%0 Journal Article %1 zhang2019comparison %A Zhang, Han %A Guo, Jiong %A Lu, Jianan %A Niu, Jinlin %A Li, Fu %A Xu, Yunlin %D 2019 %J Annals of Nuclear Energy %K 65f08-preconditioners-for-iterative-methods %P 357 - 368 %R 10.1016/j.anucene.2019.04.053 %T The comparison between nonlinear and linear preconditioning JFNK method for transient neutronics/thermal-hydraulics coupling problem %U http://www.sciencedirect.com/science/article/pii/S0306454919302373 %V 132 %X Jacobian-free Newton Krylov (JFNK) method is an advanced numerical method for solving the transient multi-physics coupling problem in nuclear reactor, where all the coupled equations are simultaneously solved in a tightly nonlinear form. Constructing a high performance preconditioning is a key issue for JFNK method to efficiently solve this complex coupled system. Two families of preconditioning method, linear preconditioning and nonlinear preconditioning, have been proposed and developed independently. Linear preconditioning is a transformation of linear equations derived from the Newton linearization. Nonlinear preconditioning is also an attractive method because it can be easily implemented as a black box coupling. The comparison between nonlinear and linear preconditioning is made and validated by numerical tests using a two-dimension simplified reactor model in this work. The results show that the similar convergence rate is achieved for nonlinear and linear preconditioning in the transient neutronics/thermal-hydraulics coupling problem. However, the computational efficiency of linear preconditioning is always higher than that of nonlinear preconditioning, because an extra inverse of the preconditioner should be calculated per Krylov iteration in nonlinear preconditioning. When the computational cost of the inverse preconditioner is usually very expensive, like using the original engineering code as the preconditioning, linear preconditioning has an absolute advantage. While compared with the nonlinear preconditioning, a relatively large burden of code development has to be paid for linear preconditioning.

@article{zhang2019comparison, abstract = {Jacobian-free Newton Krylov (JFNK) method is an advanced numerical method for solving the transient multi-physics coupling problem in nuclear reactor, where all the coupled equations are simultaneously solved in a tightly nonlinear form. Constructing a high performance preconditioning is a key issue for JFNK method to efficiently solve this complex coupled system. Two families of preconditioning method, linear preconditioning and nonlinear preconditioning, have been proposed and developed independently. Linear preconditioning is a transformation of linear equations derived from the Newton linearization. Nonlinear preconditioning is also an attractive method because it can be easily implemented as a black box coupling. The comparison between nonlinear and linear preconditioning is made and validated by numerical tests using a two-dimension simplified reactor model in this work. The results show that the similar convergence rate is achieved for nonlinear and linear preconditioning in the transient neutronics/thermal-hydraulics coupling problem. However, the computational efficiency of linear preconditioning is always higher than that of nonlinear preconditioning, because an extra inverse of the preconditioner should be calculated per Krylov iteration in nonlinear preconditioning. When the computational cost of the inverse preconditioner is usually very expensive, like using the original engineering code as the preconditioning, linear preconditioning has an absolute advantage. While compared with the nonlinear preconditioning, a relatively large burden of code development has to be paid for linear preconditioning.}, added-at = {2020-07-26T12:36:20.000+0200}, author = {Zhang, Han and Guo, Jiong and Lu, Jianan and Niu, Jinlin and Li, Fu and Xu, Yunlin}, biburl = {https://www.bibsonomy.org/bibtex/2d2f9fa59a1c048bb4e213f64743e3055/gdmcbain}, doi = {10.1016/j.anucene.2019.04.053}, interhash = {94a87ce1505849b2a4237b6ade687ece}, intrahash = {d2f9fa59a1c048bb4e213f64743e3055}, issn = {0306-4549}, journal = {Annals of Nuclear Energy}, keywords = {65f08-preconditioners-for-iterative-methods}, pages = {357 - 368}, timestamp = {2020-07-26T12:36:20.000+0200}, title = {The comparison between nonlinear and linear preconditioning {JFNK} method for transient neutronics/thermal-hydraulics coupling problem}, url = {http://www.sciencedirect.com/science/article/pii/S0306454919302373}, volume = 132, year = 2019 }