广义特征值问题的并行块Jacobi-Davidson方法及应用

Parallel block Jacobi-Davidson method for solving large generalized eigenvalue problems and it's application

给出了对称矩阵广义特征值问题AX=λBX的并行块Jacobi-Davidson方法。该方法使用投影技术将大型矩阵特征值问题转变成低维子空间中矩阵特征值问题,并利用Neumann级数展开对校正方程进行预处理。该方法可同时并行计算广义特征值问题的几个极端特征对,具有良好的并行性。将这一方法应用于某型号机翼及挂架的结构动力分析并行计算,在IBM-P650并行计算机上的数值试验结果表明,在相同迭代精确度的条件下,Jacobi-Davidson方法比子空间迭代法使用较少的迭代次数和运算时间,并具有更高的加速比和并行效率。

This paper gives a method of parallel block Jacobi-Davidson for computing large generalized eigenvalue problem AX=λBX, in which matrix A and B is symmetric. The large eigenvalue problem is transformed into an eigenvalue problem in a low dimension subspace by using orthogonal projection technique, and the Neumann series is used in the correction equation for the purpose of precondition. The method can get several eigenpairs at one time include multiply eigenpairs. The new algorithm is successfully applied in dynamic analysis of a wing and a rack of a plane,the numerical experiments on the IBM- P650 show that under the condition of the same accuracy, the parallel block Jacobi-Davidson method can get the eigenpairs in less time and less iteration steps than that of parallel subspace iterative method and has a higher speedup and efficient.