  A classical reduced order model for dynamical problems involves spatial
reduction of the problem size. However, temporal reduction accompanied by the
spatial reduction can further reduce the problem size without losing accuracy
much, which results in a considerably more speed-up than the spatial reduction
only. Recently, a novel space-time reduced order model for dynamical problems
has been developed, where the space-time reduced order model shows an order of
a hundred speed-up with a relative error of less than 0.1% for small academic
problems. However, in order for the method to be applicable to a large-scale
problem, an efficient space-time reduced basis construction algorithm needs to
be developed. We present incremental space-time reduced basis construction
algorithm. The incremental algorithm is fully parallel and scalable.
Additionally, the block structure in the space-time reduced basis is exploited,
which enables the avoidance of constructing the reduced space-time basis. These
novel techniques are applied to a large-scale particle transport simulation
with million and billion degrees of freedom. The numerical example shows that
the algorithm is scalable and practical. Also, it achieves a tremendous
speed-up, maintaining a good accuracy. Finally, error bounds for space-only and
space-time reduced order models are derived.
