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Center for Nonlinear Studies |
A 'target-matrix' paradigm for improving mesh quality by node repositioning via optimization is formulated in which target matrices describe the desired Jacobian matrix at mesh sample points. Attention is devoted to basic defnitions and properties of mesh-based matrices, local and non-local quality metrics, and objective functions based on the power-mean. Local metrics having barriers are precisely defined and the behavior of nonlocal metrics based on local metrics with barriers is studied. Hierarchical nonlocal metrics are given which measure mesh quality in terms of element or submesh quality. Properties of the power mean are shown to result in desirable properties for nonlocal metrics. Numerical examples illustrate the behavior of various types of objective functions to show, for example, the difference between hierarchical and non-hierarchical forms.
Host: Mikhail Shashkov