The inter-cycle correlation of fission source distributions(FSDs)in the Monte Carlo power iteration process results in variance underestimation of tallied physical quantities,especially in large local tallies.This stu...The inter-cycle correlation of fission source distributions(FSDs)in the Monte Carlo power iteration process results in variance underestimation of tallied physical quantities,especially in large local tallies.This study provides a mesh-free semiquantitative variance underestimation elimination method to obtain a credible confidence interval for the tallied results.This method comprises two procedures:Estimation and Elimination.The FSD inter-cycle correlation length is estimated in the Estimation procedure using the Sliced Wasserstein distance algorithm.The batch method was then used in the elimination procedure.The FSD inter-cycle correlation length was proved to be the optimum batch length to eliminate the variance underestimation problem.We exemplified this method using the OECD sphere array model and 3D PWR BEAVRS model.The results showed that the average variance underestimation ratios of local tallies declined from 37 to 87%to within±5%in these models.展开更多
This paper introduces some efficient initials for a well-known algorithm （an inverse iteration） for computing the maximal eigenpair of a class of real matrices. The initials not only avoid the collapse of the algori...This paper introduces some efficient initials for a well-known algorithm （an inverse iteration） for computing the maximal eigenpair of a class of real matrices. The initials not only avoid the collapse of the algorithm but are also unexpectedly efficient. The initials presented here are based on our analytic estimates of the maximal eigenvalue and a mimic of its eigenvector for many years of accumulation in the study of stochastic stability speed. In parallel, the same problem for computing the next to the maximal eigenpair is also studied.展开更多
This paper is a continuation of our previous paper[Front.Math.China,2017,12(5):10231043]where global algorithms for computing the maximal cigcnpair were introduced in a rather general setup.The efficiency of the globa...This paper is a continuation of our previous paper[Front.Math.China,2017,12(5):10231043]where global algorithms for computing the maximal cigcnpair were introduced in a rather general setup.The efficiency of the global algorithms is improved in this paper in terms of a good use of power iteration and two quasi-symmetric techniques.Finally,the new algorithms are applied to Hua’s economic optimization model.展开更多
基金supported by China Nuclear Power Engineering Co.,Ltd.Scientific Research Project(No.KY22104)the fellowship of China Postdoctoral Science Foundation(No.2022M721793).
文摘The inter-cycle correlation of fission source distributions(FSDs)in the Monte Carlo power iteration process results in variance underestimation of tallied physical quantities,especially in large local tallies.This study provides a mesh-free semiquantitative variance underestimation elimination method to obtain a credible confidence interval for the tallied results.This method comprises two procedures:Estimation and Elimination.The FSD inter-cycle correlation length is estimated in the Estimation procedure using the Sliced Wasserstein distance algorithm.The batch method was then used in the elimination procedure.The FSD inter-cycle correlation length was proved to be the optimum batch length to eliminate the variance underestimation problem.We exemplified this method using the OECD sphere array model and 3D PWR BEAVRS model.The results showed that the average variance underestimation ratios of local tallies declined from 37 to 87%to within±5%in these models.
基金Acknowledgements The main results of the paper have been reported at Anhui Normal University, Jiangsu Normal University, the International Workshop on SDEs and Numerical Methods at Shanghai Normal University, Workshop on Markov Processes and Their Applications at Hunan University of Arts and Science, and Workshop of Probability Theory with Applications at University of Macao. The author acknowledges Professors Dong-Jin Zhu, Wan-Ding Ding, Ying-Chao Xie, Xue-Rong Mao, Xiang-Qun Yang, Xu-Yan Xiang, Jie Xiong, Li-Hu Xu, and their teams for very warm hospitality and financial support. The author also thanks Ms. Yue-Shuang Li for her assistance in computing large matrices. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11131003）, the ＂985＂ project from the Ministry of Education in China, and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘This paper introduces some efficient initials for a well-known algorithm （an inverse iteration） for computing the maximal eigenpair of a class of real matrices. The initials not only avoid the collapse of the algorithm but are also unexpectedly efficient. The initials presented here are based on our analytic estimates of the maximal eigenvalue and a mimic of its eigenvector for many years of accumulation in the study of stochastic stability speed. In parallel, the same problem for computing the next to the maximal eigenpair is also studied.
基金This work was supported in part by the National Natural Science Foundation of China(Grant No.11771046)the Project from the Ministry of Education in China,and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘This paper is a continuation of our previous paper[Front.Math.China,2017,12(5):10231043]where global algorithms for computing the maximal cigcnpair were introduced in a rather general setup.The efficiency of the global algorithms is improved in this paper in terms of a good use of power iteration and two quasi-symmetric techniques.Finally,the new algorithms are applied to Hua’s economic optimization model.
