求解大型矩阵特征值问题的并行精化Davidson方法  

Parallel Refined Davidson Method for Solving the Large Scale Eigenproblem

作　　者：王顺绪[1,2] 戴华[1] 

机构地区：[1]南京航空航天大学理学院,南京210016 [2]淮海工学院数理系,连云港222005

出　　处：《工程数学学报》2009年第5期922-928,共7页Chinese Journal of Engineering Mathematics

摘　　要：针对共享主存的并行计算环境和微机网络并行计算环境,本文给出了求解大型稀疏对称矩阵的部分极端特征对的并行精化Davidson方法,分析了该法的内在并行性。各处理器利用矩阵的行块和投影子空间的正交基所组成矩阵的行块进行运算,结合重新启动策略求解矩阵多个特征对的近似值,并用以计算某型号机翼的固有频率,在微机网络并行计算环境和拥有共享主存并行计算环境IBM-P650上进行了数值试验。A parallel refined Davidson method is presented for large sparse symmetric eigenvalue problems, its implementation on PC network parallel systems and shared memory computer systems, as well as the parallelism are analyzed, The rows of the matrix are distributed to each processor, and the individual processors run the program by using the orthogonal basis of projection subspace and the rows of the matrix. Combine with the restarting scheme, the method can solve several eigenvalues and its associated eigenvectors of the matrix, and the method is successfully used for computing the frequency of a plane wing. The numerical experiments are done on the PC network parallel system and shared memory parallel system IBM-P650.

关 键 词：并行计算 特征值问题 Davidson方法 精化方法 

分 类 号：O241[理学—计算数学] O246[理学—数学]