  We present simulations of flux-gradient-driven superconducting rigid vortices
interacting with square and triangular arrays of columnar pinning sites in an
increasing external magnetic field. These simulations allow us to
quantitatively relate spatio-temporal microscopic information of the vortex
lattice with typically measured macroscopic quantities, such as the
magnetization $M(H)$. The flux lattice does not become completely commensurate
with the pinning sites throughout the sample at the magnetization matching
peaks, but forms a commensurate lattice in a region close to the edge of the
sample. Matching fields related to unstable vortex configurations do not
produce peaks in $M(H)$. We observe a variety of evolving complex flux
profiles, including flat terraces or plateaus separated by winding
current-carrying strings and, near the peaks in $M(H)$, plateaus only in
certain regions, which move through the sample as the field increases.
