An approximation for the boundary optimal control problem of a heat equation defined in a variable domain

In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of theboundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming （SQP） algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.

Subdivision and Correlation of Middle and Upper Cambria in North China in Light of Sequence Stratigraphy

Correlation of Middle and Late Cambrian cyclic carbonates from the widely separated Zhangxia section, Qingxing section, Xishan section and Zhaogezhuang section has defined five major third-order depositional sequences. Correlation of biostratigraphy is used to establish the equivalency of stratigraphic sequences between individual sections. Even though the individ- ual sections are composed of different lithofacies and meter-scale cycles that reflect the varied environmental settings in the localities, the overall upward shallowing character of individ- ual sequences is evident. The sequences, named on their relation to the regional stages in range, are in ascending order: Zhangxia Sequence, Gushan Sequence, Guchang Sequence, Changshan Sequence and Fengshan Sequence, of which the upper four sequences were correlated with those defined by Osleger and Read in the United States, with the aid of biostratigraphic correlation. The Middle/Upper Cambrian boundary is tentatively suggested to be between the Guchang Sequence and the Changshan Sequence in North China. The optimization of the existing litho-and regional chronostratigraphic boundaries is discussed based on the sequence boundaries.

Research on Design Method of the Full Form Ship with Minimum Thrust Deduction Factor

In the preliminary design stage of the full form ships, in order to obtain a hull form with low resistance and maximum propulsion efficiency, an optimization design program for a full form ship with the minimum thrust deduction factor has been developed, which combined the potential flow theory and boundary layer theory with the optimization technique. In the optimization process, the Sequential Unconstrained Minimization Technique（SUMT） interior point method of Nonlinear Programming（NLP） was proposed with the minimum thrust deduction factor as the objective function. An appropriate displacement is a basic constraint condition, and the boundary layer separation is an additional one. The parameters of the hull form modification function are used as design variables. At last, the numerical optimization example for lines of after-body of 50000 DWT product oil tanker was provided, which indicated that the propulsion efficiency was improved distinctly by this optimal design method.

Position optimization of particular solution sources for distributed source boundary point method by volume velocity-matching

Choosing particular solution source and its position have great influence on accu- racy of sound field prediction in distributed source boundary point method. An optimization method for determining the position of particular solution sources is proposed to get high accu- racy prediction result. In this method, tripole is chosen as the particular solution. The upper limit frequency of calculation is predicted by setting 1% volume velocity relative error limit using vibration velocity of structure surface. Then, the optimal position of particular solution sources, in which the relative error of volume velocity is minimum, is determined within the range of upper limit frequency by searching algorithm using volume velocity matching. The transfer matrix between pressure and surface volume velocity is constructed in the optimal position. After that, the sound radiation of structure is calculated by the matrix. The results of numerical simulation show that the calculation error is significantly reduced by the proposed method. When there are vibration velocity measurement errors, the calculation errors can be controlled within 5% by the method.

Weak Galerkin finite element method for valuation of American options

We introduce a weak Galerkin finite element method for the valuation of American options governed by the Black-Scholes equation. In order to implement, we need to solve the optimal exercise boundary and then introduce an artificial boundary to make the computational domain bounded. For the optimal exercise boundary, which satisfies a nonlinear Volterra integral equation, it is resolved by a higher-order collocation method based on graded meshes. With the computed optimal exercise boundary, the front-fixing technique is employed to transform the free boundary problem to a one- dimensional parabolic problem in a half infinite area. For the other spatial domain boundary, a perfectly matched layer is used to truncate the unbounded domain and carry out the computation. Finally, the resulting initial-boundary value problems are solved by weak Galerkin finite element method, and numerical examples are provided to illustrate the efficiency of the method.

Chebyshev Collocation for Optimal Control in a Thermoconvective Flow

In this paper a Chebyshev collocation method is used for solving numerically an optimal boundary control problem in a thermoconvective fluid flow.The aim of this study is to demonstrate the capabilities of these numerical techniques for handling this kind of problems.As the problem is treated in the primitive variable formulation additional boundary conditions for the pressure and the auxiliary pressure fields are required to avoid spurious modes.A dependence of the convergence of the method on the penalizing parameter that appears in the functional cost is observed.As this parameter approaches zero some singular behaviour in the control function is observed and the order of the method decreases.These singularities are irrelevant in the problem as a regularized control function produces the same results.