Achieving finite element mesh quality via optimization of the jacobian matrix norm and associated qu
By Patrick M. Knupp. 2000
363 citations recorded by the source corpus.
Structured mesh quality optimization methods are extended to optimization of unstructured triangular, quadrilateral, and mixed finite element meshes. N"ew interpretations of well-known nodally-bssed objective functions are made possible using matrices and matrix norms. The matrix perspective also suggests several new objective functions. Particularly significant is the interpretation of the Oddy metric and the Smoothness objective functions in terms of the condition number of the metric tensor and Jacobian matrix, respectively. Objective functions are grouped according to dimensionality to form weighted combinations. A simple unconstrained local optimum is computed using a modiiied N-ewton iteration. The optimization approach was implemented in the CUBIT mesh generation code and tested on several problems. Results were compared against several standard element-based quaIity measures to demonstrate that good mesh quality can be achieved with nodally-based objective functions.
Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/e23c8848c9c7699c955d20222316a4bba003b76d
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In Computational Mechanics
In Computer Graphics and Computer-Aided Design
Citations in the corpus
- An algebraic method for smoothing surface triangulations on a local parametric space (2006, background): “As it is shown in [3], [10], and [11] we can derive optimization functions from algebraic quality measures of the elements belonging to a local mesh.”
- Algebraic Mesh Quality Metrics (2001, neutral): “The work reported here is an extension of the ideas of the author presented in [12], [13], [7], [14], and [15] in which the use of matrices, norms, and the condition number for mesh quality measures were introduced.”