• 대한수학회지
• /
• 제57권5호
• /
• pp.1267-1286
• /
• 2020

We pay attention to a coupled problem by a penalty term which is induced from non-overlapping domain decomposition methods based on augmented Lagrangian methodology. The coupled problem is composed by two parts mainly; one is a problem associated with local problems in non-overlapping subdomains and the other is a coupled part over all subdomains due to the penalty term. For the speedup of iterative solvers for the coupled problem, we propose two different types of preconditioners: a block-diagonal preconditioner and an additive Schwarz preconditioner as overlapping domain decomposition methods. We analyze the coupled problem and the preconditioned problems in terms of their condition numbers. Finally we present numerical results which show the performance of the proposed methods.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1999년도 추계학술대회 논문집 학회본부 B
• /
• pp.503-505
• /
• 1999

Linear cheap control problem is a special form of linear quadratic regulator problem in which a small parameter ${\varepsilon}^2$ is multiplied with the control term. The joint problem in which cheap control is applied to a weakly coupled discrete system has not been reported in the literature. In this paper, the high-gain problem and decoupling problem on discrete weakly coupled system are considered together. We derive Hamiltonian matrix when the cheap control is applied to a weakly coupled discrete system and use it in developing numerical formulations in the process of applying parallel algorithm to the system.

• Kyungpook Mathematical Journal
• /
• 제52권4호
• /
• pp.359-373
• /
• 2012

The block LU factorization is used to solve the coupled Stokes equations arisen from an optimal control problem subject to Stokes equations. The convergence of the spectral element solution is proved. Some numerical evidences are provided for the model coupled Stokes equations. Moreover, as an application, this algorithm is performed for an optimal control problem.

• 한국기계가공학회지
• /
• 제9권3호
• /
• pp.28-34
• /
• 2010

The suggested coupled system was analyzed using FRF and mode analysis. The eigen-mode of FRF analysis is consistent with that of conventional FFT in spectrum. Also, three numerical responses of second order system, which are coupled, was obtained using the Runge-Kutta Gill method. The displacement, velocity and acceleration response were calculated for the numerical analysis of coupled system and the displacement response was used for the calculation of FRF of this system. Using the mixed response of 1st and 2nd mode in example, the FRF was analysed for the analysis of mixed mode coupled system. Also, its mode shape was acquired by solving the eigen problem of coupled system.

• 대한토목학회논문집
• /
• 제37권6호
• /
• pp.973-980
• /
• 2017

본 연구는 해수침투를 모의하는 연산의 바탕이 되는 밀도 결합 방정식을 2차원으로 유한차분한 VDFT (Visual Basic based Density-coupled Flow and Transport) 기법을 개발한 것이다. VDFT 코드는 직관적이고 간단하게 사용할 수 있다는 장점을 가지고 있으며 일반 업무용으로 널리 사용되고 있는 EXCEL Visual Basic 플랫폼을 활용할 수 있다는 장점이 있다. 일반적으로 수치모의를 위해 개발한 코드는 벤치마크 라는 대표적인 수치예제를 통하여 검증을 할 수 있다. 본 연구에서는 2가지 실내실험 결과로서 얻어진 데이터와 Henry Problem 및 Modified Henry Problem을 수치예제로 활용하여 VDFT 기법을 검증하였다. 마지막으로 결론에서는 VDFT 코드의 활용가능성을 진단하고 향후 연구의 방향성을 제시하였다.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
• /
• pp.100-104
• /
• 1993

In Part 1, we derived robust stability conditions for an LTI interconnected to time-varying nonlinear perturbations belonging to several classes of nonlinearities. These conditions were presented in terms of positive definite solutions to LMI. In this paper we address a problem of synthesizing feedback controllers for linear time-invariant systems under structured time-varying uncertainties, combined with a worst-case H$_{2}$ performance. This problem is introduced in [7, 8, 15, 35] in case of time-invariant uncertainties, where the necessary conditions involve highly coupled linear and nonlinear matrix equations. Such coupled equations are in general difficult to solve. A convex optimization approach will be employed in this synthesis problem in order to avoid solving highly coupled nonlinear matrix equations that commonly arises in multiobjective synthesis problem. Using LMI formulation, this convex optimization problem can in turn be cast as generalized eigenvalue minimization problem, where an attractive algorithm based on the method of centers has been recently introduced to find its solution [30, 361. In the present paper we will restrict our discussion to state feedback case with Popov multipliers. A more general case of output feedback and other types of multipliers will be addressed in a future paper.

• Kyungpook Mathematical Journal
• /
• 제56권1호
• /
• pp.221-233
• /
• 2016

The present paper proposes a new monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations. A new hybrid coupled fixed point theorem involving the Dhage iteration principle is proved in a partially ordered normed linear space and applied to the coupled periodic boundary value problems for proving the main existence and approximation results of this paper. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable mixed hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper.

• Coupled systems mechanics
• /
• 제1권4호
• /
• pp.345-360
• /
• 2012

In this article we have presented a unique representation for interval arithmetic. The traditional interval arithmetic is transformed into crisp by symbolic parameterization. Then the proposed interval arithmetic is extended for fuzzy numbers and this fuzzy arithmetic is used as a tool for uncertain finite element method. In general, the fuzzy finite element converts the governing differential equations into fuzzy algebraic equations. Fuzzy algebraic equations either give a fuzzy eigenvalue problem or a fuzzy system of linear equations. The proposed methods have been used to solve a test problem namely heat conduction problem along with fuzzy finite element method to see the efficacy and powerfulness of the methodology. As such a coupled set of fuzzy linear equations are obtained. These coupled fuzzy linear equations have been solved by two techniques such as by fuzzy iteration method and fuzzy eigenvalue method. Obtained results are compared and it has seen that the proposed methods are reliable and may be applicable to other heat conduction problems too.

• Journal of applied mathematics & informatics
• /
• 제35권3_4호
• /
• pp.387-397
• /
• 2017

In order to react the dynamic behavior of the system more actually, it is necessary to solve the first problem of synchronization for Markovian jump complex network system in practical engineering problem. In this paper, the problem of local stochastic synchronization for Markovian nonlinear coupled neural network system is investigated, including nonlinear coupling terms and mode-dependent delays, that is less restriction to other system. By designing the Lyapunov-Krasovskii functional and applying less conservative inequality, we get a new criterion to ensure local synchronization in mean square for Markovian nonlinear coupled neural network system. The criterion introduced some free matrix variables, which are less conservative. The simulation confirmed the validity of the conclusion.

• Journal of Ship and Ocean Technology
• /
• 제9권1호
• /
• pp.11-26
• /
• 2005

In this study, the program to investigate the multiple body interaction effects between a floating platform and a shuttle tanker considering the coupled effect of hull (FPSO) with mooring lines and risers was developed. The coupled analysis program, which is called WINPOST-MULT using the hydrodynamic analysis results by WAMIT, was made. For the verification of WINPOST-MULT by means of numerical experiments, two multiple-body models of an FPSO-FPSO and an FPSO-shuttle tanker system are adopted. With the FPSO-FPSO model and a two-mass-spring system to idealize two identical bodies for the 100-year storm wave condition in GOM, the numerical simulations were performed to investigate the interaction effects between two identical bodies. For the more reality, the coupled analysis for the FPSO-shuttle tanker model in the tandem arrangement was carried out in the consideration of the environmental condition of the West Africa Sea as a rather mild condition. Through the case studies with interaction effect and without interaction effect by the iteration method and the combined method, it is verified that the program is a very useful tool for the analysis of the interaction problem of multiple-body system and the coupled problem of the hull/mooring/riser.