The simulation of surface evolution requires the calculation of the surface velocity at every time step. For advanced models, the surface velocity depends on the particle transport. According to the surface kinetics model described in Section 2.3, the surface velocity is assumed to be a function of a certain number of surface rates (2.25). This chapter is devoted to the calculation of these surface rates under the assumption of ballistic particle transport within the feature-scale region, as described by (2.14). Particles entering the feature-scale region through the source plane follow the given arriving flux distribution . Particle reemission, modelled by the reemission probability function (2.15), must also be incorporated. In summary the problem states as follows:

- Given: , for all , and for all .
- Required: (in order to calculate ) for all .

- 5.1 Conventional Approach

- 5.2 Ray Tracing
- 5.2.1 Surface Representation
- 5.2.2 Tangential Disks
- 5.2.3 Particle Traversal
- 5.2.4 Algorithmic Complexity
- 5.2.5 Boundary Conditions
- 5.2.6 Spatial Subdivision
- 5.2.7 Splitting Strategies
- 5.2.8 Neighbor Links Arrays
- 5.2.9 Parallelization
- 5.2.10 Benchmarks

- 5.3 Generation of Random Vectors
- 5.3.1 Power Cosine Distribution
- 5.3.2 Coned Cosine Distribution
- 5.3.3 Direction Vector Calculation
- 5.3.4 Cosine Distribution
- 5.3.5 Direction Vector Sampling Benchmarks

- 5.4 Implementation Details

Otmar Ertl: Numerical Methods for Topography Simulation