  The Continuum Dislocation Dynamics (CDD) theory and the Discrete Dislocation
Dynamics (DDD) method are compared based on concise mathematical formulations
of the coarse graining of discrete data. A numerical tool for converting from a
discrete to a continuum representation of a given dislocation configuration is
developed, which allows to directly compare both simulation approaches based on
continuum quantities (e.g. scalar density, geometrically necessary densities,
mean curvature). Investigating the evolution of selected dislocation
configurations within analytically given velocity fields for both DDD and CDD
reveals that CDD contains a surprising number of important microstructural
details.
