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1.
The acoustical scattering by a cracked elastic structure is studied. The mixed method of boundary element and fractal finite element is adopted to solve the cracked structure-acoustic coupling problem. The fractal two-level finite element method is employed for the cracked structure, which can reduce the degree of freedoms (DOFs) greatly, and the boundary element method is used for the exterior acoustic field which can automatically satisfy Sommerfeld‘s radiation condition. Numerical examples show that the resonance frequency is lower with the crack‘s depth increase, and that the effect on the acoustical field by the crack is particularly pronounced in the vicinity of the crack tip. This mixed method of boundary element and finite element is effective in solving the scattering problem by a cracked structure.  相似文献   

2.
Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.  相似文献   

3.
In this article,a direct stress approach based on finite element analysis to determine the stress intensity fac-tor is improved.Firstly,by comparing the rigorous solution against the asymptotic solution for a problem of an infinite plate embedded a central crack,we found that the stresses in a restrictive interval near the crack tip given by the rigorous solution can be used to determine the stress intensity fac-tor,which is nearly equal to the stress intensity factor given by the asymptotic solution.Secondly,the crack problem is solved numerically by the finite element method.Depending on the modeling capability of the software,we designed an adaptive mesh model to simulate the stress singularity.Thus, the stress result in an appropriate interval near the crack tip is fairly approximated to the rigorous solution of the corre-sponding crack problem.Therefore,the stress intensity factor may be calculated from the stress distribution in the appro-priate interval,with a high accuracy.  相似文献   

4.
The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential equations.The electric potential equation is approximated by a mixed finite element method,and the concentration equations are approximated by a standard Galerkin method.We estimate the error of the numerical solutions in the sense of the Lqnorm.To linearize the full discrete scheme of the problem,we present an efficient two-grid method based on the idea of Newton iteration.The main procedures are to solve the small scaled nonlinear equations on the coarse grid and then deal with the linear equations on the fine grid.Error estimation for the two-grid solutions is analyzed in detail.It is shown that this method still achieves asymptotically optimal approximations as long as a mesh size satisfies H=O(h^1/2).Numerical experiments are given to illustrate the efficiency of the two-grid method.  相似文献   

5.
In this paper, a new analytical method of symplectic system, Hamiltonian system, is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain. In the system, the fundamental problem is reduced to an eigenvalue and eigensolution problem. The solution and boundary conditions can be expanded by eigensolutions using adjoint relationships of the symplectic ortho-normalization between the eigensolutions. A closed method of the symplectic eigensolution is presented based on completeness of the symplectic eigensolution space. The results show that fundamental flows can be described by zero eigenvalue eigensolutions, and local effects by nonzero eigenvalue eigensolutions. Numerical examples give various flows in a rectangular domain and show effectiveness of the method for solving a variety of problems. Meanwhile, the method can be used in solving other problems.  相似文献   

6.
Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems,a goal-oriented error estimation method with extended degrees of freedom is developed.It leads to the high quality local error bounds in the problem of the direct-solution steady-state dynamic analysis with a frequency-domain finite element,which involves the enrichments with plural variable basis functions.The solution of the steady-state dynamic procedure calculates the harmonic response directly in terms of the physical degrees of freedom in the model,which uses the mass,damping,and stiffness matrices of the system.A three-dimensional finite element example is carried out to illustrate the computational procedures.  相似文献   

7.
This paper extends the results of Matthies, Skrzypacz, and Tubiska for the Oseen problem to the Navier-Stokes problem. For the stationary incompressible Navier- Stokes equations, a local projection stabilized finite element scheme is proposed. The scheme overcomes convection domination and improves the restrictive inf-sup condition. It not only is a two-level approach but also is adaptive for pairs of spaces defined on the same mesh. Using the approximation and projection spaces defined on the same mesh, the scheme leads to much more compact stencils than other two-level approaches. On the same mesh, besides the class of local projection stabilization by enriching the approximation spaces, two new classes of local projection stabilization of the approximation spaces are derived, which do not need to be enriched by bubble functions. Based on a special interpolation, the stability and optimal prior error estimates are shown. Numerical results agree with some benchmark solutions and theoretical analysis very well.  相似文献   

8.
Local and parallel finite element algorithms based on two-grid discretization for Navier-Stokes equations in two dimension are presented. Its basis is a coarse finite element space on the global domain and a fine finite element space on the subdomain. The local algorithm consists of finding a solution for a given nonlinear problem in the coarse finite element space and a solution for a linear problem in the fine finite element space, then droping the coarse solution of the region near the boundary. By overlapping domain decomposition, the parallel algorithms are obtained. This paper analyzes the error of these algorithms and gets some error estimates which are better than those of the standard finite element method. The numerical experiments are given too. By analyzing and comparing these results, it is shown that these algorithms are correct and high efficient.  相似文献   

9.
For transient Naiver-Stokes problems, a stabilized nonconforming finite element method is presented, focusing on two pairs inf-sup unstable finite element spaces, i.e., pNC/pNC triangular and pNQ/pNQ quadrilateral finite element spaces. The semi- and full-discrete schemes of the stabilized method are studied based on the pressure projection and a variational multi-scale method. It has some attractive features: avoiding higher-order derivatives and edge-based data structures, adding a discrete velocity term only on the fine scale, being effective for high Reynolds number fluid flows, and avoiding increased computation cost. For the full-discrete scheme, it has second-order estimations of time and is unconditionally stable. The presented numerical results agree well with the theoretical results.  相似文献   

10.
Based on local algorithms, some parallel finite element(FE) iterative methods for stationary incompressible magnetohydrodynamics(MHD) are presented. These approaches are on account of two-grid skill include two major phases: find the FE solution by solving the nonlinear system on a globally coarse mesh to seize the low frequency component of the solution, and then locally solve linearized residual subproblems by one of three iterations(Stokes-type, Newton, and Oseen-type) on subdomains with fine...  相似文献   

11.
A fully discrete postprocessing mixed finite element scheme is considered for solving the time-dependent Navier–Stokes equations. In the PP method, we only consider a non-linear equation in the coarse-level subspace and a linear problem in the fine-level subspace. The analysis shows that the PP scheme can reach the same accuracy as the standard Galerkin method with a very fine mesh size h by an appropriate choice of H. Numerical examples are provided that confirm both the theoretical analysis and the corresponding improvement in computational efficiency.  相似文献   

12.
A new stabilized finite element method is considered for the time‐dependent Stokes problem, based on the lowest‐order P1?P0 and Q1?P0 elements that do not satisfy the discrete inf–sup condition. The new stabilized method is characterized by the features that it does not require approximation of the pressure derivatives, specification of mesh‐dependent parameters and edge‐based data structures, always leads to symmetric linear systems and hence can be applied to existing codes with a little additional effort. The stability of the method is derived under some regularity assumptions. Error estimates for the approximate velocity and pressure are obtained by applying the technique of the Galerkin finite element method. Some numerical results are also given, which show that the new stabilized method is highly efficient for the time‐dependent Stokes problem. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

13.
A finite element method for solution of the stream function formulation of Stokes flow is developed. The method involves complete cubic non-conforming (C0) triangular Hermite elements. This element fails the patch test. To correct the element and produce a convergent method we employ a penalty method to weakly enforce the desired continuity constraint on the normal derivative across the inter-element boundaries. Successful use of the method is demonstrated to require reduced integration of the inter-element penalty with a 1-point Gauss rule. Error estimates relate the optimal choice of penalty parameter to mesh size and are corroborated by numerical convergence studies. The need for reduced integration is interpreted using rank relations for an associated hybrid method.  相似文献   

14.
A numerical algorithm to determine the impingement of an axisymmetric free jet upon a curved deflector is presented. The problem is considered within the potential flow theory with the allowance of gravity and surface tension effects. The primary dependent variable is the Stokes streamfunction, which is approximated through finite elements using the isoparametric Hermite Zienkiewicz element. To find the correct position of the free boundaries, a trial-and-error method is employed which amounts to solving a boundary value problem (BVP) for the Stokes streamfunction at each iteration step. An efficient method is proposed to solve this BVP. The algorithm to find the correct position of the free boundaries is tested by computing the impingement upon an infinite disc and a hemispherical deflector. To confirm the correctness of the solution, each problem has been solved using several different mesh gradings. A comparison between the Zienkiewicz and the other standard C0 finite elements is also given.  相似文献   

15.
This paper discusses the influence of the stabilization parameter on the convergence factor of various iterative methods for the solution of the Stokes problem discretized by the so-called locally stabilized Q1-P0 finite element. Our objective is to point out optimal parameters which ensure rapid convergence. The first part of the paper is concerned with the dual formulation of the problem. It gives the theoretical precision and practical developments of our stabilized context Uzawa-type algorithm. We assert that the convergence factor of such a method is majored independently of the mesh size by a function of the stabilization parameter. Moreover, we point out that there exists an optimal value of this parameter that minimizes this upper bound. This gives a theoretical justification of pre-existing numerical results. We show that the optimal parameter can be determined a priori. This is a key point when the method has to be implemented. Finally, we base an interpretation of the iterated penalty method numerical behaviour on some theoretical results about the minimum eigenvalue of the stabilized dual operator. This algorithm involves a penalty parameter and a stabilization parameter and we discuss a strategy for choosing optimal parameters. The mixed formulation of the problem is dealt with in the second part of the paper, which proposes several preconditioned conjugate-gradient-type methods. The indefinite character of the problem makes it intrinsically hard. However, if one chooses a suitable preconditioner, this difficulty is overcome, since the preconditioned operator becomes positive definite. We study the eigenvalue spectrum of the preconditioned operator and thereby the convergence factor of the algorithm. In contrast with the two previous formulations, we show that this convergence factor is majored independently of the stabilization parameter. More precisely, we point out convergence factors comparable with those obtained for Poisson-type problems. Finally, we present a variant of the latter method which uses our so-called macroblock-type preconditioner. A comparison with the simple case of diagonal preconditioning is addressed and the improved performance of the macroblock-type preconditioner is evidenced. Various 2D numerical experiments are given to corroborate the theories presented herein.  相似文献   

16.
Electrical double-layer effects are unimportant in flows through porous media except when the Debye length k?1 is comparable in magnitude with the pore radius a. Under these conditions the equations governing the flow of electrolyte are those of Stokes, Nernst-Planck and Poisson. These equations are non-linear and require numerical solution. The finite element method provides a useful basis for solution and various algorithms are investigated. The numerical stability and errors of each scheme are analysed together with the development of an appropriate finite element mesh. The electro-osmotic flow of a typical electrolyte (barium chloride) through a uniformly charged cylindrical membrane pore is investigated and the ion fluxes are post-computed from the numerical solutions. The ion flux is shown to be strongly dependent on both zeta potential and pore radius, ka, indicating the effects of overlapping electrical double layers.  相似文献   

17.
General Galerkin (G2) is a new computational method for turbulent flow, where a stabilized Galerkin finite element method is used to compute approximate weak solutions to the Navier–Stokes equations directly, without any filtering of the equations as in a standard approach to turbulence simulation, such as large eddy simulation, and thus no Reynolds stresses are introduced, which need modelling. In this paper, G2 is used to compute the drag coefficient cD for the flow past a circular cylinder at Reynolds number Re=3900, for which the flow is turbulent. It is found that it is possible to approximate cD to an accuracy of a few percent, corresponding to the accuracy in experimental results for this problem, using less than 105 mesh points, which makes the simulations possible using a standard PC. The mesh is adaptively refined until a stopping criterion is reached with respect to the error in a chosen output of interest, which in this paper is cD. Both the stopping criterion and the mesh‐refinement strategy are based on a posteriori error estimates, in the form of a space–time integral of residuals times derivatives of the solution of a dual problem, linearized at the approximate solution, and with data coupling to the output of interest. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

18.
The scope of this paper is to present a nonlinear error estimation and correction for Navier-Stokes and Reynolds-averaged Navier-Stokes equations. This nonlinear corrector enables better solution or functional output predictions at fixed mesh complexity and can be considered in a mesh adaptation process. After solving the problem at hand, a corrected solution is obtained by solving again the problem with an added source term. This source term is deduced from the evaluation of the residual of the numerical solution interpolated on the h/2 mesh. To avoid the generation of the h/2 mesh (which is prohibitive for realistic applications), the residual at each vertex is computed by local refinement only in the neighborhood of the considered vertex. One of the main feature of this approach is that it automatically takes into account all the properties of the considered numerical method. The numerical examples point out that it successfully improves solution predictions and yields a sharp estimate of the numerical error. Moreover, we demonstrate the superiority of the nonlinear corrector with respect to linear corrector that can be found in the literature.  相似文献   

19.
Türk  Önder 《Meccanica》2020,55(10):2021-2031
Meccanica - In this paper, we consider a stabilized finite element method for the approximation of the Stokes eigenvalue problem on triangular domains. The method depends on orthogonal subscales...  相似文献   

20.
An adaptive finite element approximation for an optimal control problem of the Stokes flow with an L2‐norm state constraint is proposed. To produce good adaptive meshes, the a posteriori error estimates are discussed. The equivalent residual‐type a posteriori error estimators of the H 1‐error of state and L2‐error of control are given, which are suitable to carry out the adaptive multi‐mesh finite element approximation. Some numerical experiments are performed to illustrate the efficiency of the a posteriori estimators. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

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