Adjoint variable method for design sensitivity analysis of eigenproblem

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Abstract

New adjoint variable method for design sensitivity analysis of eigenvalues and eigenvectors is presented. In the viewpoint of efficiency for the design sensitivity analysis of eigenvector especially, the developed adjoint variable method is required to compute adjoint variables from simultaneous linear equations, the so-called adjoint equations, instead of linear combination of eigenvectors. Once we obtain the adjoint variables, design sensitivity analysis of response function that is given in terms of eigenvalues, eigenvectors and design variables can be computed directly. In this way, design sensitivity analysis of eigenvector can be obtained by using eigenvalue and corresponding eigenvectors of the mode being differentiated only. To verify the proposed method, numerical examples are demonstrated. This can have considerable impact on computer implementation of the developed method in the sensitivity analysis of eigenproblem needed for practical applications.

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Eigenvalues and eigenfunctions
Sensitivity analysis
Linear equations
Numerical methods

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@article{4ef401c8565243c4b3abc9c53c993781,
title = "Adjoint variable method for design sensitivity analysis of eigenproblem",
abstract = "New adjoint variable method for design sensitivity analysis of eigenvalues and eigenvectors is presented. In the viewpoint of efficiency for the design sensitivity analysis of eigenvector especially, the developed adjoint variable method is required to compute adjoint variables from simultaneous linear equations, the so-called adjoint equations, instead of linear combination of eigenvectors. Once we obtain the adjoint variables, design sensitivity analysis of response function that is given in terms of eigenvalues, eigenvectors and design variables can be computed directly. In this way, design sensitivity analysis of eigenvector can be obtained by using eigenvalue and corresponding eigenvectors of the mode being differentiated only. To verify the proposed method, numerical examples are demonstrated. This can have considerable impact on computer implementation of the developed method in the sensitivity analysis of eigenproblem needed for practical applications.",
author = "Lee, {Tae Hee}",
year = "1998",
month = "1",
day = "1",
language = "English",
volume = "3",
pages = "2192--2198",
journal = "Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference",
issn = "0273-4508",

}

TY - JOUR

T1 - Adjoint variable method for design sensitivity analysis of eigenproblem

AU - Lee, Tae Hee

PY - 1998/1/1

Y1 - 1998/1/1

N2 - New adjoint variable method for design sensitivity analysis of eigenvalues and eigenvectors is presented. In the viewpoint of efficiency for the design sensitivity analysis of eigenvector especially, the developed adjoint variable method is required to compute adjoint variables from simultaneous linear equations, the so-called adjoint equations, instead of linear combination of eigenvectors. Once we obtain the adjoint variables, design sensitivity analysis of response function that is given in terms of eigenvalues, eigenvectors and design variables can be computed directly. In this way, design sensitivity analysis of eigenvector can be obtained by using eigenvalue and corresponding eigenvectors of the mode being differentiated only. To verify the proposed method, numerical examples are demonstrated. This can have considerable impact on computer implementation of the developed method in the sensitivity analysis of eigenproblem needed for practical applications.

AB - New adjoint variable method for design sensitivity analysis of eigenvalues and eigenvectors is presented. In the viewpoint of efficiency for the design sensitivity analysis of eigenvector especially, the developed adjoint variable method is required to compute adjoint variables from simultaneous linear equations, the so-called adjoint equations, instead of linear combination of eigenvectors. Once we obtain the adjoint variables, design sensitivity analysis of response function that is given in terms of eigenvalues, eigenvectors and design variables can be computed directly. In this way, design sensitivity analysis of eigenvector can be obtained by using eigenvalue and corresponding eigenvectors of the mode being differentiated only. To verify the proposed method, numerical examples are demonstrated. This can have considerable impact on computer implementation of the developed method in the sensitivity analysis of eigenproblem needed for practical applications.

UR - http://www.scopus.com/inward/record.url?scp=0031651095&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0031651095

VL - 3

SP - 2192

EP - 2198

JO - Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

JF - Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

SN - 0273-4508

ER -