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101.
A nonclassical problem is considered for the transport equation with coefficients depending on the energy of radiation. The task is to find the discontinuity surfaces for the coefficients of the equation from measurements of the radiation flux leaving the medium. For this tomography problem, an optimization problem is stated and numerically analyzed. The latter consists in determining the radiation energy that ensures the best reconstruction of the unknown medium. A simplified optimization problem is solved analytically. 相似文献
102.
We prove that for any given c, 1 < c < 17/11, almost all natural numbers are representable in the form [x
c] + [p
c], where x is a natural number and p is a prime. 相似文献
103.
104.
Victor A. Kovtunenko 《Mathematical Methods in the Applied Sciences》2003,26(5):359-374
The 3D‐elasticity model of a solid with a plane crack under the stress‐free boundary conditions at the crack is considered. We investigate variations of a solution and of energy functionals with respect to perturbations of the crack front in the plane. The corresponding expansions at least up to the second‐order terms are obtained. The strong derivatives of the solution are constructed as an iterative solution of the same elasticity problem with specified right‐hand sides. Using the expansion of the potential and surface energy, we consider an approximate quadratic form for local shape optimization of the crack front defined by the Griffith criterion. To specify its properties, a procedure of discrete optimization is proposed, which reduces to a matrix variational inequality. At least for a small load we prove its solvability and find a quasi‐static model of the crack growth depending on the loading parameter. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
105.
In this paper, we formulate the l
p
-norm optimization problem as a conic optimization problem, derive its duality properties (weak duality, zero duality gap, and primal attainment) using standard conic duality and show how it can be solved in polynomial time applying the framework of interior-point algorithms based on self-concordant barriers. 相似文献
106.
In this paper, we use parametric quintic splines to derive some consistency relations which are then used to develop a numerical method for computing the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. It is known that a class of variational inequalities related to contact problems in elastostatics can be characterized by a sequence of variational inequations, which are solved using some numerical method. Numerical evidence is presented to show the applicability and superiority of the new method over other collocation, finite difference, and spline methods. 相似文献
107.
María G. Armentano Ricardo G. Durn 《Numerical Methods for Partial Differential Equations》2003,19(5):653-664
In this article we analyze the effect of mass‐lumping in the linear triangular finite element approximation of second‐order elliptic eigenvalue problems. We prove that the eigenvalue obtained by using mass‐lumping is always below the one obtained with exact integration. For singular eigenfunctions, as those arising in non convex polygons, we prove that the eigenvalue obtained with mass‐lumping is above the exact eigenvalue when the mesh size is small enough. So, we conclude that the use of mass‐lumping is convenient in the singular case. When the eigenfunction is smooth several numerical experiments suggest that the eigenvalue computed with mass‐lumping is below the exact one if the mesh is not too coarse. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 653–664, 2003 相似文献
108.
J. T. Haslinger K. Kunisch G. Peichl 《Computational Optimization and Applications》2003,26(3):231-251
This contribution deals with an efficient method for the numerical realization of the exterior and interior Bernoulli free boundary problems. It is based on a shape optimization approach. The state problems are solved by a fictitious domain solver using boundary Lagrange multipliers. 相似文献
109.
We study a class of shape optimization problems for semi-linear elliptic equations with Dirichlet boundary conditions in smooth
domains in ℝ2. A part of the boundary of the domain is variable as the graph of a smooth function. The problem is equivalently reformulated
on a fixed domain. Continuity of the solution to the state equation with respect to domain variations is shown. This is used
to obtain differentiability in the general case, and moreover a useful formula for the gradient of the cost functional in
the case where the principal part of the differential operator is the Laplacian.
Online publication 23 January 2004. 相似文献
110.
This paper develops a theory for the global solution of nonconvex optimization problems with parameter-embedded linear dynamic systems. A quite general problem formulation is introduced and a solution is shown to exists. A convexity theory for integrals is then developed to construct convex relaxations for utilization in a branch-and-bound framework to calculate a global minimum. Interval analysis is employed to generate bounds on the state variables implied by the bounds on the embedded parameters. These bounds, along with basic integration theory, are used to prove convergence of the branch-and-bound algorithm to the global minimum of the optimization problem. The implementation of the algorithm is then considered and several numerical case studies are examined thoroughly 相似文献