  If expanding and contracting regions coexist in the universe, the speed of
the cosmic volume expansion can be accelerated. We construct simple
inhomogeneous dust-filled universe models in which the speed of the cosmic
volume expansion is accelerated for finite periods. These models are
constructed by removing spherical domains from the Einstein-de Sitter universe
and filling each domain with a Lemaitre-Tolman-Bondi dust sphere possessing the
same gravitational mass as the removed region. This represents an exact
solution of the Einstein equations. We find that acceleration of the cosmic
volume expansion is realized in some cases when the size of the contracting
region is comparable to the horizon radius of the Einstein-de Sitter universe
though this model is very different from the universe observed today. This
result implies that non-linear general relativistic effects of inhomogeneities
are very important to realize the acceleration of the cosmic volume expansion.
