• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.125.1-125
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• 2001

This paper deals with the eigenvalue assignment technique for linear time-varying systems to achieve feedback stabilization. For this, we introduce the novel eigenvalue concepts. Then, we propose the Ackerman-like formula for linear time-varying systems. It is believed that this technique is the generalized version of the Ackerman formula forlinear time-invariant systems. The advantages of the proposed technique are that it does not require the transformation of the original system into the phase-variable form nor the computation of eigenvalues of the original system.

• 지질공학
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• 제18권4호
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• pp.381-391
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• 2008

본 연구에서는 수치해석의 시간차분에서 발생하는 절단오차를 극복하는 방안으로 고유치 기법을 도입하였다. 고유치기법은 모의를 할 때 공간만을 이산화하는 특징을 가지며, 공간적으로 이산화된 방정식을 대각화시킴으로써 선형동력학적 시스템을 분리시킨 후 시간적분을 이용한 계산이 임의의 위치에서 임의의 시간에 대해 개별적으로 또 연속적으로 수행된다. 이러한 고유치기법을 이용하여 오염물 이동을 모의하고 이를 해석해와 비교 검증하였고, 동일한 조건에서 유한요소법을 이용한 수치모형과 고유치 기법을 이용한 용질이동의 예측을 실시한 결과 고유치기법을 이용할 경우 계산시간과 저장용량이 수치모형에 비해 절약됨을 확인할 수 있었다. 고유치 기법을 이용하여 지하유류저장 공동주위의 불균일 유속장에서 용질의 이동을 분석하였다 이 방법이 모의발생에 오랜 시간이 걸리는 문제에 유용하게 사용될 수 있으므로, 공동에 인접한 오염원으로부터 공동의 안전성을 평가하기 위한 민감도 분석에 이 방법을 적용하였으며, 모의결과에 의하면, 종분산지수와 횡분산지수가 각각 50 m, 5 m일 때 공동에 도달하는 시간은 약 50년으로 추정되었다.

• Interaction and multiscale mechanics
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• 제1권2호
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• pp.211-230
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• 2008

Owing to the growing size of the eigenvalue problem and the growing number of eigenvalues desired, solution methods of iterative nature are becoming more popular than ever, which however suffer from low efficiency and lack of proper convergence criteria. In this paper, three efficient iterative eigenvalue algorithms are considered, i.e., subspace iteration method, iterative Ritz vector method and iterative Lanczos method based on the cell sparse fast solver and loop-unrolling. They are examined under the mode error criterion, i.e., the ratio of the out-of-balance nodal forces and the maximum elastic nodal point forces. Averagely speaking, the iterative Ritz vector method is the most efficient one among the three. Based on the mode error convergence criteria, the eigenvalue solvers are shown to be more stable than those based on eigenvalues only. Compared with ANSYS's subspace iteration and block Lanczos approaches, the subspace iteration presented here appears to be more efficient, while the Lanczos approach has roughly equal efficiency. The methods proposed are robust and efficient. Large size tests show that the improvement in terms of CPU time and storage is tremendous. Also reported is an aggressive shifting technique for the subspace iteration method, based on the mode error convergence criteria. A backward technique is introduced when the shift is not located in the right region. The efficiency of such a technique was demonstrated in the numerical tests.

• 전산구조공학
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• 제11권1호
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• pp.205-216
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• 1998

본 논문에서는 중복근을 갖는 비비례 감쇠시스템의 고유치 해석 방법을 제안하였다. 2차 고유치 문제의 행렬 조합을 통한 선형 방정식에 수정된 Newton-Raphson기법과 고유벡터의 직교성을 적용하여 제안방법의 알고리즘을 유도하였다. 벡터 반복법 또는 부분공간 반복법과 같은 기존의 반복법에서는 수렴성을 향상시키기 위해 변위법을 적용하였으며, 이 값이 시스템의 고유치에 근사하게 되면 행렬분해 과정에서 특이성이 발생한다. 그러나 제안방법은 구하고자 하는 고유치가 중복근이 아닐 경우에, 변위값이 시스템의 고유치 일지라도 항상 정칙성을 유지하며, 이것을 해석적으로 증명하였다. 제안방법은 수정된 Newton-Raphson기법을 이용하기 때문에 초기값을 필요로 한다. 제안방법의 초기값으로는 반복법의 중간결과나 근사법의 결과를 사용할 수 있다. 이들 방법중 Lanczon방법이 가장 효율적으로 좋은 초기값을 제공하기 때문에 Lanczon방법의 결과를 제안방법의 초기값으로 사용하였다. 제안방법의 효율성을 증명하기 위하여 두가지 예제 구조물에 대해 해석시간 및 수렴성을 가장 많이 사용하고 있는 부분공간 반복법과 Lanczon방법의 결과와 비교하였다.

• Nuclear Engineering and Technology
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• 제49권6호
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• pp.1125-1134
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• 2017

In this paper, we present a new multilevel in space and energy diffusion (MSED) method for solving multigroup diffusion eigenvalue problems. The MSED method can be described as a PI scheme with three additional features: (1) a grey (one-group) diffusion equation used to efficiently converge the fission source and eigenvalue, (2) a space-dependent Wielandt shift technique used to reduce the number of PIs required, and (3) a multigrid-in-space linear solver for the linear solves required by each PI step. In MSED, the convergence of the solution of the multigroup diffusion eigenvalue problem is accelerated by performing work on lower-order equations with only one group and/or coarser spatial grids. Results from several Fourier analyses and a one-dimensional test code are provided to verify the efficiency of the MSED method and to justify the incorporation of the grey diffusion equation and the multigrid linear solver. These results highlight the potential efficiency of the MSED method as a solver for multidimensional multigroup diffusion eigenvalue problems, and they serve as a proof of principle for future work. Our ultimate goal is to implement the MSED method as an efficient solver for the two-dimensional/three-dimensional coarse mesh finite difference diffusion system in the Michigan parallel characteristics transport code. The work in this paper represents a necessary step towards that goal.

• Computational Structural Engineering : An International Journal
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• 제1권1호
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• pp.31-38
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• 2001

In the case of the non-proportionally damped system such as the soil-structure interaction system, the structural control system and composite structures, the eigenproblem with the damping matrix should be necessarily performed to obtain the exact dynamic response. However, most of the eigenvalue analysis methods such as the subspace iteration method and the Lanczos method may miss some eigenvalues in the required ones. Therefore, the eigenvalue analysis method must include a technique to check the missed eigenvalues to become the practical tools. In the case of the undamped or proportionally damped system the missed eigenvalues can easily be checked by using the well-known Sturm sequence property, while in the case of the non-proportionally damped system a checking technique has not been developed yet. In this paper, a technique of checking the missed eigenvalues for the eigenproblem with the damping matrix is proposed by applying the argument principle. To verify the effectiveness of the proposed method, two numerical examples are considered.

• 전자공학회논문지B
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• 제33B권4호
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• pp.164-173
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• 1996

This paper presents an alternative technique for DOA (direction-of-arrival) estimation. For generating a weight vector orthogonal to the signal subspace, a modified version of MES (minimum eigenvalue searching ) method is introduced. The performance of the proposed technique is compared to that of the conventional ED (eigen decomposition) method in terms of angle resolution for a number of snapshots during agiven observation period as well as various SNR's. In addition, the superiority of the suggested technique is shown, by analyzing the required computational load of the proposed MES and conventional ED method. A novel procedure of simplifying the MES proposed in [1] is presented on that purpose. Another advnatage of the proposed technique is that it is performed independently of the detection of the number of signal components, which makes it possible to estimate the DOA's of clusters consisting of infinite number of inseparable signal components.

• International Journal of Aeronautical and Space Sciences
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• 제10권1호
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• pp.58-66
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• 2009

Formation controller for multiple spacecrafts is designed based on a decentralized approach. The objective of the proposed controller is to make each spacecraft fly to the desired waypoints, while keeping the formation shape of multiple spacecrafts. To design the decentralized formation controller, the output feedback linearization technique using error functions for goal convergence and formation keeping is utilized for spacecraft dynamics. The primary contribution of this paper is to proposed optimal controller for formation flying based on the decentralized approach. To design the optimal controller, eigenvalue assignment technique is used. To verify the effectiveness of the proposed controller, numerical simulations are performed for three-dimensional waypoint-passing missions of multiple spacecrafts.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권2호
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• pp.63-69
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• 2001

In this study, we shall be concerned with computing in parallel a few of the smallest eigenvalues and their corresponding eigenvectors of the eigenvalue problem, $Ax={\lambda}Bx$, where A is symmetric, and B is symmetric positive definite. Both A and B are large and sparse. Recently iterative algorithms based on the optimization of the Rayleigh quotient have been developed, and CG scheme for the optimization of the Rayleigh quotient has been proven a very attractive and promising technique for large sparse eigenproblems for small extreme eigenvalues. As in the case of a system of linear equations, successful application of the CG scheme to eigenproblems depends also upon the preconditioning techniques. A proper choice of the preconditioner significantly improves the convergence of the CG scheme. The idea underlying the present work is a parallel computation of the Multi-Color Block SSOR preconditioning for the CG optimization of the Rayleigh quotient together with deflation techniques. Multi-Coloring is a simple technique to obatin the parallelism of order n, where n is the dimension of the matrix. Block SSOR is a symmetric preconditioner which is expected to minimize the interprocessor communication due to the blocking. We implemented the results on the CRAY-T3E with 128 nodes. The MPI(Message Passing Interface) library was adopted for the interprocessor communications. The test problems were drawn from the discretizations of partial differential equations by finite difference methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권2호
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• pp.17-23
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• 2001

The evaluation of a few of the smallest eigenpairs of large symmetric eigenvalue problem is of great interest in many physical and engineering applications. A deflation-preconditioned conjugate gradient(PCG) scheme for a such problem has been shown to be very efficient. In the present paper we provide the numerical stability of a deflation-PCG with partial shifts.