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 This paper mainly designs artificial boundary conditions for "vortex in cell" method in solving two-dimensional incompressible inviscid fluid under two conditions: one is with periodical initial value in one direction and the other with compact supported initial value. To mimic the vortex motion, Euler equation is transformed into vorticity-stream function and the technique of vortex in cell is applied incorporating with the artificial boundary conditions.

In this paper, nonreflecting artificial boundary conditions are considered for an acoustic problem in three dimensions. With the technique of Fourier decomposition under the orthogonal basis of spherical harmonics, three kinds of equivalent exact artificial boundary conditions are obtained on a spherical artificial boundary. A numerical test is presented to show the performance of the method.

 In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal ${\rm H}^1$ and ${\rm L}^2$ error bounds independent of the plate thickness are derived under a mild assumption on the mesh partition.

In this paper, a new high accuracy numerical method for the thin-film problems of micron and submicron size ferromagnetic elements is proposed. For the computation of stray field, we use the finite element method (FEM) by introducing a semi-discrete artificial boundary condition [1,2]. In our numerical experiments about the domain patterns and their movement, we can see that the results are accordant to that of experiments and other numerical methods. Our method is very convenient to deal with arbitrary shape of thin films such as a polygon with high accuracy.

In the present work we are going to solve the boundary value problem for the quasilinear parabolic systems of partial differential equations with two space dimensions by the finite difference method with intrinsic parallelism. Some fundamental behaviors of general finite difference schemes with intrinsic parallelism for the mentioned problems are studied. By the method of a priori estimation of the discrete solutions of the nonlinear difference systems, and the interpolation formulas of the various norms of the discrete functions and the fixed point technique in finite dimensional Euclidean apace, the existence of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover, the convergence of the discrete vector solutions of these difference schemes to the unique generalized solution of the original quasilinear parabolic problem is proved.

This paper finds a way to extend the well-known Fourier methods, to so-called n+1 directions partition domains in n-dimension. In particular, in 2-D and 3-D cases, we study Fourier methods over 3-direction parallel hexagon partitions and 4-direction parallel parallelogram dodecahedron partitions, respectively. It has pointed that, the most concepts and results of Fourier methods on tensor-product case, such as periodicity, orthogonality of Fourier basis system, partial sum of Fourier series and its approximation behavior, can be moved on the new non tensor-product partition case.

 In this paper we are going to discuss the difference schemes with intrinsic parallelism for the boundary value problem of the two dimensional semilinear parabolic systems. The unconditional stability of the general finite difference schemes with intrinsic parallelism is justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problems in the discrete $W^{(1,2)}_2$ norms. Then the uniqueness of the discrete vector solution of this difference scheme follows as the consequence of the stability.

Linear systems associated with numerical methods for constrained optimization are discussed in this paper. It is shown that the corresponding subproblems arise in most well-known methods, no matter line search methods or trust region methods for constrained optimization can be expressed as similar systems of linear equations. All these linear systems can be viewed as some kinds of approximation to the linear system derived by the Lagrange-Newton method. Some properties of these linear systems are analyzed.  

  In this paper, we investigate multi-scale methods for the inverse modeling in 1-D Metal-Oxide-Silicon (MOS) capacitor. First, the mathematical model of the device is given and the numerical simulation for the forward problem of the model is implemented using finite element method with adaptive moving mesh. Then numerical analysis of these parameters in the model for the inverse problem is presented. Some matrix analysis tools are applied to explore the parameters' sensitivities. And third, the parameters are extracted using Levenberg-Marquardt optimization method. The essential difficulty arises from the effect of multi-scale physical difference of the parameters. We explore the relationship between the parameters' sensitivities and the sequence for optimization, which can seriously affect the final inverse modeling results. An optimal sequence can efficiently overcome the multi-scale problem of these parameters. Numerical experiments show the efficiency of the proposed methods.

In this paper we present high-order I-stable centered difference schemes for the numerical simulation of viscous compressible flows. Here I-stability refers to time discretizations whose linear stability regions contain part of the imaginary axis. This class of schemes has a numerical stability independent of the cell-Reynolds number $Rc$, thus allows one to simulate high Reynolds number flows with relatively larger $Rc$, or coarser grids for a fixed $Rc$. On the other hand, $Rc$ cannot be arbitrarily large if one tries to obtain adequate numerical resolution of the viscous behavior. We investigate the behavior of high-order I-stable schemes for Burgers' equation and the compressible Navier-Stokes equations. We demonstrate that, for the second order scheme, $Rc\leq3$ is an appropriate constraint for numerical resolution of the viscous profile, while for the fourth-order schemes the constraint can be relaxed to $Rc\leq6$. Our study indicates that the fourth order scheme is preferable: better accuracy, higher resolution, and larger cell-Reynolds numbers.