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Journals and Conferences
In this paper we consider the numerical simulations of the incompressible materials on an unbounded domain in <2. A series of artificial boundary conditions at a circular artificial boundary for solving incompressible materials on an unbounded domain is given. Then the original problem is reduced to a problem on a bounded domain, which be solved numerically… (More)
A local time-splitting method (LTSM) is developed to design absorbing boundary conditions for numerical solutions of time-dependent nonlinear Schrödinger equations associated with open boundaries. These boundary conditions are significant for numerical simulations of propagations of nonlinear waves in physical applications, such as nonlinear fiber optics… (More)
Bounds are obtained for the derivatives of the solution of a turning point problem. These results suggest a modification of the El-Mistikawy Werle finite difference scheme at the turning point. A uniform error estimate is obtained for the resulting method, and illustrative numerical results are given.
In this paper, we propose a tailored-finite-point method for a type of linear singular perturbation problem in two dimensions. Our finite point method has been tailored to some particular properties of the problem. Therefore, our new method can achieve very high accuracy with very coarse mesh even for very small ε, i.e. the boundary layers and interior… (More)
In this paper we present error estimates for the finite element approximation of linear elliptic problems in unbounded domains that are outside an obstacle and a semi-infinite strip in the plane. The finite element approximation is formulated on a bounded domain using a nonlocal approximate artificial boundary condition. In fact there is a family of… (More)
Abstract. In this paper, we propose to use the tailored-finite-point method (TFPM) for a type of steady-state reaction-diffusion problems in two dimensions. Three tailored finite point schemes are constructed for the given problem. Our finite point method has been tailored to some particular properties of the problem. Therefore, our TFPM satisfies the… (More)
Abstract. In this paper, we study a uniformly second order numerical method for the discreteordinate transport equation in the slab geometry in the diffusive regimes with interfaces. At the interfaces, the scattering coefficients have discontinuities, so suitable interface conditions are needed to define the unique solution. We first approximate the… (More)
In this paper, we mainly consider the three dimensional Neumann problem in linear elasticity, which is reduced to a system of integro-diierential equations on the boundary based on a new representation of the derivatives of the double-layer potential. Furthermore a new boundary nite element method for this Neumann problem is presented.
We study the numerical solution of semilinear parabolic PDEs on unbounded spatial domains in R2 whose solutions blow up in finite time. Of particular interest are the cases where = R2 or is a sectorial domain in R2. We derive the nonlinear absorbing boundary conditions for corresponding, suitably chosen computational domains and then employ a simple… (More)