  A simple model for simulating the current dynamics and the magnetic
properties of superconductors is presented. Short simulation times are achieved
by solving the differential form of Maxwell's equations inside the sample,
whereas integration is only required at the surface to meet the exact boundary
conditions. The procedure reveals the time and position dependence of the
current density and the magnetic induction (B) making it very convenient to
apply field dependent material parameters for the simulation of magnetization
loops, relaxation measurements, etc. Two examples, which are important for
standard magnetometry experiments, are discussed. Firstly, we prove that
evaluating the critical current density (J_c) from experiment by applying
Bean's model reveals almost the exact J_c(B) behavior, if the evaluation is
corrected by a simple numerical expression. Secondly, we show that the
superconducting volume fraction of a sample can be directly determined from
magnetization loops by carefully comparing experiment and simulation in the
field range, where the current loops are differently oriented within the
sample.
