A variational approach to optimal meshes |
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Authors: | M Rumpf |
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Institution: | Institut für Angewandte Mathematik,
Hermann-Herder-Stra?e 10, 79104 Freiburg, Germany;
e-mail: mart@mathematik.uni-freiburg.de, DE
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Abstract: | Summary.
A variational approach for the optimization of triangular or
tetrahedral
meshes is presented. Starting from some very basic assumptions we will
rigorously demonstrate that the functional controlling optimality is of
a certain type related to energy functionals in non linear elasticity.
It will be proved that these functionals attain their minima over
admissible sets of mesh deformations which respect boundary conditions.
In addition the injectivity of the deformed mesh is discussed.
Thereby it is possible to construct suitable meshes for various numerical
applications.
Received
March 14, 1994 / Revised version received August 8, 1994 |
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Keywords: | Mathematics Subject Classification (1991): 73C50 65K10 65M50 65N50 49M07 |
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