• 대한수학회논문집
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• 제16권3호
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• pp.437-443
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• 2001

In this paper the inverse problems for the Dirac Operator are studied. A set of values of eigenfunctions in some internal point and spectrum are taken as a data. Uniqueness theorems are obtained. The approach that was used in the investigation of inverse problems for interior spectral data of the Sturm-Liouville operator is employed.

• Nuclear Engineering and Technology
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• 제55권1호
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• pp.310-323
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• 2023

The k-eigenvalue neutronics/thermal-hydraulics coupling calculation is a key issue for reactor design and analysis. Jacobian-free Newton-Krylov (JFNK) method, featured with super-linear convergence rate and high efficiency, has been attracting more and more attention to solve the multi-physics coupling problem. However, it may converge to the high-order eigenmode because of the multiple solutions nature of the k-eigenvalue form of multi-physics coupling issue. Based on our previous work, a modified JFNK with a line search method is proposed in this work, which can find the fundamental eigenmode together with thermal-hydraulics feedback in a wide range of initial values. In detail, the existing modified JFNK method is combined with the line search strategy, so that the intermediate iterative solution can avoid a sudden divergence and be adjusted into a convergence basin smoothly. Two simplified 2-D homogeneous reactor models, a PWR model, and an HTR model, are utilized to evaluate the performance of the newly proposed JFNK method. The results show that the performance of this proposed JFNK is more robust than the existing JFNK-based methods.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 Proceedings of the Korea Automatic Control Conference, 11th (KACC); Pohang, Korea; 24-26 Oct. 1996
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• pp.362-367
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• 1996

In this paper, the eigenstructure of a class of linear time varying systems, termed as linear quasi-time invariant(LQTI) systems, is investigated. A system composed of dynamic devices such as linear time varying capacitors and resistors can be an example of the class. To effectively describe and analyze the LQTI systems, a generalized differential operator G is introduced. Then the dynamic systems described by the operator G are studied in terms of eigenvalue, frequency characteristics, stability and an extended convolution. Some basic attributes of the operator G are compared with those of the differential operator D. Also the corresponding generalized Laplace transform pair is defined and relevant properties are derived for frequency domain analysis of the systems under consideration. As an application example, a LQTI circuit is examined by using the concept of eigenstructure of LQTI system. The LQTI filter processes the sinusoidal signals modulated by some functions.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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• pp.1477-1480
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• 1997

This paper is concerned with the design of a suboptimal robust Kalman filter using LMI approach for system models in the state space, which are subjected to parameter uncertainties in both the state and measurement atrices. Under the assumption that augmented system composed of the uncertain system and the state estimation error dynamics should be stable, a Lyapunov inequality is obtained. And from this inequaltiy, the filter design problem can be transformed to the gneric LMI problems i.e., linear objective minimization problem and generalized eigenvalue minimization problem. When applied to uncertain linear system modles, the proposed filter can provide the minimum upper bound of the estimation error variance for all admissible parameter uncertainties.

• 한국생산제조학회지
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• 제22권1호
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• pp.63-69
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• 2013

In order to find the optimum design of structures that have characteristic natural frequency range, a numerical optimization method to solving eigenvalue problems is a widely used approach. However in the most cases, it is difficult to decide the accurate thickness and shape of structures that have allowable natural frequency in design constraints. Parallel analysis algorithm involving the feasible direction optimization method and Rayleigh-Ritz eigenvalue solving method is developed. The method is implemented by using finite element method. It calculates the optimal thickness and the thickness ratio of individual elements of the 2-D plane element through a parallel algorithm method which satisfy the design constraint of natural frequency. As a result this method of optimization for natural frequency by using finite element method can determine the optimal size or its ratio of geometrically complicated shape and large scale structure.

• 정보처리학회논문지A
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• 제11A권1호
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• pp.67-74
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• 2004

대부분의 병렬 알고리즘은 동기 알고리즘으로, 올바른 계산을 위해 작업을 일찍 끝낸 빠른 프로세서들은 동기점에서 느린 프로세서를 기다려야 하는데, 프로세서들의 성능이 다를 경우 연산 속도는 가장 느린 프로세서에 의해 결정된다. 본 논문에서는 거대 고유치 문제의 주요 고유쌍을 구하는 문제에 있어서 빠른 프로세서의 유휴 시간을 줄여 수렴 속도를 가속한 수 있는 동기/비동기 혼합 알고리즘을 고안하고 이를 MPMD 프로그래밍 방식을 사용하여 구현하였다.

• Journal of Electrical Engineering and Technology
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• 제2권4호
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• pp.428-433
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• 2007

This paper describes the new eigenvalue algorithm exploiting the Implicit Restarted Arnoldi Method (IRAM) and its application to power systems. IRAM is a technique for combining the implicitly shifted mechanism with a k-step Arnoldi factorization to obtain a truncated form of the implicitly shifted QR iteration. The numerical difficulties and storage problems normally associated with the Arnoldi process are avoided. Two power systems, one of which has 36 state variables and the other 150 state variables, have been tested using the ARPACK program, which uses IRAM, and the eigenvalue results are compared with the results obtained from the conventional QR method.

• 대한기계학회논문집A
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• 제21권11호
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• pp.1852-1861
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• 1997

An enhanced subspace iteration algorithm has been developed to solve eigenvalue problems reliably and efficiently. Basic subspace iteration algorithm has been improved by eliminating recalculation of converged eigenvectors, using Krylov sequence as initial vectors and incorporating with shifting techniques. The number of iterations and computational time have been considerably reduced when compared with the original one, and reliability for catching copies of the multiple roots has been retained successfully. Further research would be required for mathematical justification of the present method.

• 한국자동차공학회논문집
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• 제10권4호
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• pp.216-222
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• 2002

Brake Moan is a laud and strong noise occurring at any vehicle speed over 2 mph as a low frequency in below 600Hz. In this study, we targeted to shift the unstable mode that causes the brake moan from the moats frequency range to sufficiently higher frequency range to avoid the moan phenomenon. We simulated the finite element model and found out the nodes in which the brake moan occurs the most and we regarded the boundary and its relationship between the brake pad and the rotor as a spring coefficient k. With the binary set of the spring coefficient k, we finally used genetic algorithm (GA) to get the optimal topology of the brake pad and its shape to avoid the brake moan. The final result remarkably shows that genetic algorithm can be used in topology optimization procedures requiring complex eigenvalue problems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권1호
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• pp.13-20
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• 2009

The IPSAP which is a finite element analysis program has been developed for high parallel performance computing. This program consists of various analysis modules - stress, vibration and thermal analysis module, etc. The M orthogonal block Lanczos algorithm with shiftinvert transformation is used for solving eigenvalue problems in the vibration module. And the multifrontal algorithm which is one of the most efficient direct linear equation solvers is applied to factorization and triangular system solving phases in this block Lanczos iteration routine. In this study, the performance enhancement procedures of the IPSAP are composed of the following stages: 1) communication volume minimization of the factorization phase by modifying parallel matrix subroutines. 2) idling time minimization in triangular system solving phase by partial inverse of the frontal matrix and the LCM (least common multiple) concept.