arXiv subjects

Mahtab Uddin

Publications and source records attributed to Mahtab Uddin.

5 recordsLinked to original sources

arXiv2023

Interpolatory Projection Techniques for $\mathcal{H}_2$ Optimal Structure-Preserving Model Order Reduction of Second-Order Systems

This paper focuses on exploring efficient ways to find $\mathcal{H}_2$ optimal Structure-Preserving Model Order Reduction (SPMOR) of the second-order systems via interpolatory projection-based method Iterative Rational Krylov Algorithm (IRKA). To get the reduced models of the second-order systems, the classical IRKA deals with the equivalent first-order converted forms and estimates the first-order reduced models. The drawbacks of that of the technique are failure of structure preservation and abolishing the properties of the original models, which are the key factors for some of the physical applications. To surpass those issues, we introduce IRKA based techniques that enable us to approximate the second-order systems through the reduced models implicitly without forming the first-order forms. On the other hand, there are very challenging tasks to the Model Order Reduction (MOR) of the large-scale second-order systems with the optimal $\mathcal{H}_2$ error norm and attain the rapid rate of convergence. For the convenient computations, we discuss competent techniques to determine the optimal $\mathcal{H}_2$ error norms efficiently for the second-order systems. The applicability and efficiency of the proposed techniques are validated by applying them to some large-scale systems extracted form engineering applications. The computations are done numerically using MATLAB simulation and the achieved results are discussed in both tabular and graphical approaches.

math.OC↗

arXiv2021

Computationally efficient optimal control for unstable power system models

In this article, the focus is mainly on gaining the optimal control for the unstable power system models and stabilizing them through the Riccati-based feedback stabilization process with sparsity-preserving techniques. We are to find the solution of the Continuous-time Algebraic Riccati Equations (CAREs) governed from the unstable power system models derived from the Brazilian Inter-Connected Power System (BIPS) models, which are large-scale sparse index-1 descriptor systems. We propose the projection-based Rational Krylov Subspace Method (RKSM) for the iterative computation of the solution of the CAREs. The novelties of RKSM are sparsity-preserving computations and the implementation of time-convenient adaptive shift parameters. We modify the Low-Rank Cholesky-Factor integrated Alternating Direction Implicit (LRCF-ADI) technique based nested iterative Kleinman-Newton (KN) method to a sparse form and adjust this to solve the desired CAREs. We compare the results achieved by the Kleinman-Newton method with that of using the RKSM. The applicability and adaptability of the proposed techniques are justified numerically with MATLAB simulations. Transient behaviors of the target models are investigated for comparative analysis through the tabular and graphical approaches.

math.OC↗

arXiv2021

Hydrothermal Behavior of Fluid Flow and Heat Transfer through a Curved Square Duct with Curvature Effects

Due to ample applications from medical services to industrial activities, the study of flow and heat transfer through a curved duct has attracted considerable attention to the researchers. In this paper, a comprehensive numerical study is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a curved square duct for various curvatures. The spectral method is used as a basic tool to solve the system of nonlinear partial differential equations. Numerical calculations are carried out over a wide range of the Dean number, $0<D_n\le 5000$, for curvature ratio $δ=0.001$, $0.1$, and $0.5$. A temperature difference is applied across the horizontal walls for the Grashof number $Gr = 1000$, where the bottom wall is heated while cooling from the ceiling, the outer and inner walls being thermally insulated. First, the bifurcation structure of steady solutions is investigated. As a result, two branches of steady solutions consisting of two- to eight-vortex solutions are obtained for $δ=0.001$ and $0.1$ while three branches for $δ=0.5$. Then we performed time evolution calculation to investigate unsteady flow characteristics, and it is found that the unsteady flow undergoes through various flow instabilities, if $D_n$ is increased. Flow transitions are well determined by obtaining phase space of the time evolution results. Typical contours of streamlines and isotherms are obtained at several values of $D_n$ and it is found that the unsteady flow consists of two-to-eight-vortex solutions. The present study demonstrates the role of secondary vortices on convective heat transfer and it is found that convective heat transfer is significantly enhanced by the secondary flow and as the number of secondary vortices increases, that occurs for the chaotic solution, heat transfer is boosted substantially.

physics.flu-dyn↗

arXiv2021

Interpolatory projection technique for Riccati-based feedback stabilization of index-1 descriptor systems

The work aims to stabilize the unstable index-1 descriptor systems by Riccati-based feedback stabilization via a modified form of Iterative Rational Krylov Algorithm (IRKA), which is a bi-tangential interpolation-based technique. In the basic IRKA, for the stable systems the Reduced Order Models (ROMs) can be found conveniently, but it is unsuitable for the unstable ones. In the proposed technique, the initial feedback is implemented within the construction of the projectors of the IRKA approach. The solution of the Riccati equation is estimated from the ROM achieved by IRKA and hence the low-rank feedback matrix is attained. Using the reverse projecting process, for the full model the optimal feedback matrix is retrieved from the low-rank feedback matrix. Finally, to validate the aptness and competency of the proposed technique it is applied to unstable index-1 descriptor systems. The comparison of the present work with two previous works is narrated. The simulation is done by numerical computation using MATLAB, and both the tabular method and graphical method are used as the supporting tools of comparative analysis.

math.OC↗

arXiv2020

Tangential interpolatory projections for a class of second-order index-1 descriptor systems and application to Mechatronics

This paper studies the model order reduction of second-order index-1 descriptor systems using a tangential interpolation projection method based on the Iterative Rational Krylov Algorithm (IRKA). Our primary focus is to reduce the system into a second-order form so that the structure of the original system can be preserved. For this purpose, the IRKA based tangential interpolatory method is modified to deal with the second-order structure of the underlying descriptor system efficiently in an implicit way. The paper also shows that by exploiting the symmetric properties of the system the implementing computational costs can be reduced significantly. Theoretical results are verified for the model reduction of the piezo actuator based adaptive spindle support which is second-order index-1 differential-algebraic form. The efficiency and accuracy of the method are demonstrated by analyzing the numerical results.

math.OC↗