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 two-level space-time domain decomposition method for solving an inverse source 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 system induced from reformulating the inverse problem as an output least-squares optimization problem in the entire space-time domain. The new full space-time approach eliminates the sequential steps in 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 will present strong scalability results obtained on a supercomputer with more than 1000 processors.

In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady source identification problem governed by the linear convectiondiffusion equation. Traditional approaches require to solve repeatedly a forward parabolic system, an adjoint system and a system with respect to the unknowns.The three systems have to be solved one after another. These sequential steps are not desirable for large scale parallel computing. A space-time restrictive additive Schwarz method is proposed for a fully implicit space-time coupled discretization scheme to recover the time-dependent pollutant source intensity functions. We show with numerical experiments that the scheme works well with noise in the observation data. More importantly it is demonstrated that the parallel space-time Schwarz preconditioner is scalable on a supercomputer with over 10 3 processors, thus promising for large scale applications.

No abstract

No abstract