共查询到20条相似文献,搜索用时 46 毫秒
1.
The solution for a line source of oscillatory strength kept at the origin in a wall bounding a semi-infinite viscous imcompressible stratified fluid is presented in an integral form. The behaviour of the flow at far field and near field is studied by an asymptotic expansion procedure. The streamlines for different parameters are drawn and discussed. The real characteristic straight lines present in the inviscid problem are modified by the viscosity and the solutions obtained are valid even at the resonance frequency. 相似文献
2.
In [4,6], the authors have presented a numerical method for the solution of complex minimax problems, which implicitly solves discretized versions of the equivalent semi-infinite programming problem on increasingly finer grids. While this method only requires the most violated constraint at the current iterate on a finite subset of the infinitely many constraints of the problem, we consider here a related and more direct approach (applicable to general convex semi-infinite programming problems) which makes use of the globally most violated constraint. Numerical examples with up to 500 unknowns, which partially originate from digital filter design problems, are discussed. 相似文献
3.
F.R. Villatoro J. Pérez J.L.G. Santander Yu.L. Ratis P. Fernández de Córdoba 《Journal of Mathematical Analysis and Applications》2011,374(1):57-70
An approximate analytical solution for the one-dimensional problem of heat transfer between an inert gas and a porous semi-infinite medium is presented. Perturbation methods based on Laplace transforms have been applied using the solid thermal conductivity as small parameter. The leading order approximation is the solution of Nusselt (or Schumann) problem. Such solution is corrected by means of an outer approximation. The boundary condition at the origin has been taking into account using an inner approximation for a boundary layer. The gas temperature presents a discontinuous front (due to the incompatibility between initial and boundary conditions) which propagates at constant velocity. The solid temperature at the front has been smoothed out using an internal layer asymptotic approximation. The good accuracy of the resulting asymptotic expansion shows its usefulness in several engineering problems such as heat transfer in porous media, in exhausted chemical reactions, mass transfer in packed beds, or in the analysis of capillary electrochromatography techniques. 相似文献
4.
The behaviour of a Herschel-Bulkley material near the apex ofa semi-infinite plate is studied. The plate is immersed in thecentre of a longitudinal strip the sides of which are subjectedto equal and opposite velocities. The problem is consideredin the hodograph plane, where it is possible to obtain a solution.Transforming this solution back to the real plane yields anexact expansion of the velocity field near the apex of the plate.The leading term of the velocity field is checked by using aninvariant integral which involves the energy-momentum tensorof the system. A reciprocal theorem is also derived, wherebythe coefficient of the singular strain rate field at the plateedge is related to finite integrals in the hodograph plane.A check of this method is effected by comparison with the solutionof the above problem. 相似文献
5.
Liu Y. Ito S. Lee H. W. J. Teo K. L. 《Journal of Optimization Theory and Applications》2001,108(3):617-632
Consider the class of linear-quadratic (LQ) optimal control problems with continuous linear state constraints, that is, constraints imposed on every instant of the time horizon. This class of problems is known to be difficult to solve numerically. In this paper, a computational method based on a semi-infinite programming approach is given. The LQ optimal control problem is formulated as a positive-quadratic infinite programming problem. This can be done by considering the control as the decision variable, while taking the state as a function of the control. After parametrizing the decision variable, an approximate quadratic semi-infinite programming problem is obtained. It is shown that, as we refine the parametrization, the solution sequence of the approximate problems converges to the solution of the infinite programming problem (hence, to the solution of the original optimal control problem). Numerically, the semi-infinite programming problems obtained above can be solved efficiently using an algorithm based on a dual parametrization method. 相似文献
6.
《Communications in Nonlinear Science & Numerical Simulation》2011,16(1):274-283
Based on a new approximation method, namely pseudospectral method, a solution for the three order nonlinear ordinary differential laminar boundary layer Falkner–Skan equation has been obtained on the semi-infinite domain. The proposed approach is equipped by the orthogonal Hermite functions that have perfect properties to achieve this goal. This method solves the problem on the semi-infinite domain without truncating it to a finite domain and transforming domain of the problem to a finite domain. In addition, this method reduces solution of the problem to solution of a system of algebraic equations. We also present the comparison of this work with numerical results and show that the present method is applicable. 相似文献
7.
G. Still 《Mathematical Programming》2001,91(1):53-69
The discretization approach for solving semi-infinite optimization problems is considered. We are interested in the convergence
rate of the error between the solution of the semi-infinite problem and the solution of the discretized program depending
on the discretization mesh-size. It will be shown how this rate depends on whether the minimizer is strict of order one or
two and on whether the discretization includes boundary points of the index set in a specific way. This is done for ordinary
and for generalized semi-infinite problems.
Received: November 21, 2000 / Accepted: May 2001?Published online September 17, 2001 相似文献
8.
A. E. Barabanov 《Proceedings of the Steklov Institute of Mathematics》2008,262(1):26-43
A solution to the minimax linear-quadratic problem of control of an operator system on a semi-infinite time interval is presented. The solution is based on the abstract maximum principle, Willems’ behavioral approach, the direct method of basic operators, and a small gain theorem. 相似文献
9.
The process of harmonic wave propagation is investigated in a semi-infinite rigidly-clamped elastic layer. An analytic solution of the problem is obtained by the superposition method. The wave field expansion in the form of a normal mode series for a corresponding infinite waveguide is established. According to residue theory, the explicit form of the expansion coefficients is established with physical requirements of the radiation conditions taken into account.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 3–10, 1988. 相似文献
10.
《Applied Mathematical Modelling》2014,38(17-18):4528-4537
In this work we consider the sound radiation of a fundamental plane wave mode from a semi-infinite soft–hard duct. This duct is symmetrically located inside an infinite duct. This infinite waveguide consist of soft and hard plates. The whole system constitutes a three spaced waveguide. A closed form solution is obtained by using eigenfunction expansion matching method. This particular problem has been solved previously by Rawlins in closed form but without numerical work. Here the numerical results for reflection coefficient are given when the lowest mode propagates out from the semi-infinite duct. At the end we give comparison to both methods. 相似文献
11.
12.
《Finite Elements in Analysis and Design》1988,4(3):225-236
The aim of this paper is to find a suitable finite element method for solving a tissue problem in a semi-infinite strip with a singularity at the origin. The problem is modelled using Laplace's equation in an infinite strip, simplified to a semi-infinite strip. An analytic form of the solution is derived and this is used for comparing with the finite element solution obtained in the semi-infinite strip using novel infinite elements. Numerical results for various values of the parameters present in the solution are reported and an optimum solution is presented. 相似文献
13.
Angelos Tsoukalas Berç Rustem Efstratios N. Pistikopoulos 《Journal of Global Optimization》2009,44(2):235-250
We propose an algorithm for the global optimization of three problem classes: generalized semi-infinite, continuous coupled
minimax and bi-level problems. We make no convexity assumptions. For each problem class, we construct an oracle that decides
whether a given objective value is achievable or not. If a given value is achievable, the oracle returns a point with a value
better than or equal to the target. A binary search is then performed until the global optimum is obtained with the desired
accuracy. This is achieved by solving a series of appropriate finite minimax and min-max-min problems to global optimality.
We use Laplace’s smoothing technique and a simulated annealing approach for the solution of these problems. We present computational
examples for all three problem classes. 相似文献
14.
Conditions for the uniqueness of the optimal solution in linear semi-infinite programming 总被引:1,自引:0,他引:1
In this paper, we establish different conditions for the uniqueness of the optimal solution of a semi-infinite programming problem. The approach here is based on the differentiability properties of the optimal value function and yields the corresponding extensions to the general linear semi-infinite case of many results provided by Mangasarian and others. In addition, detailed optimality conditions for the most general problem are supplied, and some features of the optimal set mapping are discussed. Finally, we obtain a dimensional characterization of the optimal set, provided that a usual closedness condition (Farkas-Minkowski condition) holds. 相似文献
15.
16.
讨论了半平面中的倾斜裂纹问题。集中力作用于裂纹表面上,或作用于开裂半平面的边界上。利用有理保角映像函数方法求解这个问题,同时得到了闭合形式的解。最后,给出了二个数值例子和计算结果。 相似文献
17.
Liondas CA; Chrissoulidis DP 《The Quarterly Journal of Mechanics and Applied Mathematics》2007,60(3):275-287
This paper is intended to clarify a misunderstanding concerningthe source singularity of the electric Green's tensor for aperfectly conducting semi-infinite cone of circular cross-section.Tai's series expansion of the Green's tensor is known to lacka singular term at the source region. Jones has reconstructedthe solution to this problem and has pointed out the differencebetween his result and that of Tai. The aim of our paper isto demonstrate that, although Jones's closed-form solution iscorrect, there is a mistake in his comparison with Tai's seriessolution. We conclude that one of the two additional singularterms that Jones claims as missing from Tai's formula must beomitted. Besides, we compare Jones's closed-form solution withSmyshlyaev's solution to the very same problem. We concludethat the magnetic field expressions given by Jones and Smyshlyaevcoincide, but a singular term is missing from Smyshlyaev's expressionfor the electric field. 相似文献
18.
We consider a boundary value problem over a semi-infinite interval for a nonlinear autonomous system of second-order ordinary differential equations with a small parameter at the leading derivatives. We impose certain constraints on the Jacobian under which a solution to the problem exists and is unique. To transfer the boundary condition from infinity, we use the well-known approach that rests on distinguishing the variety of solutions satisfying the limit condition at infinity. To solve an auxiliary Cauchy problem, we apply expansions of a solution in the parameter. 相似文献
19.
Mostafa Nasri 《Optimization》2016,65(2):467-478
The analysis of the principal-agent problem usually requires the classical first-order approach (FOA). However, the validity of the FOA makes restrictive assumptions on the problem under consideration such as the convexity of the distribution function condition. The main aim of this paper is to compute the optimal wages and characterize a closed form solution to the risk-neutral principal-agent problem with limited liability constraints. The development in this paper mainly invokes certain techniques in the semi-infinite programming rather than the FOA. 相似文献
20.
A bifurcated circular waveguide problem 总被引:1,自引:0,他引:1
A rigorous and exact solution is obtained for the problem ofthe radiation of sound from a semi-infinite rigid duct insertedaxially into a larger acoustically lined tube of infinite length.The solution to this problem is obtained by the Wiener-Hopftechnique. The transmission and reflection coefficients, whenthe fundamental mode propagates in the semi-infinite tube, areobtained. The present results could be of use for exhaust design,and as a possible instrument for impedance measurement. 相似文献