In this study, the effects of magnetic field and nanoparticle on the Jeffery- Hamel flow are studied using a powerful analytical method called the Adomian decomposition method （ADM）. The traditional Navier-Stokes eq...In this study, the effects of magnetic field and nanoparticle on the Jeffery- Hamel flow are studied using a powerful analytical method called the Adomian decomposition method （ADM）. The traditional Navier-Stokes equation of fluid mechanics and Maxwell＇s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different a, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann ：number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.展开更多
We provide a concise review of the exponentially convergent multiscale finite element method(ExpMsFEM)for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave pr...We provide a concise review of the exponentially convergent multiscale finite element method(ExpMsFEM)for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation.The ExpMsFEM is built on the non-overlapped domain decomposition in the classical MsFEM while enriching the approximation space systematically to achieve a nearly exponential convergence rate regarding the number of basis functions.Unlike most generalizations of the MsFEM in the literature,the ExpMsFEM does not rely on any partition of unity functions.In general,it is necessary to use function representations dependent on the right-hand side to break the algebraic Kolmogorov n-width barrier to achieve exponential convergence.Indeed,there are online and offline parts in the function representation provided by the ExpMsFEM.The online part depends on the right-hand side locally and can be computed in parallel efficiently.The offline part contains basis functions that are used in the Galerkin method to assemble the stiffness matrix;they are all independent of the right-hand side,so the stiffness matrix can be used repeatedly in multi-query scenarios.展开更多
In this paper, we discuss the problem of stability of Volterra integrodifferential equationwith the decompositionwhere andin which is an matrix of functionB continuous forin which is an matrix of functionscontinuous f...In this paper, we discuss the problem of stability of Volterra integrodifferential equationwith the decompositionwhere andin which is an matrix of functionB continuous forin which is an matrix of functionscontinuous for 0≤S≤ t<∞.According to the decomposition theory of large scale system and with the help of Liapunovfunctional, we give a criterion for concluding that the zero solution of (2) (i.e. large scale system(1)) is uniformly asymptotically stable.We also discuss the large scale system with the decompositionand give a criterion for determining that the solutions of (4) (i.e. large scale system (3)) areuniformly bounded and uniformly ultimately bounded.Those criteria are of simple forms, easily checked and applied.展开更多
文摘In this study, the effects of magnetic field and nanoparticle on the Jeffery- Hamel flow are studied using a powerful analytical method called the Adomian decomposition method （ADM）. The traditional Navier-Stokes equation of fluid mechanics and Maxwell＇s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different a, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann ：number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.
基金part supported by the NSF Grants DMS-1912654 and DMS 2205590。
文摘We provide a concise review of the exponentially convergent multiscale finite element method(ExpMsFEM)for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation.The ExpMsFEM is built on the non-overlapped domain decomposition in the classical MsFEM while enriching the approximation space systematically to achieve a nearly exponential convergence rate regarding the number of basis functions.Unlike most generalizations of the MsFEM in the literature,the ExpMsFEM does not rely on any partition of unity functions.In general,it is necessary to use function representations dependent on the right-hand side to break the algebraic Kolmogorov n-width barrier to achieve exponential convergence.Indeed,there are online and offline parts in the function representation provided by the ExpMsFEM.The online part depends on the right-hand side locally and can be computed in parallel efficiently.The offline part contains basis functions that are used in the Galerkin method to assemble the stiffness matrix;they are all independent of the right-hand side,so the stiffness matrix can be used repeatedly in multi-query scenarios.
基金This project is supported by the National Natural Science Foundation of China
文摘In this paper, we discuss the problem of stability of Volterra integrodifferential equationwith the decompositionwhere andin which is an matrix of functionB continuous forin which is an matrix of functionscontinuous for 0≤S≤ t<∞.According to the decomposition theory of large scale system and with the help of Liapunovfunctional, we give a criterion for concluding that the zero solution of (2) (i.e. large scale system(1)) is uniformly asymptotically stable.We also discuss the large scale system with the decompositionand give a criterion for determining that the solutions of (4) (i.e. large scale system (3)) areuniformly bounded and uniformly ultimately bounded.Those criteria are of simple forms, easily checked and applied.
