Fast approximation of synthesized frequency response functions with automated multi-level substructuring (AMLS)

Ragnarsson, Patrik; Gaál, Tamás; Pluymers, Bert; Donders, Stijn; Vandepitte, Dirk; Desmet, Wim

doi:10.1016/j.finel.2010.08.009

Cited by 4 publications

(5 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Due to its ability to quickly achieve dramatic reductions in the size of FE models, AMLS has been shown to be quite efficient in frequency response and eigenvalue analysis of real-world engineering problems. 7,[31][32][33][34][35] Nonetheless, the accuracy of the approximate eigenpairs returned by AMLS can be rather low for general algebraic eigenvalue problems. Moreover, as AMSLS is based on nested dissection, its suitability for execution on distributed memory computing environments is limited.…”

Section: Introductionmentioning

confidence: 99%

“…Once the leaf substructures are reached, AMLS computes a number of eigenmodes from each substructure (e.g., those below a cut‐off threshold) and traverses the elimination tree in an upwards fashion, each time multiplying the interface eigenmodes at the current level with the corresponding block Gaussian elimination matrix. Due to its ability to quickly achieve dramatic reductions in the size of FE models, AMLS has been shown to be quite efficient in frequency response and eigenvalue analysis of real‐world engineering problems 7,31‐35 . Nonetheless, the accuracy of the approximate eigenpairs returned by AMLS can be rather low for general algebraic eigenvalue problems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Enhanced algebraic substructuring for symmetric generalized eigenvalue problems

Kalantzis

Horesh

2022

Numerical Linear Algebra App

View full text Add to dashboard Cite

This article proposes a new substructuring algorithm to approximate the algebraically smallest eigenvalues and corresponding eigenvectors of a symmetric positive-definite matrix pencil (A, M). The proposed approach partitions the graph associated with (A, M) into a number of algebraic substructures and builds a Rayleigh-Ritz projection subspace by combining spectral information associated with the interior and interface variables of the algebraic domain. The subspace associated with interior variables is built by computing substructural eigenvectors and truncated Neumann series expansions of resolvent matrices. The subspace associated with interface variables is built by computing eigenvectors and associated leading derivatives of linearized spectral Schur complements. The proposed algorithm can take advantage of multilevel partitionings when the size of the pencil. Experiments performed on problems stemming from discretizations of model problems showcase the efficiency of the proposed algorithm and verify that adding eigenvector derivatives can enhance the overall accuracy of the approximate eigenpairs, especially those associated with eigenvalues located near the origin.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Enhanced algebraic substructuring for symmetric generalized eigenvalue problems

Kalantzis

Horesh

2022

Numerical Linear Algebra App

View full text Add to dashboard Cite

show abstract

“…The low-frequency modes are extremal eigenvectors of a large and sparse generalized eigenvalue problem (GEP), associated with the free vibrations of the conservative system (no damping). In structural dynamics, the most widely-used eigenvalue solvers include the Lanczos algorithm [4][5][6][7][8][9][10], the subspace iteration method (SIM, [11][12][13][14][15]), the Craig-Bampton (CB, [16,17]) component mode synthesis (CMS, [14,[18][19][20][21]), and the automated multilevel substructuring (AMLS, [22][23][24][25][26]) solver. Dynamic substructuring [27][28][29][30][31] is another name for CMS.…”

Section: Introductionmentioning

confidence: 99%

Multiscale modal analysis of fully-loaded spent nuclear fuel canisters

Ezvan

Zeng

Ghanem

et al. 2020

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

In this paper, an efficient numerical procedure is proposed, adapted to the modal analysis of a fully-loaded spent nuclear fuel canister, which exhibits distinct structural levels associated with a hierarchy of components. On the one hand, the fully-loaded spent nuclear fuel canister is constituted of the repetition of identical components, resulting in a pseudo-periodicity; and the components of a given level are separated from each other and only connected to their upper level through localized attachments, which gives rise to an advantageous structural connectivity that can be exploited for efficiency. On the other hand, the necessary fine mesh resolution of the small levels leads to a high-dimensional computational model and, in addition, the independent resonant vibrations of each of the components produce a very large number of vibration eigenmodes. The aforementioned opportunities and difficulties are respectively leveraged and tackled by an adapted method that combines domain decomposition, shift-invert Lanczos eigenvalue solver, and Craig-Bampton substructuring technique. A parallel eigensolution via spectrum slicing is facilitated by an efficient block factorization by Schur complement that is enabled by the sparsity of the Craig-Bampton matrices. A computational gain of four orders of magnitude is obtained, at the expense of negligible errors that are exactly characterized. The proposed methodology enables a high-fidelity vibration analysis of the sealed fully-loaded spent nuclear fuel canister, useful for non-intrusive inverse identification of the structural integrity of the internal structural levels holding the nuclear material.

show abstract

“…This paper presents a new methodology that tackles this difficulty inherited from the multilevel nature of the structure. In structural dynamics, the prominent eigenvalue solvers include the Shift-Invert Lanczos (SIL [5,6]) solver, the Subspace Iteration Method (SIM [7,8]), Craig-Bampton (CB [9,10]) substructuring technique, and Automated Multilevel Substructuring (AMLS [11,12]). SIL and SIM are iterative solvers that converge to the true eigensolutions whereas CB and AMLS deliver approximate eigenso-lutions.…”

Section: Introductionmentioning

confidence: 99%

Dominant substructural vibration modes for fully-loaded spent nuclear fuel canisters

et al. 2020

View full text Add to dashboard Cite

This paper investigates the dynamic characteristics of a multilevel structure for the transportation and storage of spent nuclear fuel (SNF) from commercial power plants. The nuclear fuel is stored in slender rods that are grouped together into fuel assemblies (FA). In a sealed cylindrical container called "canister", the FA are inserted into a honeycomb basket. The objective of this paper is to develop a computational model that accurately describes the structural dynamics of the canister, based on measurements collected from its external surface. Based on these measurements, the computational model is intended to capture the signature of the structural integrity of the internal components (FA and fuel rods). The numerous components lead to a large finite element (FE) model and numerous vibration modes and eigenfrequencies. Nevertheless, the localized connections between components enable an efficient domain decomposition with few interface coordinates. Craig-Bampton (CB) substructuring is thus used to perform the modal analysis. However, the high modal density yields a large-scale CB eigenvalue problem that necessitates a sparse solver. A block factorization by Schur complement that exploits the sparsity of the CB matrices allows an efficient calculation of the numerous eigenpairs. Many local vibration modes contribute little to the dynamics of the SNF canister. The main contribution of this paper is the development of an efficient methodology for determining the importance of each of

show abstract

Fast approximation of synthesized frequency response functions with automated multi-level substructuring (AMLS)

Cited by 4 publications

References 17 publications

Enhanced algebraic substructuring for symmetric generalized eigenvalue problems

Enhanced algebraic substructuring for symmetric generalized eigenvalue problems

Multiscale modal analysis of fully-loaded spent nuclear fuel canisters

Dominant substructural vibration modes for fully-loaded spent nuclear fuel canisters

Contact Info

Product

Resources

About