THE REDUCED BASIS TECHNIQUE AS A COARSE SOLVER FOR PARAREAL IN TIME SIMULATIONS
THE REDUCED BASIS TECHNIQUE AS A COARSE SOLVER FOR PARAREAL IN TIME SIMULATIONS
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DOI：
10.4208/jcm.1003-m2980
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发表时间：
2010
影响因子：
0.9
通讯作者：
Li-ping He
中科院分区：
文献类型：
--
作者：
Li-ping He
本文将参数相关问题的约化基方法扩展到Lions等人[12]提出的并行时间算法，并求解了非线性发展抛物型偏微分方程。该方法空间上采用有限单元法或谱单元法，时间上采用半隐式龙格-库塔格式。粗解器是基于时间上的半隐式格式和空间上的缩减基近似。开发了在线计算程序，并证明了在线计算的复杂性仅取决于缩减基空间的维数（通常很小）。本文还提出了基于多重网格有限单元法和多自由度有限单元法的并行时间算法。一些数值结果的报告。
In this paper, we extend the reduced basis methods for parameter dependent problems to the parareal in time algorithm introduced by Lions et al. [12] and solve a nonlinear evolutionary parabolic partial difierential equation. The flne solver is based on the flnite element method or spectral element method in space and a semi-implicit Runge-Kutta scheme in time. The coarse solver is based on a semi-implicit scheme in time and the reduced basis approximation in space. O†ine-online procedures are developed, and it is proved that the computational complexity of the on-line stage depends only on the dimension of the reduced basis space (typically small). Parareal in time algorithms based on a multi-grids flnite element method and a multi-degrees flnite element method are also presented. Some numerical results are reported.