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1.
This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality. The unknown coefficient of the operator depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained.  相似文献   

2.
Numerical Analysis on Effects of Wall Structures on Bubble Groups   总被引:1,自引:1,他引:0  
With the volume of fluid (VOF) method for a dam-break problem, the effects of wall structures on compressible bubble groups were studied through measurement of the spatial average pressure on the wall. An obstacle was set up at the bottom of the tank, which helps create air bubbles in the collapsing water impacting on it. Three kinds of structures were set up on the left wall, namely, a cuboidal structure, an ellipsoidal structure and a conical structure. It is found that when water hits the left wall, the topology of the bubble wrapped in the water will be changed by the wall structure, which leads to the change of pressure on the wall. The example analysis shows that, the cuboidal structure has the maximum effect in reducing the average pressure amplitude on the wall among those three kinds of wall structures. Especially, a proper adjustment of the position and the size of the cuboidal structure can eliminate the oscillation of the wall pressure.  相似文献   

3.
In this paper,we extend the following results to the case of two variables:S.Mandelbrojit'stheorems on the differentiable classes and on the trigonometric classes;H.Cartan's theorems on theclasses of composition and on the equivalence of two classes on a finite interval.All the results in thispaper can be transfered immediately to the case of more than two variables.  相似文献   

4.
《应用数学和力学》2016,(Z1):105-116
The foundation structure with piles and slab is widely used in o?shore wind farm construction in shallow water. Experimental studies on the hydrodynamic loads acting on the piles and slab under irregular waves and currents are summarized with discussion on the e?ects of pile grouping on the wave forces and wave impact loads on the slab locating near the free surface. By applying the theoretical solution of the wave di?racted by the slab and using the Morison equation to evaluate the wave force on the piles, the e?ects of the slab on the wave forces acting on the piles are analyzed. Based on the Reynolds-averaged Navier-Stokes (RANS) equations and the volume of ?uid (VOF) method, a numerical wave basin is developed to simulate the wave-structure interaction. The computed maximum wave force on the foundation structure with piles and slab agrees well with the measured data. The violent deformation, breaking, and run-up of the wave around the structure are presented and discussed. Further work on the turbulent ?ow structures and large deformation of the free surface due to interaction of the waves and foundation structures of o?shore wind farms needs more e?cient approaches for evaluating hydrodynamic loads under the e?ects of nonlinear waves and currents.  相似文献   

5.
In this survey paper we report on recent developments of the hp-version of the boundary element method (BEM). As model problems we consider weakly singular and hypersingular integral equations of the first kind on a planar, open surface. We show that the Galerkin solutions (computed with the hp-version on geometric meshes) converge exponentially fast towards the exact solutions of the integral equations. An hp-adaptive algorithm is given and the implementation of the hp-version BEM is discussed together with the choice of efficient preconditioners for the ill-conditioned boundary element stiffness matrices. We also comment on the use of the hp-version BEM for solving Signorini contact problems in linear elasticity where the contact conditions are enforced only on the discrete set of Gauss-Lobatto points. Numerical results are presented which underline the theoretical results.  相似文献   

6.
This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation. The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained in the appropriate class of admissible coefficients.  相似文献   

7.
Field experiments are performed on a two-bladed 33 kW horizontal-axis wind turbine (HAWT). The pressures are measured with 191 pressure sensors positioned around the surfaces of seven spanwise section airfoils on one of the two blades. Three-dimensional (3D) and two-dimensional (2D) numerical simulations are performed, respectively, on the rotor and the seven airfoils of the blade. The results are compared with the experimental results of the pressure distribution on the seven airfoils and the lift coe?cients. The 3D rotational e?ect on the blade aerodynamic characteristics is then studied with a numerical approach. Finally, some conclusions are drawn as follows. From the tip to the root of the blade, the experimental di?erential pressure of the blade section airfoil increases at ?rst and then decreases gradually. The calculated 3D result of the pressure distribution on the blade surface is closer to that of the experiment than the 2D result. The 3D rotational e?ect has a signi?cant impact on the blade surface ?ow and the aerodynamic load, leading to an increase of the di?erential pressure on the airfoils and their lift coe?cient than that with the 2D one because of the stall delay. The in?uence of the 3D rotational e?ect on the wind turbine blade especially takes place on the sections with ?ow separation.  相似文献   

8.
The proof of the index formula of the Toeplitz operator with a continuous symbol on the Hardy space for the unit circle in the complex plane depends on the Hopf theorem. However, the analogue result of the Hopf theorem does not hold on a general connected domain. Hence, the extension of the index formula of the Toeplitz operator on a general domain needs a method which is different from that for the case of the unit circle. In the present paper, the index formula of the Toeplitz operator with a continuous symbol on the finite complex connected domain in the complex plane is obtained, and the cohomology groups of Toeplitz algebras on general domains are discussed. In addition, the Toeplitz operators with symbols in QC are also discussed.  相似文献   

9.
Geometry of Ricci Solitons   总被引:1,自引:0,他引:1  
Ricci solitons are natural generalizations of Einstein metrics on one hand, and are special solutions of the Ricci flow of Hamilton on the other hand. In this paper we survey some of the recent developments on Ricci solitons and the role they play in the singularity study of the Ricci flow.  相似文献   

10.
The screening effect is the phenomenon that optimal linear prediction of a spatial process on an unobserved location mostly depends on nearby observations.That is,the optimal predictor based on just nearby observations yields a good approximation of which based on the whole large dataset.However,the approximation does not always perform well since the screening effect may not hold in all situations.To determine when the screening effect holds is an important issue in spatial statistics.This paper provides some sufficient conditions for ensuring an asymptotic screening effect in Rd based on the spectral density of the underlying isotropic Gaussian process and the geometries of nearby observations.These results apply to isotropic processes with an arbitrary degree of differentiability.Assuming we are predicting at origin,the conditions are(1)the spectral density is nearly a constant in balls of finite radius far from the origin,(2)the positions of nearby observations do not fall on a curve with non-zero intercept whose degree is less or equal to the order of mean square differentiability of the process.These conditions are easy to verify in practice.Convergence rates of the asymptotic screening effect are also obtained.These rates depend on the rate of decrease of the spectral density.Simulation studies on the screening effect for finite samples are also provided.  相似文献   

11.
In this paper, we investigate the negative extremums of fundamental functions of Lagrange interpolation based on Chebyshev nodes. Moreover, we establish some companion results to the theorem of J. Szabados on the positive extremum.  相似文献   

12.
With Newton's interpolating formula, we construct a kind of block based Newton-like blending osculatory interpolation.The interpolation provides us many flexible interpolation schemes for choices which include the expansive Newton's polynomial inter- polation as its special case. A bivariate analogy is also discussed and numerical examples are given to show the effectiveness of the interpolation.  相似文献   

13.
Lagrange插值和Hermite-Fejér插值在Wiener空间下的平均误差   总被引:1,自引:0,他引:1  
许贵桥 《数学学报》2007,50(6):1281-129
在L_q-范数逼近的意义下,确定了基于Chebyshev多项式零点的Lagrange插值多项式列和Hermite-Fejér插值多项式列在Wiener空间下的p-平均误差的弱渐近阶.从我们的结果可以看出,当2≤q<∞,1≤p<∞时,基于第一类Chebyshev多项式零点的Lagrange插值多项式列和Hermite-Fejér插值多项式列的p-平均误差弱等价于相应的最佳逼近多项式列的p-平均误差.在信息基计算复杂性的意义下,如果可允许信息泛函为计算函数在固定点的值,那么当1≤p,q<∞时,基于第一类Chebyshev多项式零点的Lagrange插值多项式列和Hermite-Fejér插值多项式列在Wiener空间下的p-平均误差弱等价于相应的最小非自适应p-平均信息半径.  相似文献   

14.
This paper is an extension of earlier papers [8, 9] on the "native" Hilbert spaces of functions on some domain Ωbelong toR^d Rd in which conditionally positive definite kernels are reproducing kernels. Here, the focus is on subspaces of native spaces which are induced via subsets of Ω, and we shall derive a recursive subspace structure of these, leading to recur- sively defined reproducing kernels. As an application, we get a recursive Neville-Aitken- type interpolation process and a recursively defined orthogonal basis for interpolation by translates of kernels.  相似文献   

15.
Multivariate Hermite interpolation is widely applied in many fields, such as finite element construction, inverse engineering, CAD etc.. For arbitrarily given Hermite interpolation conditions, the typical method is to compute the vanishing ideal I (the set of polynomials satisfying all the homogeneous interpolation conditions are zero) and then use a complete residue system modulo I as the interpolation basis. Thus the interpolation problem can be converted into solving a linear equation system. A generic algorithm was presented in [18], which is a generalization of BM algorithm [22] and the complexity is O(τ^3) where r represents the number of the interpolation conditions. In this paper we derive a method to obtain the residue system directly from the relative position of the points and the corresponding derivative conditions (presented by lower sets) and then use fast GEPP to solve the linear system with O((τ + 3)τ^2) operations, where τ is the displacement-rank of the coefficient matrix. In the best case τ = 1 and in the worst case τ = [τ/n], where n is the number of variables.  相似文献   

16.
This paper is concerned with a Chebyshev quadrature rule for approximating one sided finite part integrals with smooth density functions. Our quadrature rule is based on the Chebyshev interpolation polynomial with the zeros of the Chebyshev polynomial TN+1(τ)−TN−1(t). We analyze the stability and the convergence for the quadrature rule with a differentiable function. Also we show that the quadrature rule has an exponential convergence when the density function is analytic.  相似文献   

17.
This paper is to study the convergence and superconvergence of rectangular finite elements under anisotropic meshes. By using of the orthogonal expansion method, an anisotropic Lagrange interpolation is presented. The family of Lagrange rectangular elements with all the possible shape function spaces are considered, which cover the Intermediate families, Tensor-product families and Serendipity families. It is shown that the anisotropic interpolation error estimates hold for any order Sobolev norm. We extend the convergence and superconvergence result of rectangular finite elements to arbitrary rectangular meshes in a unified way.  相似文献   

18.
In this paper we study the problem of explicit representation and convergence of Pal type (0;1) interpolation and its converse, with some additional conditions, on the non-uniformly distributed nodes on the unit circle obtaIned by projecting the interlaced zeros of Pn (x) and Pn′ (x) on the unit circle. The motivation to this problem can be traced to the recent studies on the regularity of Birkhoff interpolation and Pal type interpolations on non-uniformly distributed zeros on the unit circle.  相似文献   

19.
We obtain explicit expansions of the fundamental Hermite interpolation polynomials in terms of Chebyshev polynomials in the case where the nodes considered are either zeros of the (n + 1)th-degree Chebyshev polynomial or extremum points of the nth-degree Chebyshev polynomial.  相似文献   

20.
In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other.  相似文献   

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