This paper considers the uumerical method and error analyses for two phase incompresaible miscible displacement in porous media.A time-stepping procedure is introduced using Sckwarz domain decomposition algorithm with...This paper considers the uumerical method and error analyses for two phase incompresaible miscible displacement in porous media.A time-stepping procedure is introduced using Sckwarz domain decomposition algorithm with eded element for the pressure equation and with finite dement for concentration equation. The author has analysed the relationship between convergence rates and discretization parameters,optimal order error estimates are derived under certain constraintes about the discretisation parameters.It is shown that the constraintes can be satisfied by the natural choices of these parameters.展开更多
In this paper,we explore the convergence and convergence rate results for a new methodology termed the half-proximal symmetric splitting method(HPSSM).This method is designed to address linearly constrained two-block ...In this paper,we explore the convergence and convergence rate results for a new methodology termed the half-proximal symmetric splitting method(HPSSM).This method is designed to address linearly constrained two-block non-convex separable optimization problem.It integrates a half-proximal term within its first subproblem to cancel out complicated terms in applications where the subproblem is not easy to solve or lacks a simple closed-form solution.To further enhance adaptability in selecting relaxation factor thresholds during the two Lagrange multiplier update steps,we strategically incorporate a relaxation factor as a disturbance parameter within the iterative process of the second subproblem.Building on several foundational assumptions,we establish the subsequential convergence,global convergence,and iteration complexity of HPSSM.Assuming the presence of the Kurdyka-Łojasiewicz inequality of Łojasiewicz-type within the augmented Lagrangian function(ALF),we derive the convergence rates for both the ALF sequence and the iterative sequence.To substantiate the effectiveness of HPSSM,sufficient numerical experiments are conducted.Moreover,expanding upon the two-block iterative scheme,we present the theoretical results for the symmetric splitting method when applied to a three-block case.展开更多
The Accelerated Hermitian/skew-Hermitian type Richardson(AHSR)iteration methods are presented for solving non-Hermitian positive definite linear systems with three schemes,by using Anderson mixing.The upper bounds of ...The Accelerated Hermitian/skew-Hermitian type Richardson(AHSR)iteration methods are presented for solving non-Hermitian positive definite linear systems with three schemes,by using Anderson mixing.The upper bounds of spectral radii of iteration matrices are studied,and then the convergence theories of the AHSR iteration methods are established.Furthermore,the optimal iteration parameters are provided,which can be computed exactly.In addition,the application to the model convection-diffusion equation is depicted and numerical experiments are conducted to exhibit the effectiveness and confirm the theoretical analysis of the AHSR iteration methods.展开更多
文摘This paper considers the uumerical method and error analyses for two phase incompresaible miscible displacement in porous media.A time-stepping procedure is introduced using Sckwarz domain decomposition algorithm with eded element for the pressure equation and with finite dement for concentration equation. The author has analysed the relationship between convergence rates and discretization parameters,optimal order error estimates are derived under certain constraintes about the discretisation parameters.It is shown that the constraintes can be satisfied by the natural choices of these parameters.
基金Supported by the Fundamental Research Funds for the Central Universities(Grant No.2025QN1147)。
文摘In this paper,we explore the convergence and convergence rate results for a new methodology termed the half-proximal symmetric splitting method(HPSSM).This method is designed to address linearly constrained two-block non-convex separable optimization problem.It integrates a half-proximal term within its first subproblem to cancel out complicated terms in applications where the subproblem is not easy to solve or lacks a simple closed-form solution.To further enhance adaptability in selecting relaxation factor thresholds during the two Lagrange multiplier update steps,we strategically incorporate a relaxation factor as a disturbance parameter within the iterative process of the second subproblem.Building on several foundational assumptions,we establish the subsequential convergence,global convergence,and iteration complexity of HPSSM.Assuming the presence of the Kurdyka-Łojasiewicz inequality of Łojasiewicz-type within the augmented Lagrangian function(ALF),we derive the convergence rates for both the ALF sequence and the iterative sequence.To substantiate the effectiveness of HPSSM,sufficient numerical experiments are conducted.Moreover,expanding upon the two-block iterative scheme,we present the theoretical results for the symmetric splitting method when applied to a three-block case.
基金Supported by National Science Foundation of China(Grant Nos.41725017 and 42004085)Guangdong Basic and Applied Basic Research Foundation(Grant No.2019A1515110184)the National Key R&D Program of the Ministry of Science and Technology of China(Grant Nos.2020YFA0713400 and 2020YFA0713401)。
文摘The Accelerated Hermitian/skew-Hermitian type Richardson(AHSR)iteration methods are presented for solving non-Hermitian positive definite linear systems with three schemes,by using Anderson mixing.The upper bounds of spectral radii of iteration matrices are studied,and then the convergence theories of the AHSR iteration methods are established.Furthermore,the optimal iteration parameters are provided,which can be computed exactly.In addition,the application to the model convection-diffusion equation is depicted and numerical experiments are conducted to exhibit the effectiveness and confirm the theoretical analysis of the AHSR iteration methods.
