In this paper, we use the flux ENO scheme for the multiresolution scheme and simplify the original scheme based on the cell average ENO. As it is well known that the present scheme may will not be conservative at disc...In this paper, we use the flux ENO scheme for the multiresolution scheme and simplify the original scheme based on the cell average ENO. As it is well known that the present scheme may will not be conservative at discontinuities, but numerical solutions are acceptable in practice.展开更多
The proper orthogonal decomposition （POD） is a model reduction technique for the simulation Of physical processes governed by partial differential equations （e.g., fluid flows）. It has been successfully used in th...The proper orthogonal decomposition （POD） is a model reduction technique for the simulation Of physical processes governed by partial differential equations （e.g., fluid flows）. It has been successfully used in the reduced-order modeling of complex systems. In this paper, the applications of the POD method are extended, i.e., the POD method is applied to a classical finite difference （FD） scheme for the non-stationary Stokes equation with a real practical applied background. A reduced FD scheme is established with lower dimensions and sufficiently high accuracy, and the error estimates are provided between the reduced and the classical FD solutions. Some numerical examples illustrate that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the reduced FD scheme based on the POD method is feasible and efficient in solving the FD scheme for the non-stationary Stokes equation.展开更多
In this paper, we study, via variational methods, the problem of scattering of time harmonic acoustic waves by unbounded inhomogeneous layers above a sound soft rough surface. We first propose a variational formulatio...In this paper, we study, via variational methods, the problem of scattering of time harmonic acoustic waves by unbounded inhomogeneous layers above a sound soft rough surface. We first propose a variational formulation and exploit it as a theoretical tool to prove the well-posedness of this problem when the media is non-absorbing for arbitrary wave number and obtain an estimate about the solution, which exhibit explicitly dependence of bound on the wave number and on the geometry of the domain. Then, based on the non-absorbing results, we show that the variational problem remains uniquely solvable when the layer is absorbing by means of a priori estimate of the solution. Finally, we consider the finite element approximation of the problem and give an error estimate.展开更多
文摘In this paper, we use the flux ENO scheme for the multiresolution scheme and simplify the original scheme based on the cell average ENO. As it is well known that the present scheme may will not be conservative at discontinuities, but numerical solutions are acceptable in practice.
基金Project supported by the National Natural Science Foundation of China (Nos. 10871022, 11061009, and 40821092)the National Basic Research Program of China (973 Program) (Nos. 2010CB428403, 2009CB421407, and 2010CB951001)the Natural Science Foundation of Hebei Province of China (No. A2010001663)
文摘The proper orthogonal decomposition （POD） is a model reduction technique for the simulation Of physical processes governed by partial differential equations （e.g., fluid flows）. It has been successfully used in the reduced-order modeling of complex systems. In this paper, the applications of the POD method are extended, i.e., the POD method is applied to a classical finite difference （FD） scheme for the non-stationary Stokes equation with a real practical applied background. A reduced FD scheme is established with lower dimensions and sufficiently high accuracy, and the error estimates are provided between the reduced and the classical FD solutions. Some numerical examples illustrate that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the reduced FD scheme based on the POD method is feasible and efficient in solving the FD scheme for the non-stationary Stokes equation.
基金The Education Department.(12531136) of Heilongjiangthe NSF(10971083,51178001) of ChinaScience and Technology Research Project.(2014213) of Jilin Province Department of Education
文摘In this paper, we study, via variational methods, the problem of scattering of time harmonic acoustic waves by unbounded inhomogeneous layers above a sound soft rough surface. We first propose a variational formulation and exploit it as a theoretical tool to prove the well-posedness of this problem when the media is non-absorbing for arbitrary wave number and obtain an estimate about the solution, which exhibit explicitly dependence of bound on the wave number and on the geometry of the domain. Then, based on the non-absorbing results, we show that the variational problem remains uniquely solvable when the layer is absorbing by means of a priori estimate of the solution. Finally, we consider the finite element approximation of the problem and give an error estimate.
