexity

Abstract

Abstract A variational method that can provably construct 3D quasi-isometric mappings between domains of a complex shape is introduced. A local maximum principle for polyconvex mesh element distortion measures is formulated. It allows us to control the invertibility and distortion bounds for non-simplicial elements in the minimization process. A simple and efficient technique for construction of boundary orthogonal meshes suggested in Garanzha (2000) is applied to the construction of hexahedral meshes and thick prismatic mesh layers around complex shapes. The mesh untangling technique, which is a generalization of the penalty method suggested in Garanzha and Kaporin (1999), is verified on a wide set of challenging test problems. Another untangling technique based on theoretical ideas from Ivanenko (1997) is implemented and tested. It provably constructs admissible meshes using a finite number of minimization steps. A minimization technique for the mesh distortion functional is described. The approach is based on the global gradient search technique with preconditioning and domain decomposition for local mesh optimization and untangling. Application areas for explicit and implicit minimization methods are evaluated.

There are no comments yet on this publication. Be the first to share your thoughts.

Statistics

Seen <100 times
0 Comments

More articles like this

Optimization of variational methods

on Ocean Engineering Jan 01, 1995

A dynamic variational multiscale method for large...

on Computer Methods in Applied Me... Jan 01, 2006

Variational methods for generating meshes on surfa...

on Journal of Computational Physi... Jan 01, 1986

Untangling of 2D meshes in ALE simulations

on Journal of Computational Physi... Jan 01, 2004
More articles like this..