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

Two-level space-time domain decomposition methods for unsteady inverse problems