American Institute of Mathematical Sciences

November  2015, 9(4): 1069-1091. doi: 10.3934/ipi.2015.9.1069

A parallel space-time domain decomposition method for unsteady source inversion problems

 1 Laboratory for Engineering and Scientific Computing, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, Guangdong 518055, China 2 Department of Computer Science, University of Colorado, Boulder, CO 80309, United States 3 Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

Received  June 2014 Revised  November 2014 Published  October 2015

In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady source identification problem governed by the linear convection-diffusion equation. Traditional approaches require to solve repeatedly a forward parabolic system, an adjoint system and a system with respect to the unknown sources. 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.
Citation: Xiaomao Deng, Xiao-Chuan Cai, Jun Zou. A parallel space-time domain decomposition method for unsteady source inversion problems. Inverse Problems & Imaging, 2015, 9 (4) : 1069-1091. doi: 10.3934/ipi.2015.9.1069
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References:
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