Journal ArticleDOI
Dynamic analysis of structures using lanczos co-ordinates
Bahram Nour-Omid,Ray W. Clough +1 more
TLDR
In this article, the Lanczos vectors are obtained by an inverse iteration procedure in which orthogonality is imposed between the vectors resulting from successive iteration cycles, which provides for a very efficient time-stepping solution.Abstract:
A procedure for deriving the Lanczos vectors is explained and their use in structural dynamics analysis as an alternative to modal co-ordinates is discussed. The vectors are obtained by an inverse iteration procedure in which orthogonality is imposed between the vectors resulting from successive iteration cycles. Using these Lanczos vectors the equations of motion are transformed to tridiagonal form, which provides for a very efficient time-stepping solution. The effectiveness of the method is demonstrated by a numerical example.read more
Citations
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Dissertation
Krylov Projection Methods for Model Reduction
TL;DR: The cornerstone of this dissertation is a collection of theory relating Krylov projection to rational interpolation, based on which three algorithms for model reduction are proposed, which are suited for parallel or approximate computations.
Journal ArticleDOI
Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems
TL;DR: This paper gives an overview of the recent progress in other Krylov subspace techniques for a variety of dynamical systems, including second-order and nonlinear systems, and case studies arising from circuit simulation, structural dynamics and microelectromechanical systems are presented.
Journal ArticleDOI
A rational Lanczos algorithm for model reduction
TL;DR: A variant of the nonsymmetric Lanczos method, rational Lanczos, is shown to yield a rational interpolant (multi-point Padé approximant) for the large-scale system.
Journal ArticleDOI
Spectral approach to solving three-dimensional Maxwell's diffusion equations in the time and frequency domains
TL;DR: A new explicit three-dimensional solver for the diffusion of electromagnetic fields in arbitrarily heterogeneous conductive media is described, based on a global Krylov subspace (Lanczos) approximation of the solution in the time and frequency domains.
Journal ArticleDOI
Two polynomial methods of calculating functions of symmetric matrices
TL;DR: Methods of calculating f ( A), where A is a symmetric matrix andis a vector, using operator Chebyshev series and the Lanczos method are considered, demonstrating the efficiency of the proposed methods.
References
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Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
Journal ArticleDOI
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
TL;DR: In this article, a systematic method for finding the latent roots and principal axes of a matrix, without reducing the order of the matrix, has been proposed, which is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the process of minimized iterations.
Book
The computation of eigenvalues and eigenvectors of very large sparse matrices
TL;DR: A particular computation algorithm for the method without reorthogonalization is shown to have remarkably good error properties, and this suggests that this variant of the Lanczos process is likely to become an extremely useful algorithm for finding several extreme eigenvalues, and their eigenvectors if needed, of very large sparse symmetric matrices.
Journal ArticleDOI
Evaluation of orthogonal damping matrices
Edward L. Wilson,J. Penzien +1 more
TL;DR: In this article, two methods for the numerical evaluation of orthogonal damping matrices are developed: the first relates the modal damping ratios to the coefficients of the Caughey series, and the second is a direct approach which expresses the damping matrix as a sum of a series of matrices each of which produces damping in a particular mode.
Journal ArticleDOI
On the accuracy of mode superposition analysis in structural dynamics
Ole Edvard Hansteen,Kolbein Bell +1 more
TL;DR: In this article, the number of modes which should be included in a mode superposition dynamic response analysis depends on both the frequency content and the distribution of the loading, and a technique is described for calculating this static contribution from the higher modes; the total response is then represented by the sum of the lower mode dynamic response and the higher mode static effects.