In this article, we provide a first full a posteriori error analysis for variational approximations of the ground state eigenvector of a nonlinear elliptic problem of the Gross-Pitaevskii type, more precisely of the f...
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In this article, we provide a first full a posteriori error analysis for variational approximations of the ground state eigenvector of a nonlinear elliptic problem of the Gross-Pitaevskii type, more precisely of the form -Delta u+ Vu+ u(3) = lambda u, parallel to u parallel to(2)(L) = 1, with periodic boundary conditions in one dimension. Denoting by (u(N), lambda(N)) the variational approximation of the ground state eigenpair (u, lambda) based on a Fourier spectral approximation and by (u(N)(k), lambda(k)(N)) the approximate solution at the kth iteration of an algorithm used to solve the nonlinear problem, we first provide a precise a priori analysis of the convergence rates of parallel to u -u(N)parallel to(1)(H), parallel to u -u(N)parallel to(2)(L), vertical bar lambda-lambda(N)vertical bar and then present original a posteriori estimates of the convergence rates of parallel to u -u(N)(k)parallel to(1)(H) when N and k go to infinity. We introduce a residual representing the global error R-N(k) = -Delta u(N)(k) + Vu(N)(k) +(u(N)(k))(3) -lambda(k)(N)u(N)(k) and we divide it into two residuals characterizing, respectively, the error due to the discretization of space and the finite number of iterations when solving the problem numerically. Finally, in a series of numerical tests, we illustrate numerically the performance of this a posteriori analysis.
作者：
Li, TaoVirginia Tech
Charles E Via Jr Dept Civil & Environm Engn Blacksburg VA 24060 USA
The importance of historical travel demand has been well recognized by transportation researchers and practitioners. This paper presents a new nonlinear demand estimator that can be applied in both ground and air tran...
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The importance of historical travel demand has been well recognized by transportation researchers and practitioners. This paper presents a new nonlinear demand estimator that can be applied in both ground and air transportation. The estimator is formulated such that the distribution of the estimated demand follows a nested logit model. To solve the demand estimator, we develop an exact solutionalgorithm, which maximizes its dual problem sequentially along unit directions and keeps some of the first-order optimality conditions satisfied for the estimator. We investigate the convergence of the algorithm. We prove that all of the accumulation points produced by the solutionalgorithm satisfy some optimality conditions. A large example (a real U.S. network), which contains 66,767 origin-destination pairs, is presented.
In order to improve the guidance precision of the ballistic missile interception,the target's trajectory prediction and the impact point prediction solutionalgorithm for interceptor's mid-course guida...
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ISBN:
(纸本)9781479946983
In order to improve the guidance precision of the ballistic missile interception,the target's trajectory prediction and the impact point prediction solutionalgorithm for interceptor's mid-course guidance are ***,in allusion to the drawbacks of current ballistic missile's trajectory predication,the high precision ballistic missile prediction algorithms based on predictor-corrector method considering the radar's measurement noise are designed on the premise of ballistic missile ***,in allusion to the drawbacks of dead circulation,heavy computation,and engineering unavailability in current impact point prediction solving,the basic strategy of impact point prediction guidance is studied,and the iterative solution algorithm of forecasting impact point based on time series is designed with common applicability,less computation and engineering availability,and then the computing circuit is *** results show that the proposed algorithms of ballistic trajectory prediction and impact point prediction solution have better precision and availability,which could offer some theoretical meaning and some references for engineering application.
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