SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2655-A2677, January 2020.
A type of parallel augmented subspace scheme for eigenvalue problems is proposed by using coarse space in the multigrid method. With the help of coarse space in the multigrid method, solving the eigenvalue problem in the finest space is decomposed into solving the standard linear boundary value problems and very-low-dimensional eigenvalue problems. The computational efficiency can be improved since there is no direct eigenvalue solving in the finest space and the multigrid method can act as the solver for the deduced linear boundary value problems. Furthermore, for different eigenvalues, the corresponding boundary value problem and low-dimensional eigenvalue problem can be solved in the parallel way since they are independent of each other and there exists no data exchanging. This property means that we do not need to do the orthogonalization in the highest-dimensional spaces. This is the main aim of this paper since avoiding orthogonalization can improve the scalability of the proposed numerical method. Some numerical examples are provided to validate the proposed parallel augmented subspace method.

中文翻译：

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特征值问题的并行增强子空间方法

SIAM科学计算杂志，第42卷，第5期，第A2655-A2677页，2020年1月。
通过在多网格方法中使用粗糙空间，提出了一种用于特征值问题的并行扩充子空间方案。借助于多重网格方法中的粗糙空间，将在最细空间中求解特征值分解为求解标准线性边界值问题和极低维特征值问题。由于在最精细的空间中没有直接的特征值求解，并且多重网格方法可以用作推导的线性边界值问题的求解器，因此可以提高计算效率。此外，对于不同的特征值，由于它们彼此独立并且不存在数据交换，因此可以并行地解决相应的边界值问题和低维特征值问题。此属性意味着我们不需要在最高维空间中进行正交化。这是本文的主要目的，因为避免正交化可以提高所提出数值方法的可扩展性。提供一些数值示例来验证所提出的并行增强子空间方法。