  As the number of processor cores on supercomputers becomes larger and larger,
algorithms with high degree of parallelism attract more attention. In this
work, we propose a novel space-time coupled algorithm for solving an inverse
problem associated with the time-dependent convection-diffusion equation in
three dimensions. We introduce a mixed finite element/finite difference method
and a one-level and a two-level space-time parallel domain decomposition
preconditioner for the Karush-Kuhn-Tucker (KKT) system induced from
reformulating the inverse problem as an output least-squares optimization
problem in the space-time domain. The new full space approach eliminates the
sequential steps of the optimization outer loop and the inner forward and
backward time marching processes, thus achieves high degree of parallelism.
Numerical experiments validate that this approach is effective and robust for
recovering unsteady moving sources. We report strong scalability results
obtained on a supercomputer with more than 1,000 processors.

Numerical Analysis;Optimization and Control