Due to the bad scaling behavior, the conventional approach is limited to small problem sizes. For large three-dimensional problems, where the number of surface discretization elements easily reaches several million, the calculation of the particle transport is very time and memory intensive without further simplifications.

One possible way to reduce the computational effort is the choice of a coarser discretization at regions with low curvature, as proposed in [41]. However, this approach does not only reduce the number of surface elements, it also reduces the spatial resolution of the flux distribution. This is a problem, since even on plane regions of the surface the flux can change abruptly due to shadowing. Hence, the size of the discretization elements should be in the order of the grid spacing used for the LS method.

Another drawback is the non-trivial and error-prone calculation of the matrix elements. Especially for more complicated basis functions, the evaluation of (5.7) is cumbersome. In [19] a simpler technique to calculate the system matrix elements based on a MC approach was investigated; however, this has not been proven to be very practical.

Otmar Ertl: Numerical Methods for Topography Simulation