Hajar Alimorad; Alireza Fakharzadeh Jahromi
Abstract
In this paper, we model and solve the problem of optimal shaping and placing to put sensors for a 3-D wave equation with constant damping in a bounded open connected subset of 3-dimensional space. The place of sensor is modeled by a subdomain of this region ...
Read More
In this paper, we model and solve the problem of optimal shaping and placing to put sensors for a 3-D wave equation with constant damping in a bounded open connected subset of 3-dimensional space. The place of sensor is modeled by a subdomain of this region of a given measure. By using an approach based on the embedding process, first, the system is formulated in variational form; then, by defining two positive Radon measures, the problem is represented in a space of measures. In this way, the shape design problem is turned into an infinite linear problem whose solution is guaranteed. In this step, the optimal solution (optimal control, optimal region, and optimal energy) is identified by a 2-phase optimization search technique applying two subsequent approximation steps. Moreover, some numerical simulations are given to compare this new method with other methods.
Control and Optimization
Alireza Fakharzadeh Jahromi; Zahra Alamdar Ghahferokhi
Volume 2, Issue 1 , April 2017, , Pages 65-76
Abstract
This paper describes a new optimization method for solving continuous semi-infinite linear problems. With regard to the dual properties, the problem is presented as a measure theoretical optimization problem, in which the existence of the solution is guaranteed. ...
Read More
This paper describes a new optimization method for solving continuous semi-infinite linear problems. With regard to the dual properties, the problem is presented as a measure theoretical optimization problem, in which the existence of the solution is guaranteed. Then, on the basis of the atomic measure properties, a computation method was presented for obtaining the near optimal solution by means of famous and simple simplex method. Some numerical results are reported to indicate the efficiency of the new method.