Surface registration is a fundamental problem in computer graphics and computer-aided design. The problem consists in finding a deformation from one surface to another that preserves some properties. For instance, in our inverse engineering context, we aim at finding the best, as isometric as possible, map between an input triangular model, and a large point cloud acquired on the actual mechanical part being processed. Existing solutions are not able to handle very large models with a good level of precision. We propose a method which is accurate and fast. Our solution combines an efficient iterative energy minimization scheme on a hierarchical decomposition of the problem geometry. Our experiments show that we obtain a fast and efficient algorithm compared to the state-of-the art method, while keeping its numerical accuracy.