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
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 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.
