A ROM-accelerated parallel-in-time preconditioner for solving all-at-once systems in unsteady convection-diffusion PDEs
A ROM-accelerated parallel-in-time preconditioner for solving all-at-once systems in unsteady convection-diffusion PDEs
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DOI：
10.1016/j.amc.2021.126750
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发表时间：
2022-03
期刊：
影响因子：
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通讯作者：
Jun Liu;Zhu Wang
中科院分区：
文献类型：
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作者：
Jun Liu;Zhu Wang
在本文中，我们提出了一种模型简化技术，以加快对角化为基础的并行时间（ParaDIAG）预处理，迭代求解所有在一次系统从进化偏微分方程。特别是，我们使用减少的基础方法来寻求一个低维近似的序列所产生的步骤-（B）的ParaDIAG预处理过程的复杂的移位系统。不同于标准的降阶建模，使用离线和在线阶段的分离，我们必须建立降阶模型（ROM）在线所考虑的系统在每次迭代。因此，几个启发式的加速技术被引入到贪婪基生成算法，这是建立在基于残差的错误指示，以进一步提高其计算效率。几个数值实验进行，这说明了良好的计算效率，我们提出的ROM加速的ParaDIAG预处理器，相比基于多重网格。
In this paper we propose a model reduction technique to speed up the diagonalization-based parallel-in-time (ParaDIAG) preconditioner, for iteratively solving all-at-once systems from evolutionary PDEs. In particular, we use the reduced basis method to seek a low-dimensional approximation to the sequence of complex-shifted systems arising from Step-(b) of the ParaDIAG preconditioning procedure. Different from the standard reduced order modeling that uses the separation of offline and online stages, we have to build the reduced order model (ROM) online for the considered systems at each iteration. Therefore, several heuristic acceleration techniques are introduced in the greedy basis generation algorithm, that is built upon a residual-based error indicator, to further boost up its computational efficiency. Several numerical experiments are conducted, which illustrate the favorable computational efficiency of our proposed ROM-accelerated ParaDIAG preconditioner, in comparison with the multigrid-based one.