What are the available algorithms by which one can handle large mesh deformations? The problem I have at hand is a dynamic one and involves large deformations of boundaries, which then requires the interior grid points to adjust accordingly in such a manner that it preserves the quality of the deformed mesh to a certain extent. Does anybody have any experience about how to take care of this issue?
“A multiobjective mesh optimization framework for mesh quality
improvement and mesh untangling”, Jibum Kim, Thap Panitanarak, and Suzanne M. Shontz, Int. J. Numer. Meth. Engng 2013; 94:20–42. Maybe this paper can help you.
It sounds like you want to adjust the distances between the nodes of the mesh, and one key point here is, these distances need not to be computed from the coordinates (i.e., using the obvious metric of R^n). Instead you can keep the coordinates fixed and adjust the distances between the nodes by picking another metric tensor. On a practical level you just need to give the material parameters of the constitutive laws to match with the desired distances. See the following papers in the list of my publications:
Applications of manifolds: mesh generation,
Parametric Models in Quasi-Static Electromagnetics,
How can we deal with moving objects on a fixed mesh?
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