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3.4.2 Hierarchical Meshes

The initial mesh is coarse. Local refinement is performed by recursive subdivision that follows varying simple patterns. All recursion levels are stored in a tree data structure. Local coarsening of a previously refined area can be performed easily by traversing the tree. Such hierarchical meshes are typically employed for multigrid methods [171] which require changing from coarse meshes to refined meshes and vice versa iteratively. The tradeoff lies in a refinement limited to simple patterns, the higher memory consumption, and the more complex mesh management. The last issue is especially important for moving boundary situations. A carefully chosen tree data structure and a well designed implementation are important to unify mesh updates for all levels of the mesh hierarchy. It can be advantageous to store only one mesh and to rely on fast remeshing techniques for the purposes of adjusting to a moved boundary as well as coarsening and refining.

Peter Fleischmann