Many applications require the solution of large nonsymmetric linear systems with multiple right hand sides. Instead of applying an iterative method to each of these systems individually, it is often more efficient to...Many applications require the solution of large nonsymmetric linear systems with multiple right hand sides. Instead of applying an iterative method to each of these systems individually, it is often more efficient to use a block version of the method that generates iterates for all the systems simultaneously. In this paper, we propose a block version of generalized minimum backward (GMBACK) for solving large multiple nonsymmetric linear systems. The new method employs the block Arnoldi process to construct a basis for the Krylov subspace K m(A, R 0) and seeks X m∈X 0+K m(A, R 0) to minimize the norm of the perturbation to the data given in A.展开更多
In this paper, a nonlinear control scheme of two identical hyperchaotic Chert systems is developed to realize their modified projective synchronization. We achieve modified projective synchronization between the two i...In this paper, a nonlinear control scheme of two identical hyperchaotic Chert systems is developed to realize their modified projective synchronization. We achieve modified projective synchronization between the two identical hyperchaotic systems by directing the scaling factor onto the desired value. With symbolic computation system Maple and Lyapunov stability theory, numerical simulations are given to perform the process of the synchronization.展开更多
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
文摘Many applications require the solution of large nonsymmetric linear systems with multiple right hand sides. Instead of applying an iterative method to each of these systems individually, it is often more efficient to use a block version of the method that generates iterates for all the systems simultaneously. In this paper, we propose a block version of generalized minimum backward (GMBACK) for solving large multiple nonsymmetric linear systems. The new method employs the block Arnoldi process to construct a basis for the Krylov subspace K m(A, R 0) and seeks X m∈X 0+K m(A, R 0) to minimize the norm of the perturbation to the data given in A.
文摘In this paper, a nonlinear control scheme of two identical hyperchaotic Chert systems is developed to realize their modified projective synchronization. We achieve modified projective synchronization between the two identical hyperchaotic systems by directing the scaling factor onto the desired value. With symbolic computation system Maple and Lyapunov stability theory, numerical simulations are given to perform the process of the synchronization.
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.
