Recently,inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications.After the discretization,many of inverse problems are reduced...Recently,inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications.After the discretization,many of inverse problems are reduced to linear systems.Due to the typical ill-posedness of inverse problems,the reduced linear systems are often illposed,especially when their scales are large.This brings great computational difficulty.Particularly,a small perturbation in the right side of an ill-posed linear system may cause a dramatical change in the solution.Therefore,regularization methods should be adopted for stable solutions.In this paper,a new class of accelerated iterative regularization methods is applied to solve this kind of large-scale ill-posed linear systems.An iterative scheme becomes a regularization method only when the iteration is early terminated.And a Morozov’s discrepancy principle is applied for the stop criterion.Compared with the conventional Landweber iteration,the new methods have acceleration effect,and can be compared to the well-known acceleratedν-method and Nesterov method.From the numerical results,it is observed that using appropriate discretization schemes,the proposed methods even have better behavior when comparing withν-method and Nesterov method.展开更多
A pneumatic launcher is theoretically investigated to study its natural transverse vibration in water. Considering the mass effect of the sealing cover, the launcher is simplified as a uniform cantilever beam with a t...A pneumatic launcher is theoretically investigated to study its natural transverse vibration in water. Considering the mass effect of the sealing cover, the launcher is simplified as a uniform cantilever beam with a top point mass. By introducing the boundary and continuity conditions into the motion equation, the natural frequency equation and the mode shape function are derived. An iterative calculation method for added mass is also presented using the velocity potential function to account for the mass effect of the fluid on the launcher. The first 2 order natural frequencies and mode shapes are discussed in external flow fields and both external and internal flow fields. The results show good agreement with both natural frequencies and mode shapes between the theoretical analysis and the FEM studies. Also, the added mass is found to decrease with the increase of the mode shape orders of the launcher. And because of the larger added mass in both the external and internal flow fields than that in only the external flow field, the corresponding natural frequencies of the former are relatively smaller.展开更多
基金supported by the Natural Science Foundation of China (Nos. 11971230, 12071215)the Fundamental Research Funds for the Central Universities(No. NS2018047)the 2019 Graduate Innovation Base(Laboratory)Open Fund of Jiangsu Province(No. Kfjj20190804)
文摘Recently,inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications.After the discretization,many of inverse problems are reduced to linear systems.Due to the typical ill-posedness of inverse problems,the reduced linear systems are often illposed,especially when their scales are large.This brings great computational difficulty.Particularly,a small perturbation in the right side of an ill-posed linear system may cause a dramatical change in the solution.Therefore,regularization methods should be adopted for stable solutions.In this paper,a new class of accelerated iterative regularization methods is applied to solve this kind of large-scale ill-posed linear systems.An iterative scheme becomes a regularization method only when the iteration is early terminated.And a Morozov’s discrepancy principle is applied for the stop criterion.Compared with the conventional Landweber iteration,the new methods have acceleration effect,and can be compared to the well-known acceleratedν-method and Nesterov method.From the numerical results,it is observed that using appropriate discretization schemes,the proposed methods even have better behavior when comparing withν-method and Nesterov method.
基金Foundation item： Supported by the National Natural Science Foundation of China （51379083） and the Specialized Research Fund for the Doctoral Program of Hiher Education （20120142110051）.
文摘A pneumatic launcher is theoretically investigated to study its natural transverse vibration in water. Considering the mass effect of the sealing cover, the launcher is simplified as a uniform cantilever beam with a top point mass. By introducing the boundary and continuity conditions into the motion equation, the natural frequency equation and the mode shape function are derived. An iterative calculation method for added mass is also presented using the velocity potential function to account for the mass effect of the fluid on the launcher. The first 2 order natural frequencies and mode shapes are discussed in external flow fields and both external and internal flow fields. The results show good agreement with both natural frequencies and mode shapes between the theoretical analysis and the FEM studies. Also, the added mass is found to decrease with the increase of the mode shape orders of the launcher. And because of the larger added mass in both the external and internal flow fields than that in only the external flow field, the corresponding natural frequencies of the former are relatively smaller.
