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A geometric discretization and a simple implementation for variational mesh generation and adaptation.

Authors :
Huang, Weizhang
Kamenski, Lennard
Source :
Journal of Computational Physics. Nov2015, Vol. 301, p322-337. 16p.
Publication Year :
2015

Abstract

We present a simple direct discretization for functionals used in the variational mesh generation and adaptation. Meshing functionals are discretized on simplicial meshes and the Jacobian matrix of the continuous coordinate transformation is approximated by the Jacobian matrices of affine mappings between elements. The advantage of this direct geometric discretization is that it preserves the basic geometric structure of the continuous functional, which is useful in preventing strong decoupling or loss of integral constraints satisfied by the functional. Moreover, the discretized functional is a function of the coordinates of mesh vertices and its derivatives have a simple analytical form, which allows a simple implementation of variational mesh generation and adaptation on computer. Since the variational mesh adaptation is the base for a number of adaptive moving mesh and mesh smoothing methods, the result in this work can be used to develop simple implementations of those methods. Numerical examples are given. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00219991
Volume :
301
Database :
Academic Search Index
Journal :
Journal of Computational Physics
Publication Type :
Academic Journal
Accession number :
110009346
Full Text :
https://doi.org/10.1016/j.jcp.2015.08.032