• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권1호
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• pp.17-26
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• 2014

This paper presents development of an improved domain decomposition method for large scale structural problem that aims to provide high computational efficiency. In the previous researches, we developed the domain decomposition algorithm based on augmented Lagrangian formulation and proved numerical efficiency under both serial and parallel computing environment. In this paper, new computational analysis by the proposed domain decomposition method is performed. For this purpose, reduction in computational time achieved by the proposed algorithm is compared with that obtained by the dual-primal FETI method under serial computing condition. It is found that the proposed methods significantly accelerate the computational speed for a linear structural problem.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.759-772
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• 2012

In this paper, semi-infinite constrained programming, a class of constrained nonsmooth optimization problems, are transformed into unconstrained nonsmooth convex programs under the help of exact penalty function. The unconstrained objective function which owns the primal-dual gradient structure has connection with $\mathcal{VU}$-space decomposition. Then a $\mathcal{VU}$-space decomposition method can be applied for solving this unconstrained programs. Finally, the superlinear convergence algorithm is proved under certain assumption.

• Korean Journal of Mathematics
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• 제31권4호
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• pp.419-431
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• 2023

In this paper, we propose an iterative method for a symmetric interior penalty Galerkin method for heterogeneous elliptic problems. The iterative method consists mainly of two parts based on a non-overlapping domain decomposition approach. One is an intermediate preconditioner constructed by understanding the properties of the discontinuous finite element functions and the other is a preconditioning related to the dual-primal finite element tearing and interconnecting (FETI-DP) methodology. Numerical results for the proposed method are presented, which demonstrate the performance of the iterative method in terms of various parameters associated with the elliptic model problem, the finite element discretization, and non-overlapping subdomain decomposition.

• 대한수학회논문집
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• 제9권2호
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• pp.317-325
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• 1994

Suppose X is a complex Banach space and write B(X) for the Banach algebra of bounded linear operators on X, X＊ for the dual space of X, and T＊$\in$ B(X＊) for the dual operator of T. For T $\in$ B(X) write a(T) = dim T$^{-1}$ (0) and $\beta$(T) = codim T(X).(omitted)

• Carbon letters
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• 제7권4호
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• pp.277-281
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• 2006

In this study, in order to easily provide functional groups on the surface of carbon nanotubes, dual structural multiwalled carbon nanotubes which have crystalline graphite and turbostratic carbon wall were synthesized by modified vertical thermal decomposition method. Synthesized dual structural MWCNTs were characterized by FE-SEM, TGA, HR-TEM, Raman spectroscopy and BET specific surface area analyzer. The average innermost and outermost diameters of the synthesized nanotubes were around 45 and 75 nm, respectively. The large empty inner space and the presence of graphitic carbons on the surface may open potential applications for gas storage and collection of hazardous materials.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제16권12호
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• pp.4024-4041
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• 2022

Robust reversible watermarking has attracted widespread attention in the field of information hiding in recent years. It should not only have robustness against attacks in transmission but also meet the reversibility of distortion-free transmission. According to our best knowledge, the most recent robust reversible watermarking methods adopt a single image as the carrier, which might lead to low efficiency in terms of carrier utilization. To address the issue, a novel dual-image robust reversible watermarking framework is proposed in this paper to effectively utilize the correlation between both carriers (namely dual images) and thus improve the efficiency of carrier utilization. In the dual-image robust reversible watermarking framework, a two-layer robust watermarking mechanism is designed to further improve the algorithm performances, i.e., embedding capacity and robustness. In addition, an optimization model is built to determine the parameters. Finally, the proposed framework is applied in different domains (namely domain-independent), i.e., Slantlet Transform and Singular Value Decomposition domain, and Zernike moments, respectively to demonstrate its effectiveness and generality. Experimental results demonstrate the superiority of the proposed dual-image robust reversible watermarking framework.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 26-27 Oct. 1990
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• pp.1265-1270
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• 1990

A prototype integrated system and its theories for distributed SISO control structure synthesis of complete chemical plants is developed. The scope of this work includes control structure synthesis not only of simple units with unspecified control loops but also of the complex process at preliminary and basic design stage. Hierarchical approach and dual-decomposition strategy (that is multi-layer decomposition and multi-echelon decomposition) is applied to this system. Because automatic control structure synthesis of complex plants is a problem defined as a series of knowledge-intensive tasks within multiple spaces, the established methodology is complemented by not only techniques from knowledge-based expert systems but also shortcut and rigorous control theories. This system is used for education of control designers, process engineers, operators and students as well as for operability studying, in-line and on-line process control structure synthesis.

• 대한수학회논문집
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• 제9권4호
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• pp.847-852
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• 1994

Let $H$ be a separable, infinite dimensional, complex Hilbert space and let $L(H)$ be the algebra of all bounded linear operator on $H$. A dual algebra is a subalgebra of $L(H)$ that contains the identity operator $I_H$ and is closed in the ultraweak operator topology on $L(H)$.

• 대한수학회지
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• 제54권2호
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• pp.461-477
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• 2017

A dual substructuring method with a penalty term was introduced in the previous works by the authors, which is a variant of the FETI-DP method. The proposed method imposes the continuity not only by using Lagrange multipliers but also by adding a penalty term which consists of a positive penalty parameter ${\eta}$ and a measure of the jump across the interface. Due to the penalty term, the proposed iterative method has a better convergence property than the standard FETI-DP method in the sense that the condition number of the resulting dual problem is bounded by a constant independent of the subdomain size and the mesh size. In this paper, a further study for a dual iterative substructuring method with a penalty term is discussed in terms of its convergence analysis. We provide an improved estimate of the condition number which shows the relationship between the condition number and ${\eta}$ as well as a close spectral connection of the proposed method with the FETI-DP method. As a result, a choice of a moderately small penalty parameter is guaranteed.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제12권5호
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• pp.2063-2081
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• 2018

A resource allocation algorithm is proposed in this paper to simultaneously minimize the total system power consumption and maximize the system throughput for the downlink of multi-user multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) systems. With the Lagrange dual decomposition method, we transform the original problem to its convex dual problem and prove that the duality gap between the two problems is zero, which means the optimal solution of the original problem can be obtained by solving its dual problem. Then, we use convex optimization method to solve the dual problem and utilize bisection method to obtain the optimal dual variable. The numerical results show that the proposed algorithm is superior to traditional single-objective optimization method in both the system throughput and the system energy consumption.