快速子空间迭代法、迭代Ritz向量法与迭代Lanczos法的比较

以高效的细胞稀疏直接快速解法为核心步骤，实现了快速的固有振动广义特征值问题解法。并在相同的允许模态误差的意义下检验了三种常用的大型矩阵特征模态算法——子空间迭代法、迭代Ritz向量法和迭代Lanczos法的计算效率。迭代Ritz向量法平均最快，子空间迭代法最慢，三种解法效率相差不是太大。与ANSYS的子空间迭代和Lanczos法相比。本文的子空间迭代比ANSYS的效率高很多，Lanczos法和ANSYS的效率差不多。大量较大规模的例题显示。本文对特征值算法的改进是十分有效的。算法的健壮性，通用性都达到了高水平。

Comparison of subspace iteration, iterative Ritz vector method and iterative Lanczos method

Based on the cell sparse fast solver and loop-unrolling, this paper implements three efficient eigenvalue algorithms-subspace iteration, iterative Ritz method and iterative Lanczos method. Slight modifications are made for iterative Ritz method and iterative Lanczos method. These eigenvalue algorithms are examined under the mode error, i.e, the ratio of out-of-balance nodal point forces that is the difference of maximum elastic nodal point forces and maximum inertia nodal point forces, and the maximum elastic nodal point. Averagely, iterative Ritz method is the most effcient one among them. Engineering projects are used as examples to verify the methods. Under the mode error convergence criterion the eigenvalue extracting processes are more stable than eigenvalue convergence criteria. Compared with ANSYS's subspace iteration and block Lanczos approaches, the subspace iteration of this paper is much more efficient, and Lanczos approach has almost equal efficiency. The methods proposed are of industrial strength and efficient. Large scale tests show that the improvement in terms of CPU time and storage request is tremendous.