General topography simulations require the treatment of different material regions (see Section 2.1). Etch processes especially require the distinction of different material regions, such as a mask and a substrate, to which different etch rates have to be applied. Hence, the geometric information of material regions is necessary during time evolution. Usually the initial geometry is given as a triangulated mesh, where each element is assigned to a certain material. In the case of etching, this irregular grid must be accessed many times to query the material region of surface points in order to calculate the correct surface velocities. Therefore, if search trees are used, for which queries are of logarithmic complexity, a linearithmic algorithm for time evolution can be expected. If consecutive deposition and etching processes must be simulated, a costly and challenging modification of the irregular mesh is necessary after each processing step.
Instead of using an irregular mesh for the material regions and a regular grid for the LS method simultaneously, multiple LS functions can be used instead. The initial geometric information is simply mapped from the irregular mesh to the regular grid by means of additional LS functions. In the following sections a multi-LS technique using the sparse field method and the H-RLE data structure is described. With the ability to resolve the material-dependent surface velocities with sub-time-step accuracy, a more accurate final profile is obtained, especially in the presence of thin layers or large etch rate ratios.