The simulation of the topography changing processes requires a method capable to describe geometric deformations over time. To observe the final profile it is primarily important to track the surface over time. The initial surface can be extracted from the initial geometry ( ). During topography simulations the surface velocities in normal direction are calculated at the surface points . To obtain the final profile after the complete process time, , the following problem must be solved:

- Given: and for all and ,
- Required: .

This chapter first gives an overview of different numerical methods for tracking moving boundaries. The pros and cons of these techniques are briefly discussed. Finally the focus is placed on the LS method which is probably the most popular method used in modern topography simulators, especially for three dimensions.

- 3.1 Boundary Evolution Techniques

- 3.2 Solving the Level Set Equation

- 3.3 Approximations to Geometric Variables

- 3.4 Acceleration Techniques

- 3.5 Level Set Data Structures

Otmar Ertl: Numerical Methods for Topography Simulation