2019/08/27 by Fei Xu, Xu, Fei, Hehu Xie +3
Computer Science · Engineering · Mathematics · #65B99 #65L15 #65N25 #65N30 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods in engineering #cs.NA #math.NA #msc:65B99 #msc:65L15 #msc:65N25 #msc:65N30
paper · pdf · doi:10.48550/arxiv.1908.10251
23 pages, 16 figures
openalex publication_date 2019/08/27 · arxiv created 2020/08/18 · arxiv updated 2020/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.