Sixth Mississippi State Conference on Differential Equations and Computational Simulations.
Electron. J. Diff. Eqns., Conference 15 (2007), pp. 141-151.

Issues in adaptive mesh refinement implementation

Noureddine Hannoun, Vasilios Alexiades

Physical phenomena often involve discontinuities and/or localized high-gradient areas. The numerical simulation of these problems and conventional techniques (Finite Elements, Finite Volumes, Finite Differences, and Spectral Methods) with a uniform grid is inefficient when high accuracy is required. Adaptive Mesh Refinement (AMR) is a technique that allows local refinement of the grid. In this presentation, we describe a typical AMR technique and address implementation and algorithmic issues. Triangular unstructured grids and a regular 1 to 4 refinement are considered.

Published February 28, 2007.
Math Subject Classifications: 68U99, 65M50, 65Y20.
Key Words: Adaptive mesh refinement; data structure; computational method; object oriented programming; conservation laws.

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Noureddine Hannoun
Department of Mathematics
University of Tennessee
Knoxville, TN 37996-1300, USA
Vasilios Alexiades
Department of Mathematics
University of Tennessee, Knoxville, TN 37996, USA.
and Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA.

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