In this paper we study the algorithms and their parallel implementation for solving large-scale generalized eigenvalue problems in modal analysis.Three predominant subspace algorithms,i.e.,Krylov-Schur method,implicit...In this paper we study the algorithms and their parallel implementation for solving large-scale generalized eigenvalue problems in modal analysis.Three predominant subspace algorithms,i.e.,Krylov-Schur method,implicitly restarted Arnoldi method and Jacobi-Davidson method,are modified with some complementary techniques to make them suitable for modal analysis.Detailed descriptions of the three algorithms are given.Based on these algorithms,a parallel solution procedure is established via the PANDA framework and its associated eigensolvers.Using the solution procedure on a machine equipped with up to 4800processors,the parallel performance of the three predominant methods is evaluated via numerical experiments with typical engineering structures,where the maximum testing scale attains twenty million degrees of freedom.The speedup curves for different cases are obtained and compared.The results show that the three methods are good for modal analysis in the scale of ten million degrees of freedom with a favorable parallel scalability.展开更多
在文献[1]中,作者M E Hochstenbach和B Plestenjak认为精化的方法不适合两参数特征值问题,原因是求解两参数特征值问题的精化方法存在着三个问题:即精化Ritz向量收敛性差,运算量大,不能计算多个特征值.本文指出,事实并非如此.针对右定...在文献[1]中,作者M E Hochstenbach和B Plestenjak认为精化的方法不适合两参数特征值问题,原因是求解两参数特征值问题的精化方法存在着三个问题:即精化Ritz向量收敛性差,运算量大,不能计算多个特征值.本文指出,事实并非如此.针对右定两参数特征值问题,本文提出了一种有效的精化数值方法.并通过理论证明和数值实验说明了Ritz值的收敛性,以及精化Ritz向量具有比通常的Ritz向量更好的收敛性.展开更多
The continuation power flow method combined with the Jacobi-Davidson method is presented to trace the critical eigenvalues for power system small signal stability analysis. The continuation power flow based on a predi...The continuation power flow method combined with the Jacobi-Davidson method is presented to trace the critical eigenvalues for power system small signal stability analysis. The continuation power flow based on a predictor- corrector technique is applied to evaluate a continuum of steady state power flow solutions as system parameters change;meanwhile, the critical eigenvalues are found by the Jacobi-Davidson method, and thereby the trajectories of the critical eigenvalues, Hopf bifurcation and saddle node bifurcation points can also be found by the proposed method. The numerical simulations are studied in the IEEE 30-bus test system.展开更多
基金supported by the National Defence Basic Fundamental Research Program of China(Grant No.C1520110002)the Fundamental Development Foundation of China Academy Engineering Physics(Grant No.2012A0202008)
文摘In this paper we study the algorithms and their parallel implementation for solving large-scale generalized eigenvalue problems in modal analysis.Three predominant subspace algorithms,i.e.,Krylov-Schur method,implicitly restarted Arnoldi method and Jacobi-Davidson method,are modified with some complementary techniques to make them suitable for modal analysis.Detailed descriptions of the three algorithms are given.Based on these algorithms,a parallel solution procedure is established via the PANDA framework and its associated eigensolvers.Using the solution procedure on a machine equipped with up to 4800processors,the parallel performance of the three predominant methods is evaluated via numerical experiments with typical engineering structures,where the maximum testing scale attains twenty million degrees of freedom.The speedup curves for different cases are obtained and compared.The results show that the three methods are good for modal analysis in the scale of ten million degrees of freedom with a favorable parallel scalability.
文摘在文献[1]中,作者M E Hochstenbach和B Plestenjak认为精化的方法不适合两参数特征值问题,原因是求解两参数特征值问题的精化方法存在着三个问题:即精化Ritz向量收敛性差,运算量大,不能计算多个特征值.本文指出,事实并非如此.针对右定两参数特征值问题,本文提出了一种有效的精化数值方法.并通过理论证明和数值实验说明了Ritz值的收敛性,以及精化Ritz向量具有比通常的Ritz向量更好的收敛性.
文摘The continuation power flow method combined with the Jacobi-Davidson method is presented to trace the critical eigenvalues for power system small signal stability analysis. The continuation power flow based on a predictor- corrector technique is applied to evaluate a continuum of steady state power flow solutions as system parameters change;meanwhile, the critical eigenvalues are found by the Jacobi-Davidson method, and thereby the trajectories of the critical eigenvalues, Hopf bifurcation and saddle node bifurcation points can also be found by the proposed method. The numerical simulations are studied in the IEEE 30-bus test system.
