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CivilComp Proceedings
ISSN 17593433 CCP: 94
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru and M.L. Romero
Paper 57
Advanced Numerical Methods in Mesh Generation and Mesh Adaptation A. Agouzal^{1}, A. Danilov^{2}, K. Lipnikov^{3} and Yu. Vassilevski^{2}
^{1}University of Lyon 1, France
A. Agouzal, A. Danilov, K. Lipnikov, Yu. Vassilevski, "Advanced Numerical Methods in Mesh Generation and Mesh Adaptation", in B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru, M.L. Romero, (Editors), "Proceedings of the Seventh International Conference on Engineering Computational Technology", CivilComp Press, Stirlingshire, UK, Paper 57, 2010. doi:10.4203/ccp.94.57
Keywords: advancing front technique, Delaunay triangulation, mesh adaptation, tensor metric, quasioptimal mesh.
Summary
Numerical solution of partial differential equations requires appropriate
meshes, efficient solvers and robust and reliable error estimates. Generation
of highquality meshes for complex engineering models is a nontrivial task.
This task is made more difficult when the mesh has to be adapted to a problem
solution. This article is focused on a synergistic approach to the mesh
generation and mesh adaptation, where best properties of various mesh
generation methods are combined to build efficiently simplicial meshes.
First, the advancing front technique (AFT) is combined with the incremental Delaunay triangulation (DT) to build an initial mesh [1]. Second, the metricbased mesh adaptation (MBA) method [2] is employed to improve quality of the generated mesh and, or to adapt it to a problem solution. We demonstrate with numerical experiments that combination of all three methods is required for robust meshing of complex engineering models. The key to successful mesh generation is the highquality of the triangles in the initial front. We use a blackbox technique to improve surface meshes exported from an unattainable CAD system. The initial surface mesh is refined into a shaperegular triangulation which approximates the boundary with the same accuracy as the CAD mesh. The DT method adds robustness to the AFT. The resulting mesh is topologically correct but may contain a few slivers. The MBA uses seven local operations to modify the mesh topology. It improves significantly the mesh quality. The MBA method is also used to adapt the mesh to a problem solution to minimize computational resources required for solving the problem. The MBA has a solid theoretical background [2]. In the first two experiments, we consider the convectiondiffusion and elasticity problems. We demonstrate the optimal reduction rate of the discretization error on a sequence of adaptive strongly anisotropic meshes. The key element of the MBA method is construction of a tensor metric from hierarchical edgebased error estimates. We conclude that the quasioptimal mesh must be quasiuniform in this metric. All numerical experiments are based on the publicly available Ani3D package [3], the collection of advanced numerical instruments. References
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