Reconstructing the Time-Dependent Thermal Coefcient in 2D Free Boundary Problems

The inverse problem of reconstructing the time-dependent thermal conductivity and free boundary coefcients along with the temperature in a two-dimensional parabolic equation with initial and boundary conditions and additional measurements is,for the rst time,numerically investigated.This inverse problem appears extensively in the modelling of various phenomena in engineering and physics.For instance,steel annealing,vacuum-arc welding,fusion welding,continuous casting,metallurgy,aircraft,oil and gas production during drilling and operation of wells.From literature we already know that this inverse problem has a unique solution.However,the problem is still ill-posed by being unstable to noise in the input data.For the numerical realization,we apply the alternating direction explicit method along with the Tikhonov regularization to nd a stable and accurate numerical solution of nite differences.The root mean square error(rmse)values for various noise levels p for both smooth and non-smooth continuous time-dependent coef-cients Examples are compared.The resulting nonlinear minimization problem is solved numerically using the MATLAB subroutine lsqnonlin.Both exact and numerically simulated noisy input data are inverted.Numerical results presented for two examples show the efciency of the computational method and the accuracy and stability of the numerical solution even in the presence of noise in the input data.

Identical Machine Scheduling Problem with Sequence-Dependent Setup Times: MILP Formulations Computational Study

This work aims to give a systematic construction of the two families of mixed-integer-linear-programming (MILP) formulations, which are graph- based and sequence-based, of the well-known scheduling problem. Two upper bounds of job completion times are introduced. A numerical test result analysis is conducted with a two-fold objective 1) testing the performance of each solving methods, and 2) identifying and analyzing the tractability of an instance according to the instance structure in terms of the number of machines, of the jobs setup time lengths and of the jobs release date distribution over the scheduling horizon.

On Identical Problems of Natural Convection in Enclosures and Applications of the Identity Character

In this paper, a concept of 'identical problems' of natural convection in enclosures is presented. A pair of problems of natural convection in enclosures is said to be identical if they look different in appearance but with appropriate selection of coordinates and appropriate definition of dimensionless variables for each problem, they will have identical geometric configurations and identical dimensionless governing equations and related boundary conditions. The identical characteristics of a pair of problems of natural convection in enclosures with an internal isolated island are demonstrated via dimensionless mathematical formulation and flow visualization results. Numerical computations are performed and the predicted streamlines agree with the flow visualization results. A number of other possible pairs of identical problems are also presented. Applications of the identical character are provided and assumptions under which the identical problems may exist are discussed.