论文标题
用于从进化PDE求解全面系统的ROM加速并行预处理
A ROM-accelerated parallel-in-time preconditioner for solving all-at-once systems from evolutionary PDEs
论文作者
论文摘要
在本文中，我们建议使用模型还原技术来加速基于对角线的平行时间（Paradiag）预处理，以迭代地从进化PDES迭代求解全面的系统。特别是，我们使用还原的基准方法来寻求与Paradiag预处理程序步骤（b）产生的复杂变速系统序列的低维近似。与使用离线和在线阶段分开的标准减少订单建模不同，我们必须在线构建减少的订单模型（ROM），以便在每次迭代中考虑的系统。因此，在贪婪的基础生成算法中引入了几种启发式加速技术，该算法建立在基于残留的误差指标上，以进一步提高其计算效率。进行了几项数值实验，这说明了我们提出的ROM加速Paradiag Proventitioner的有利计算效率，与基于Multigrid的Paradiag Paradiag Proventioner相比。
In this paper we propose to use model reduction techniques for speeding 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 state of the art multigrid-based ParaDIAG preconditioner.
