Abstract
This paper is concerned with the implementation of variational arbitrary
Lagrangian-Eulerian formulations, also known as variational r-adaption
methods. These methods seek to minimize the energy function with
respect to the finite-element mesh over the reference configuration
of the body. We propose a solution strategy based on a viscous regularization
of the configurational forces. This procedure eliminates the ill-posedness
of the problem without changing its solutions, i.e. the minimizers
of the regularized problems are also minimizers of the original functional.
We also develop strategies for optimizing the triangulation, or mesh
connectivity, and for allowing nodes to migrate in and out of the
boundary of the domain. Selected numerical examples demonstrate the
robustness of the solution procedures and their ability to produce
highly anisotropic mesh refinement in regions of high energy density.
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