Manifold Evolution with Tangential Redistribution of Points

In this paper we propose several techniques for tangential redistribution of points on evolving surfaces. This is an important issue in numerical approximation of any Lagrangian evolution model, since the quality of the mesh has a significant impact on the result of the computation. We explain the volume-oriented and length-oriented tangential redistribution methods in a general setting of an m-dimensional manifold evolving in an n-dimensional manifold. Then, we apply the proposed techniques to several manifold evolution problems. We explain the numerical approximation of the models and present experiments illustrating the performance of our redistribution techniques.