The incompressible Navier-Stokes (INS) equations upon discretization on fixed meshes become a system of differential algebraic equations (DAE) of index 2. It is proved in this paper that for the general explicit and i...
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The incompressible Navier-Stokes (INS) equations upon discretization on fixed meshes become a system of differential algebraic equations (DAE) of index 2. It is proved in this paper that for the general explicit and implicit Runge-Kutta (RK)methods, the time accuracy of velocity is the same as that for the ordinary differential equations, by taking into consideration of the special form of the resulting DAE; (the time accuracy of pressure can be lower). For the three-stage secondorder explicit RK method, algorithms with less (than three) Poisson solutions of pressure are proposed and verified by numerical experiments. However, in practical computation of complex flows it is found that the method must satisfy the so-called consistency condition for the components of the solution (here the velocity and the pressure) of the DAE for the method to be robust.
In this papert we discuss the inverse problem of 1-dimensional acoustic wave equation and propose an approximate inversion method, called multi-reflection elimination method, with which the approximate reflectivity fu...
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In this papert we discuss the inverse problem of 1-dimensional acoustic wave equation and propose an approximate inversion method, called multi-reflection elimination method, with which the approximate reflectivity function can be directly obtained by applying a certain transform to the response. The computation efforts for such method is only of the order N log N, much less than that of solving the direct problem, which is O(N2). On the basis of the proposed method, we also construct an iterative algorithm, and prove that the convergent order of iteration is two.
In this paper, we develop a two-level additive Schwarz preconditioner for Morley element using nonnested meshes. We define an intergrid transfer operator that satisfies certain stable approximation properties by using...
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In this paper, we develop a two-level additive Schwarz preconditioner for Morley element using nonnested meshes. We define an intergrid transfer operator that satisfies certain stable approximation properties by using a conforming interpolation operator and construct a uniformly bounded decomposition for the finite element space. Both coarse and fine grid spaces are nonconforming. We get optimal convergence properties of the additive Schwarz algorithm that is constructed on nonnested meshes and with a not necessarily shape regular subdomain partitioning. Our analysis is based on the theory of Dryja and *** is interesting to mention that when coarse and fine spaces are all nonconforming, a natural intergrid operator seems to be one defined by taking averages of the nodal parameters. In this way, we obtain the stable factor (H/h)3/2, and show that this factor can not be improved. However, to get an optimal preconditioner,we need in general the stability with a factor C independent of mesh ***. the latter can not be used in this case.
A new finite volume scheme, based on first order monotone scheme and limited linear reconstruction, is constructed for scalar hyperbolic conservation laws in two dimension,the scheme satisfies the maximum principle an...
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A new finite volume scheme, based on first order monotone scheme and limited linear reconstruction, is constructed for scalar hyperbolic conservation laws in two dimension,the scheme satisfies the maximum principle and approximation the flux with second order accuracy. Numerical results for constant coefficient linear advection and Burgers’equation are presented.
SLMQN is a subspace limited memory quasi-Newton algorithm for solving largescale bound constrained nonlinear programming problems. The algorithm is suitable to these large problems in which the Hessian matrix is diffi...
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SLMQN is a subspace limited memory quasi-Newton algorithm for solving largescale bound constrained nonlinear programming problems. The algorithm is suitable to these large problems in which the Hessian matrix is difficult to compute or is dense,or the number of variables is too large to store and compute an n x n matris. Due to less storage requirement, this algorithm can be used in PCs for solving medium-sized and large problems. The algorithm is implemented in Fortran 77.
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