In FEM simulation, adjusting the mesh by deformation, e.g. by redistributing the grid points, has the advantage over mesh adaptation procedures using hanging nodes to preserve the topology of the underlying mesh. This is essential for high performance computing aspets due to a better use of caches and internal pipelining. Starting with locally structured grids, this allows hardware-oriented and therefore fast codes featuring high flexibility in mesh geometry at the same time. 
In this talk we will present a new deformation method for FEM based on Liao`s method. In contrast to common deformation methods, our method does not require the solution of nonlinear PDEs, but only to solve a Poisson problem and a decoupled system of ODEs. It is applicable to arbitrary meshes, and the desired local mesh size can be precisely achieved. We tackle the theoretical background of this method and focus on its numerical analysis. Furthermore, practical aspects and the realisation in the new FEM pacakage FEAST are considered.