In this paper, a generalized augmented Lagrangian-successive over-relaxation （GAL- SOR） iteration method is presented for solving saddle-point systems arising from distributed control problems. The convergence prope...In this paper, a generalized augmented Lagrangian-successive over-relaxation （GAL- SOR） iteration method is presented for solving saddle-point systems arising from distributed control problems. The convergence properties of the GAL-SOR method are studied in the spectral properties for the precondidetail. Moreover, when0 ≤ω≤ 1 and Q=1/γI , tioned matrix are analyzed. Numerical experiments show that if the mass matrix from the distributed control problems is not easy to inverse and the regularization parameter β is very small, the GAL-SOR iteration method can work well.展开更多
We present a higher-order in-space characteristic method for the solution of the tran- sient advection diffusion equations in two space dimensions. This method uses biquadratic trial and test functions within the fram...We present a higher-order in-space characteristic method for the solution of the tran- sient advection diffusion equations in two space dimensions. This method uses biquadratic trial and test functions within the framework of the Eulerian-Lagrangian localized Adjoint Methods （ELLAM）. It therefore maintains the advantages of previous ELLAM schemes. Namely, it treats general boundary conditions naturally in a systematic manner, conserves mass, and symmetrizes the governing transport equations. Moreover, it generates accurate numerical solutions even if large time steps are used in the simulation. Numerical exper- iments are presented to illustrate the performance of this method and establish its order of convergence numerically.展开更多
基金Acknowledgements. The authors are very much indebted to the referees for providing very valuable suggestions and comments, which greatly improved the original manuscript of this paper. This work was supported by the National Natural Science Foundation of China （No. 11271174 and No. 11511130015） and the Scientific Research Project of Putian University （No. 2015061）.
文摘In this paper, a generalized augmented Lagrangian-successive over-relaxation （GAL- SOR） iteration method is presented for solving saddle-point systems arising from distributed control problems. The convergence properties of the GAL-SOR method are studied in the spectral properties for the precondidetail. Moreover, when0 ≤ω≤ 1 and Q=1/γI , tioned matrix are analyzed. Numerical experiments show that if the mass matrix from the distributed control problems is not easy to inverse and the regularization parameter β is very small, the GAL-SOR iteration method can work well.
文摘We present a higher-order in-space characteristic method for the solution of the tran- sient advection diffusion equations in two space dimensions. This method uses biquadratic trial and test functions within the framework of the Eulerian-Lagrangian localized Adjoint Methods （ELLAM）. It therefore maintains the advantages of previous ELLAM schemes. Namely, it treats general boundary conditions naturally in a systematic manner, conserves mass, and symmetrizes the governing transport equations. Moreover, it generates accurate numerical solutions even if large time steps are used in the simulation. Numerical exper- iments are presented to illustrate the performance of this method and establish its order of convergence numerically.
