Comparison of Various Methods for the Calculation of the Distance   Potential Field
  The distance from a given position toward one or more destinations, exits, and way points is a more or less important input variable in most models of pedestrian dynamics. Except for the special case when there are no obstacles in a concave scenario -- i.e. each position is visible from any other -- the calculation of these distances is a non-trivial task. This isn't that big a problem, as long as the model only demands the distances to be stored in a Static Floor Field also called Potential Field, which never changes throughout the whole simulation. In this case a pre-calculation once before the simulation starts is sufficient. But if one wants to allow changes of the geometry during a simulation run -- imagine doors or the blocking of a corridor due to some hazard -- in the Distance Potential Field, calculation time matters strongly. This contribution gives an overview over existing and new exact and approximate methods to calculate a potential field, analytical investigations for their exactness, and tests of their computation speed. The advantages and drawbacks of the methods are discussed. 
Tobias Kretz, Cornelia B\"onisch, and Peter Vortisch