We propose a new global light simulation method for diffuse (or moderately glossy) scenes comprising highly tesselated models with simple topology (e.g., scanned meshes). By using the topological coherence of the surface, we show how to extend a classic Finite Element method called the Master Element: We generalize this method to efficiently handle tessellated models by using mesh parameterization and mesh extrapolation techniques. In addition, we propose a high-order and hierarchical extension of the Master Element method. Our method computes a compact representation of vector irradiance, represented by high-order wavelet bases. For totally diffuse scenes, the so-computed vector irradiance maps can be transformed into light maps. For moderatly glossy scenes, approximated view-dependent lighting can be computed and displayed in real-time by the GPU from the vector irradiance maps. Using our methods, view-dependent solutions for scenes with over one million polygons are computed in minutes and displayed in real time. As with clustering methods, the time complexity of the method is independent on the number of polygons. By efficiently capturing the lighting signal at a suitable scale, the method is made independent of the geometric discretization and solely depends on the lighting complexity. We demonstrate our method in various settings, with both sharp and soft shadows accurately represented by our hierarchical function basis.