A Generalized Graph-Theoretic Mesh Optimization Model

Proceedings, 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories, SAND #2004-3765C, pp.255-264, September 19-22 2004

MESHING
RESEARCH
CORNER

13th International Meshing Roundtable
Willimasburg, Virginia, USA
September 19-22, 2004

Department of Earth Sciences and Engineering, Imperial College, London, UK.
A.Mezentsev@imperial.ac.uk

Abstract
This paper presents a generic approach to mesh global optimization via node movement, based on a discrete graph-theoretic model. Mesh is considered as an electric system with lumped parameters, governed by the Kirchhoff’s voltage and circuit laws. Each mesh element is treated as a multi-pole electric component, relating input electric potentials to the output via a transfer function. We automatically derive an element transfer function and finally a mesh optimization model using a formal analysis of the coefficients couplings in the finite element stiffness matrix, similar to the method, used in Algebraic Multigrid. Our mesh model is a transient dynamic system and proposed optimization can be also used for mesh deformation problems. We will show that new method works well for realistic 3D meshes and provide a number of mesh optimization examples and details of our implementation.

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