• Title/Summary/Keyword: Lanczos vectors

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Dynamic Analysis of Structures by Superposition of Modified Lanczos Vectors (수정된 Lanczos 벡터의 중첩을 통한 구조물의 동적해석)

  • Kim, Byoung-Wan;Jung, Hyung-Jo;Kim, Woon-Hak;Lee, In-Won
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2003.04a
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    • pp.11-18
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    • 2003
  • This paper proposes modified Lanczos vector superposition method for efficient dynamic analysis of structures. Proposed method is based on the modified Lanczos algorithm that generates stiffness-orthonormal Lanczos vectors. Proposed method has better computing efficiency than the conventional Lanczos vector superposition method in the analysis of multi-input-loaded structures. The efficiency of proposed method is verified through numerical examples. Comparison with other vector superposition methods is also presented through numerical examples.

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Efficient Vector Superposition Method for Dynamic Analysis of Structures (구조물의 동적해석을 위한 효율적인 벡터중첩법)

  • 김병완;정형조;김운학;이인원
    • Journal of the Earthquake Engineering Society of Korea
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    • v.7 no.3
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    • pp.39-45
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    • 2003
  • Modified Lanczos vector superposition method is proposed for efficient dynamic analysis of structures, The proposed method is based on the modified Lanczos algorithm that generates stiffness-orthonormal Lanczos vectors. The proposed Lanczos vector superposition method has the same accuracy and efficiency as the conventional Lonczos vector superposition method in the analysis of structures under single input loads. On the other hand, the proposed method is more efficient than the conventional method in the analysis of structures under multi-input loads. The effectiveness of the proposed method is verified by analyzing two numerical examples.

NUMERICAL IMPLEMENTATION OF THE QMR ALGORITHM BY USING DISCRETE STOCHASTIC ARITHMETIC

  • TOUTOUNIAN FAEZEH;KHOJASTEH SALKUYEH DAVOD;ASADI BAHRAM
    • Journal of applied mathematics & informatics
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    • v.17 no.1_2_3
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    • pp.457-473
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    • 2005
  • In each step of the quasi-minimal residual (QMR) method which uses a look-ahead variant of the nonsymmetric Lanczos process to generate basis vectors for the Krylov subspaces induced by A, it is necessary to decide whether to construct the Lanczos vectors $v_{n+l}\;and\;w{n+l}$ as regular or inner vectors. For a regular step it is necessary that $D_k\;=\;W^{T}_{k}V_{k}$ is nonsingular. Therefore, in the floating-point arithmetic, the smallest singular value of matrix $D_k$, ${\sigma}_min(D_k)$, is computed and an inner step is performed if $\sigma_{min}(D_k)<{\epsilon}$, where $\epsilon$ is a suitably chosen tolerance. In practice it is absolutely impossible to choose correctly the value of the tolerance $\epsilon$. The subject of this paper is to show how discrete stochastic arithmetic remedies the problem of this tolerance, as well as the problem of the other tolerances which are needed in the other checks of the QMR method with the estimation of the accuracy of some intermediate results. Numerical examples are used to show the good numerical properties.

Comparative study on dynamic analyses of non-classically damped linear systems

  • Greco, Annalisa;Santini, Adolfo
    • Structural Engineering and Mechanics
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    • v.14 no.6
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    • pp.679-698
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    • 2002
  • In this paper some techniques for the dynamic analysis of non-classically damped linear systems are reviewed and compared. All these methods are based on a transformation of the governing equations using a basis of complex or real vectors. Complex and real vector bases are presented and compared. The complex vector basis is represented by the eigenvectors of the complex eigenproblem obtained considering the non-classical damping matrix of the system. The real vector basis is a set of Ritz vectors derived either as the undamped normal modes of vibration of the system, or by the load dependent vector algorithm (Lanczos vectors). In this latter case the vector basis includes the static correction concept. The rate of convergence of these bases, with reference to a parametric structural system subjected to a fixed spatial distribution of forces, is evaluated. To this aim two error norms are considered, the first based on the spatial distribution of the load and the second on the shear force at the base due to impulsive loading. It is shown that both error norms point out that the rate of convergence is strongly influenced by the spatial distribution of the applied forces.

Nonlinear Transient Heat Transfer Analysis Based on LANCZOS Coordinates (LANCZOS 알고리즘에 기초한 비선형 트랜지언트 열전달 해석)

  • Im, Chang Kyun;Chang, Sung Pil
    • Journal of Korean Society of Steel Construction
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    • v.10 no.2 s.35
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    • pp.317-326
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    • 1998
  • This paper describes a reduced finite element formulation for nonlinear transient heat transfer analysis based on Lanczos Algorithm. In the proposed reduced formulation all material nonlinearities of irradiation boundary element are included using the pseudo force method and numerical time integration of the reduced formulation is conducted by Galerkin method. The results of numerical examples demonstrate the applicability and the accuracy of the proposed method for the nonlinear transient heat transfer analysis.

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Accelerated Starting Vectors for Analysis of Natural Modes of Structures (구조물의 고유모드 해석을 위한 가속화된 초기벡터 구성기법)

  • 김병완;정형조;이인원
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2004.05a
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    • pp.784-787
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    • 2004
  • Modified version of subspace iteration method using accelerated starting vectors is proposed to efficiently calculate free vibration modes of structures. Proposed method employs accelerated Lanczos starting vectors that can reduce the number of iterations in the subspace iteration method. Proposed method is more efficient than the conventional method when the number of required modes is relatively small. To verify the efficiency of proposed method, two numerical examples are presented.

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Solution of Eigenproblems for Non-proportional Damping Systems by Lanczos Method (Lanczos 방법에 의한 비비례 감쇠 시스템의 고유치 해석)

  • 김만철;정형조;오주원;이인원
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 1998.04a
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    • pp.283-290
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    • 1998
  • A solution method is presented to solve the eigenproblem arising in tile dynamic analysis of non-proportional damping systems with symmetric matrices. The method is based on tile use of Lanczos method to generate a Krylov subspace of trial vectors, witch is then used to reduce a large eigenvalue problem to a much smaller one. The method retains the η order quadratic eigenproblem, without the need to the method of matrix augmentation traditionally used to cast the problem as a linear eigenproblem of order 2n. In the process, the method preserves tile sparseness and symmetry of the system matrices and does not invoke complex arithmetics, therefore, making it very economical for use in solving large problems. Numerical results are presented to demonstrate the efficiency and accuracy of the method.

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Investigation of Efficiency of Starting Iteration Vectors for Calculating Natural Modes (고유모드 계산을 위한 초기 반복벡터의 효율성 연구)

  • Kim, Byoung-Wan;Kyoung, Jo-Hyun;Hong, Sa-Young;Cho, Seok-Kyu;Lee, In-Won
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.15 no.1 s.94
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    • pp.112-117
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    • 2005
  • Two modified versions of subspace iteration method using accelerated starting vectors are proposed to efficiently calculate free vibration modes of structures. Proposed methods employ accelerated Lanczos vectors as starting iteration vectors in order to accelerate the convergence of the subspace iteration method. Proposed methods are divided into two forms according to the number of starting vectors. The first method composes 2p starting vectors when the number of required modes is p and the second method uses 1.5p starting vectors. To investigate the efficiency of proposed methods, two numerical examples are presented.

Accelerated Subspace Iteration Method for Computing Natural Frequencies and Mode Shapes of Structures (구조물의 고유진동수 및 모드형상의 계산을 위한 가속화된 부분공간반복법)

  • Kim, Byoung-Wan;Kim, Chun-Ho;Lee, In-Won
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2003.10a
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    • pp.503-508
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    • 2003
  • This paper proposes modified subspace iteration method for efficient frequency analysis of structures. Proposed method uses accelerated Lanczos vectors as starting vectors in order to reduce the number of iterations in the subspace iteration method. Proposed method has better computing efficiency than the conventional method when the number of desired frequencies is relatively small. The efficiency of proposed method is verified through numerical examples.

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Investigation of Convergence of Starting Iteration Vectors for Calculating Natural Modes (고유모드 계산을 위한 초기 반복벡터의 수렴성 연구)

  • Kim, Byoung-Wan;Kyoung, Jo-Hyun;Hong, Sa-Young;Cho, Seok-Kyu;Lee, In-Won
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2004.11a
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    • pp.717-720
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    • 2004
  • Two modified versions of subspace iteration method using accelerated starting vectors are proposed to efficiently calculate free vibration modes of structures. Proposed methods employ accelerated Lanczos vectors as starting iteration vectors in the subspace iteration method. To investigate the efficiency of proposed methods, two numerical examples are presented.

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