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I'm currently developing MAdLib, a mesh adaptation library which transiently adapts a tetrahedral mesh by local modifications.
Mesh adaptivity can be required in problems involving large displacements or deformations of objects. For instance, in fluid-structure simulations in which the structure is highly deformable, the common node relocation techniques cannot always provide an acceptable mesh. Mesh adaptivity is also a strong tool to concentrate the resources on particular parts of the domain and save resources elsewhere. Error estimators for instance can provide a criterion about an optimal size of the elements, accurate solutions are often required at the vicinity of shocks or discontinuities in a medium, etc.
In the previous examples, the transient aspect is important, as the mesh is supposed to be modified frequently. In such a case, local mesh modifications present significant advantages compared to global remeshing since it allows to modify the mesh frequently, the solution is only transfered locally, the procedure can be performed in parallel, ...
Parallel mesh adaptation procedures, mesh adaptation on geometries (using the geometry module of Gmsh) and anisotropic meshes are also considered.
Further details about MAdLib can be found on the MAdLib web page.
Here are some animations of adapting meshes:
In the framework of my PhD, I am also looking into the modeling of fluid-structure interaction problems. In particular I experiment partitioned methods for applications involving large structural deformations. Possible applications are the modeling of arterial flows or more generally the behavior of thin structures in a flow.
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