PASE：一种用于大规模特征值问题的大规模并行增广子空间特征求解器
PASE: A Massively Parallel Augmented Subspace Eigensolver for Large Scale Eigenvalue Problems
AI总结：
本文提出并行增广子空间方法并开发PASE软件包，将大规模特征值问题转化为线性方程组和低维特征值问题求解，通过实现技术提升可扩展性与效率，并用数值算例验证了方法的有效性。
摘要：
本文提出了一种新颖的并行增广子空间方法，并构建了一个软件包——并行增广子空间特征求解器（PASE），用于通过大规模并行有限元离散求解大规模特征值问题。基于增广子空间，求解高维特征值问题可以转化为求解相应的线性方程组以及增广子空间上的低维特征值问题。因此，采用增广子空间方法求解特征值问题的复杂度将与求解同维线性方程组的复杂度相当。为了提高可扩展性和效率，我们还提出了一些针对并行增广子空间方法的实现技术。基于并行增广子空间方法和相关的实现技术，构建了用于求解大规模特征值问题的软件包PASE。文中提供了若干数值算例，以验证所提数值方法的效率和可扩展性。
英文摘要：
In this paper, we present a novel parallel augmented subspace method and build a package Parallel Augmented Subspace Eigensolver (PASE) for solving large scale eigenvalue problems by the massively parallel finite element discretization. Based on the augmented subspace, solving high dimensional eigenvalue problems can be transformed to solving the corresponding linear equations and low dimensional eigenvalue problems on the augmented subspace. Thus the complexity of solving the eigenvalue problems by augmented subspace method will be comparable to that of solving the same dimensinal linear equations. In order to improve the scalability and efficiency, we also present some implementing techniques for the parallel augmented subspace method. Based on parallel augmented subspace method and the concerned implementing techniques, a package PASE is built for solving large scale eigenvalue problems. Some numerical examples are provided to validate the efficiency and scalability of the proposed numerical methods.
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