论文标题
基于小波的边缘多尺度瘫痪算法，用于具有异质系数的抛物线方程
Wavelet-based Edge Multiscale Parareal Algorithm for Parabolic Equations with Heterogeneous Coefficients
论文作者
论文摘要
我们在本文中提出了基于小波的边缘多尺度瘫痪（WEMP）算法，以有效地求解具有异质系数的抛物线方程。该算法结合了多尺度方法的优势，这些方法可以有效地处理空间域中的异质性，以及在有足够的处理器时加快时间演化问题的瘫痪算法的强度。我们根据空间域中的网格大小，多尺度方法中使用的级别参数，粗尺度时间步长和细尺度时间步长得出该算法的收敛速率。提出了几项数值测试，以证明我们的算法的性能，这些算法完美验证了我们的理论结果。
We propose in this paper the Wavelet-based Edge Multiscale Parareal (WEMP) Algorithm to efficiently solve parabolic equations with heterogeneous coefficients. This algorithm combines the advantages of multiscale methods that can deal with heterogeneity in the spacial domain effectively, and the strength of parareal algorithms for speeding up time evolution problems when sufficient processors are available. We derive the convergence rate of this algorithm in terms of the mesh size in the spatial domain, the level parameter used in the multiscale method, the coarse-scale time step and the fine-scale time step. Several numerical tests are presented to demonstrate the performance of our algorithm, which verify our theoretical results perfectly.
