Hamilton--Jacobi Equations on a Manifold and Applications to Grid Generation or Refinement
Ph. Hoch, Michel Rascle · SIAM Journal on Scientific Computing · 2002
In this paper, we consider Hamilton--Jacobi equations on a manifold, typically on the graph of some previously computed function z(x,y), and we show how the corresponding level set method allows us to generate and/or to refine a mesh in regions where this function z has large derivatives. Such as it is, the method needs to be strongly improved and accelerated, but the principle is awfully natural, and in principle the method is fully automatic. Similar ideas are also useful in image processing, in particular for the active contours method.