Geological structures often exhibit smooth characteristics away from sharp discontinuities. One aim of geophysical inversion is to recover information about the smooth structures as well as about the sharp discontinui...Geological structures often exhibit smooth characteristics away from sharp discontinuities. One aim of geophysical inversion is to recover information about the smooth structures as well as about the sharp discontinuities. Because no specific operator can provide a perfect sparse representation of complicated geological models, hyper-parameter regularization inversion based on the iterative split Bregman method was used to recover the features of both smooth and sharp geological structures. A novel preconditioned matrix was proposed, which counteracted the natural decay of the sensitivity matrix and its inverse matrix was calculated easily. Application of the algorithm to synthetic data produces density models that are good representations of the designed models. The results show that the algorithm proposed is feasible and effective.展开更多
A preconditioning method for the finite element stiffness matrix is given in this paper. The triangulation is refined in a subregion; the preconditioning process is composed of resolution of two regular subproblems; t...A preconditioning method for the finite element stiffness matrix is given in this paper. The triangulation is refined in a subregion; the preconditioning process is composed of resolution of two regular subproblems; the condition number of the preconditioned matrix is 0(1 + log H/h), where H and h are mesh sizes of the unrefined and local refined triangulations respectively.展开更多
In recent years,many efforts have been made to numerically solving the constrained optimization distributed control problems,in which the most common one is to discretize the partial differential equation first and th...In recent years,many efforts have been made to numerically solving the constrained optimization distributed control problems,in which the most common one is to discretize the partial differential equation first and then solve the resulting system of linear equations.A number of preconditioned Krylov subspace methods have been constructed to solve the resulting system of linear equations in the literature.In this paper,by analyzing the block-diagonal preconditioner presented by Zhang,et al.(Zhang X Y,Yan H Y,Huang Y M.On preconditioned MINRES method for solving the distributed control problems.Commun Appl Math Comput,2014,28:128-132.),we propose a parameterized block-diagonally preconditioned linear system where a parameterized preconditioner is utilized and the preconditioned MINRES method is applied to solve the system of linear equations.The spectral analysis of the proposed preconditioned matrix shows that the spectral distribution of the parameterized preconditioning matrix should be much more clustered if the parameter is greater than 1.Numerical Experiments show that the preconditioned MINRES method is efficient for solving the distributed control problems.展开更多
We propose,in this paper,the preconditioned accelerated generalized successive overrelaxation(PAGSOR)iteration method for efficiently solving the large complex symmetric linear systems.To solve the nonlinear systems w...We propose,in this paper,the preconditioned accelerated generalized successive overrelaxation(PAGSOR)iteration method for efficiently solving the large complex symmetric linear systems.To solve the nonlinear systems whose Jacobian matrices are complex and symmetric,treating the PAGSOR method as internal iteration,we construct a modified Newton-PAGSOR(MN-PAGSOR)method to provide an effective approach for solving a wide range of problems in various scientific and engineering fields.Based on the Hölder continuous condition we present the theoretical framework of the modified method,demonstrate its local convergence properties,and provide numerical experiments to validate its effectiveness in solving a class of nonlinear systems.展开更多
基金Projects(41174061,41374120)supported by the National Natural Science Foundation of China
文摘Geological structures often exhibit smooth characteristics away from sharp discontinuities. One aim of geophysical inversion is to recover information about the smooth structures as well as about the sharp discontinuities. Because no specific operator can provide a perfect sparse representation of complicated geological models, hyper-parameter regularization inversion based on the iterative split Bregman method was used to recover the features of both smooth and sharp geological structures. A novel preconditioned matrix was proposed, which counteracted the natural decay of the sensitivity matrix and its inverse matrix was calculated easily. Application of the algorithm to synthetic data produces density models that are good representations of the designed models. The results show that the algorithm proposed is feasible and effective.
文摘A preconditioning method for the finite element stiffness matrix is given in this paper. The triangulation is refined in a subregion; the preconditioning process is composed of resolution of two regular subproblems; the condition number of the preconditioned matrix is 0(1 + log H/h), where H and h are mesh sizes of the unrefined and local refined triangulations respectively.
基金Project supported by the National Natural Science Foundation of China(11571156)
文摘In recent years,many efforts have been made to numerically solving the constrained optimization distributed control problems,in which the most common one is to discretize the partial differential equation first and then solve the resulting system of linear equations.A number of preconditioned Krylov subspace methods have been constructed to solve the resulting system of linear equations in the literature.In this paper,by analyzing the block-diagonal preconditioner presented by Zhang,et al.(Zhang X Y,Yan H Y,Huang Y M.On preconditioned MINRES method for solving the distributed control problems.Commun Appl Math Comput,2014,28:128-132.),we propose a parameterized block-diagonally preconditioned linear system where a parameterized preconditioner is utilized and the preconditioned MINRES method is applied to solve the system of linear equations.The spectral analysis of the proposed preconditioned matrix shows that the spectral distribution of the parameterized preconditioning matrix should be much more clustered if the parameter is greater than 1.Numerical Experiments show that the preconditioned MINRES method is efficient for solving the distributed control problems.
基金National Natural Science Foundation of China with Grant Nos.12161030,12171216.
文摘We propose,in this paper,the preconditioned accelerated generalized successive overrelaxation(PAGSOR)iteration method for efficiently solving the large complex symmetric linear systems.To solve the nonlinear systems whose Jacobian matrices are complex and symmetric,treating the PAGSOR method as internal iteration,we construct a modified Newton-PAGSOR(MN-PAGSOR)method to provide an effective approach for solving a wide range of problems in various scientific and engineering fields.Based on the Hölder continuous condition we present the theoretical framework of the modified method,demonstrate its local convergence properties,and provide numerical experiments to validate its effectiveness in solving a class of nonlinear systems.
