A Generalized Graph-Theoretic Mesh Optimization Model
Mezentsev, Andrey A.
Proceedings, 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories, SAND #2004-3765C, pp.255-264, September 19-22 2004
13th International Meshing Roundtable
Willimasburg, Virginia, USA
September 19-22, 2004
Department of Earth Sciences and Engineering, Imperial College, London, UK.
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 Kirchhoffís 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
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