隐式重启的Arnoldi方法及其在高阶谐波求解中的应用

Krylov子空间方法的出现是近年来大型线性方程组和特征值问题求解领域的重大进展,介绍其中一类适用于求解反应堆k-本征值问题的隐式重启的Arnoldi方法(IRAM),以及该方法在高阶谐波求解中的应用。研究结果表明,IRAM方法求解高阶谐波具有和源修正法同样的精度,但计算速度更快,尤其是当所求的谐波阶次较高时,IRAM方法可获得10倍以上的速度优势。同时,IRAM方法还具备较好的处理重特征值问题的能力。

Implicitly restarted Arnoldi method and its application to the solution of higher order harmonics

The recent development of Krylov subspace method is a major progress in the area of large-scale linear equation and eigen-value problem research.One type of Krylov subspace method suitable for eigenvalue problem is Implicitly Restarted Arnoldi Method(IRAM) it is introduced and applied to the solution of higher order harmonics.Numerical results demonstrate that while its accuracy is comparable with the conventional modified source iteration method(MSIM),IRAM method runs much faster than MSIM.In the case of high order harmonics,IRAM can run more than 10 times faster than MSIM.Moreover,IRAM is more efficient to solve the eigenvalue problem with duplicate eigenvalues.