The reduced basis methods (RBMs) are widely use in fast solution of the parametrized parametrized linear systems. In some problems lacking good order-reduction condition, only the RBMs are not competent to give a high-precision solution with an affordable computational cost of the offline stage. To develop a high-precision solution and balance the offline and online cost, we explore a reasonable and effective framework for accelerating the iterative methods that is based on the RBMs. Firstly, the highly efficient reduced basis (RB) solver is used as the generation tool of accurate initial values. This data-driven initialization method could provide a warm start for the iterative methods. Secondly, we analyze the further acceleration of the RBMs as a preconditioner. For the purpose of high-precision solution, the RBM-preconditioner not only fail to accelerate the convergence but also need to pay more cost for the overuse of the RBMs. Two numerical test on 3D steady-state diffusion equations for two- and six-dimensional parameter space are presented to demonstrate the capability and efficiency of the RBM-initialized pure high-fidelity iterative methods.

翻译：约化基方法（RBMs）广泛应用于参数化线性系统的快速求解。在缺乏良好降阶条件的问题中，仅依靠RBMs无法以可承受的离线计算成本获得高精度解。为了发展高精度解并平衡离线与在线计算成本，我们探索了一种基于RBMs加速迭代方法的合理有效框架。首先，将高效约化基（RB）求解器用作精确初始值的生成工具。这种数据驱动的初始化方法可为迭代方法提供暖启动。其次，我们分析了将RBMs进一步加速为预处理器的可能性。对于高精度解的目标，RBM预处理器不仅未能加速收敛，反而因过度使用RBMs而需要付出更多成本。通过两个三维稳态扩散方程在二维和六维参数空间上的数值试验，展示了RBM初始化的纯高保真迭代方法的能力与效率。