Two-Level Space–Time Domain Decomposition Methods for Three-Dimensional Unsteady Inverse Source Problems
Two-Level Space–Time Domain Decomposition Methods for Three-Dimensional Unsteady Inverse Source Problems
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DOI：
10.1007/s10915-015-0109-1
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发表时间：
2015-09
影响因子：
2.5
通讯作者：
Xiaomao Deng;X. Cai;J. Zou
中科院分区：
文献类型：
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作者：
Xiaomao Deng;X. Cai;J. Zou
随着超级计算机上处理器核的数量越来越多，具有高度并行性的算法受到了越来越多的关注。在这项工作中，我们提出了一种求解三维含时对流扩散方程逆源问题的两层时空域分解方法。将Karush-Kuhn-Tucker系统的反问题转化为整个时空的输出最小二乘优化问题，提出了一种混合有限元/有限差分方法以及一层和两层时空并行区域分解预条件。新的全空时方法省去了优化外环中的顺序步骤和内层的正反向时间推进过程，从而实现了高度的并行性。数值实验验证了该方法对恢复非定常运动源的有效性和稳健性。我们将展示在拥有1000多个处理器的超级计算机上获得的强大可伸缩性结果。
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.