Anisotropic mesh adaption by metric-driven optimization

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We describe a Gauss-Seidel algorithm for optimizing a three-dimensional unstructured grid so as to conform to a given metric. The objective function for the optimization process is based on the maximum value of an elemental residual measuring the distance of any simplex in the grid to the local target metric. We analyse different possible choices for the objective function, and we highlight their relative merits and deficiencies. Alternative strategies for conducting the optimization are compared and contrasted in terms of resulting grid quality and computational costs. Numerical simulations are used for demonstrating the features of the proposed methodology, and for studying some of its characteristics.

Original languageEnglish
Pages (from-to)597-639
Number of pages43
JournalInternational Journal for Numerical Methods in Engineering
Issue number3
StatePublished - 21 May 2004
Externally publishedYes


  • Anisotropic grids
  • Mesh adaptivity
  • Mesh optimization
  • Riemannian metric
  • Unstructured grids


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