scholarly journals A discrete Fourier analysis of coarse mesh rebalancing and some associated iterative methods

1983 ◽  
Vol 25 (2) ◽  
pp. 190-216 ◽  
Author(s):  
J. M. Barry ◽  
J. H. Jenkinson ◽  
J. P. Pollard
Keyword(s):  
Fourier Analysis ◽  
Iterative Methods ◽  
Local Mode ◽  
Test Problems ◽  
Relaxation Techniques ◽  
Potential Candidate ◽  
Coarse Mesh ◽  
Relaxation Methods ◽  
Global Mode ◽  
Discrete Fourier Analysis

AbstractIterative methods for solving systems of linear equations may be accelerated by coarse mesh rebalance techniques. The iterative technique, the Method of Implicit Non-stationary Iteration (MINI), is examined through a local-mode Fourier analysis and compared to relaxation techniques as a potential candidate for such acceleration. Results of a global-mode Fourier analysis for MINI, relaxation methods, and the conjugate gradient method are reported for two test problems.

scholarly journals A Revisit to CMFD Schemes: Fourier Analysis and Enhancement

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 424
Author(s):  
Dean Wang ◽  
Zuolong Zhu
Keyword(s):  
Fourier Analysis ◽  
Eigenvalue Problems ◽  
Neutron Transport ◽  
Coarse Mesh ◽  
Successive Overrelaxation ◽  
Computational Cell ◽  
Artificial Diffusion ◽  
Acceleration Method ◽  
The Stability ◽  
Partial Current

The coarse-mesh finite difference (CMFD) scheme is a very effective nonlinear diffusion acceleration method for neutron transport calculations. CMFD can become unstable and fail to converge when the computational cell optical thickness is relatively large in k-eigenvalue problems or diffusive fixed-source problems. Some variants and fixups have been developed to enhance the stability of CMFD, including the partial current-based CMFD (pCMFD), optimally diffusive CMFD (odCMFD), and linear prolongation-based CMFD (lpCMFD). Linearized Fourier analysis has proven to be a very reliable and accurate tool to investigate the convergence rate and stability of such coupled high-order transport/low-order diffusion iterative schemes. It is shown in this paper that the use of different transport solvers in Fourier analysis may have some potential implications on the development of stabilizing techniques, which is exemplified by the odCMFD scheme. A modification to the artificial diffusion coefficients of odCMFD is proposed to improve its stability. In addition, two explicit expressions are presented to calculate local optimal successive overrelaxation (SOR) factors for lpCMFD to further enhance its acceleration performance for fixed-source problems and k-eigenvalue problems, respectively.

scholarly journals Discrete Fourier analysis with lattices on planar domains

2010 ◽  
Vol 55 (2-3) ◽  
pp. 279-300 ◽  
Author(s):  
Huiyuan Li ◽  
Jiachang Sun ◽  
Yuan Xu
Keyword(s):  
Fourier Analysis ◽  
Discrete Fourier Analysis ◽  
Planar Domains

A Study on the Design Curves for Pultruded Composite Columns

2007 ◽  
Vol 26-28 ◽  
pp. 337-340 ◽  
Author(s):  
Seung Sik Lee ◽  
Soo Ha Chae ◽  
Soon Jong Yoon ◽  
Sun Kyu Cho
Keyword(s):  
Local Mode ◽  
Design Equation ◽  
Global Mode ◽  
Buckling Loads ◽  
Steel Columns ◽  
Short Columns ◽  
Theoretical Approaches ◽  
Interaction Mode ◽  
Column Design ◽  
Thin Walled

The strengths of PFRP thin-walled columns are determined according to the modes of buckling which consist of local mode for short columns, global mode for long columns, and interaction mode between local and global modes for intermediate columns. Unlike the local and global buckling, the buckling strength of interaction mode is not theoretically predictable. Refined theoretical approaches which can account for different elastic properties of each plate component consisting of a PFRP thin-walled member are used. Based on both the analytical buckling loads and the experimentally measured buckling loads from literatures, the accuracies of Ylinen’s equation and modified AISC/LRFD column design equation for isotropic steel columns were compared. From the comparison, it was found that the modified AISC/LRFD column design equation is more suitable for the prediction of the buckling loads of PFRP thin-walled members than Ylinen’s equations.

CLASSIFICATION OF BUCKLING MODES IN STIFFENED FUNCTIONALLY GRADED COMPOSITE TUBES SUBJECT TO BENDING

2021 ◽  
Author(s):  
LUAN TRINH ◽  
PAUL WEAVER
Keyword(s):  
Wall Thickness ◽  
Functionally Graded ◽  
Geometric Parameters ◽  
Mode Shapes ◽  
Local Mode ◽  
Buckling Mode ◽  
Global Mode ◽  
Local Modes ◽  
Linear Discriminant ◽  
Finite Element Software

Bamboo poles, and other one-dimensional thin-walled structures are usually loaded under compression, which may also be subject to bending arising from eccentric loading. Many of these structures contain diaphragms or circumferential stiffeners to prevent cross-sectional distortions and so enhance overall load-carrying response. Such hierarchical structures can compartmentalize buckling to local regions in addition to withstanding global buckling phenomena. Predicting the buckling mode shapes of such structures for a range of geometric parameters is challenging due to the interaction of these global and local modes. Abaqus finite element software is used to model thousands of circular hollow tubes with random geometric parameters such that the ratios of radius to periodic length range from 1/3-1/7, the ratio of wall thickness to radius varies from 1/4-1/10. The material used in this study is a type of bamboo, where the Young’s and shear moduli are point-wise orthotropic and gradually increase in magnitude in the radial direction. Under eccentric loads with varying eccentricity, the structures can buckle into a global mode or local modes within an internode, i.e. periodic unit. Moreover, the local modes may contain only one wave or multiple waves in the circumferential direction. As expected, numerical results show that the global mode is more likely to occur in small and thick tubes, whereas the local modes are observed in larger tubes with a smaller number of circumferential waves present in thicker walls. Also, greater eccentricity pushes the local mode domains towards smaller tubes. An efficient classification method is developed herein to identify the domains of each mode shape in terms of radius, wall thickness and eccentricity. Based on linear discriminant analysis, explicit boundary surfaces for the three domains are defined for the obtained data, which can help designers in predicting the mode shapes of tubular structures under axial bending.

Non-Linear Dynamic Analysis of a Cable-Stayed Beam

2005 ◽  
Author(s):  
Carlos E. N. Mazzilli ◽  
Franz Rena´n Villarroel Rojas
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Multiple Scale ◽  
Local Mode ◽  
Numerical Application ◽  
Global Mode ◽  
Lower Mode ◽  
Reduced Equations ◽  
External Resonance ◽  
Non Linear

The dynamic behaviour of a simple clamped beam suspended at the other end by an inclined cable stay is surveyed in this paper. The sag due to the cable weight, as well as the non-linear coupling between the cable and the beam motions are taken into account. The formulation for in-plane vibration follows closely that of Gattulli et al. [1] and confirms their findings for the overall features of the equations of motion and the system modal properties. A reduced non-linear mathematical model, with two degrees of freedom, is also developed, following again the steps of Gattulli and co-authors [2,3]. Hamilton’s Principle is evoked to allow for the projection of the displacement field of both the beam and the cable onto the space defined by the first two modes, namely a “global” mode (beam and cable) and a “local” mode (cable). The method of multiple scales is then applied to the analysis of the reduced equations of motion, when the system is subjected to the action of a harmonic loading. The steady-state solutions are characterised in the case of internal resonance between the local and the global modes, plus external resonance with respect to either one of the modes considered. A numerical application is presented, for which multiple-scale results are compared with those of numerical integration. A reasonable qualitative and quantitative agreement is seen to happen particularly in the case of external resonance with the higher mode. Discrepancies should obviously be expected due to strong non-linearities present in the reduced equations of motion. That is specially the case for external resonance with the lower mode.

Accelerating Vector Iteration Methods

1986 ◽  
Vol 53 (2) ◽  
pp. 291-297 ◽  
Author(s):  
M. Papadrakakis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Iterative Methods ◽  
Conjugate Gradient ◽  
Test Problems ◽  
Convergence Properties ◽  
Dynamic Relaxation ◽  
Element Level ◽  
Iteration Methods ◽  
Partial Elimination

This paper describes a technique for accelerating the convergence properties of iterative methods for the solution of large sparse symmetric linear systems that arise from the application of finite element method. The technique is called partial preconditioning process (PPR) and can be combined with pure vector iteration methods, such as the conjugate gradient, the dynamic relaxation, and the Chebyshev semi-iterative methods. The proposed triangular splitting preconditioner combines Evans’ SSOR preconditioner with a drop-off tolerance criterion. The (PPR) is attractive in a FE framework because it is simple and can be implemented at the element level as opposed to incomplete Cholesky preconditioners, which require a sparse assembly. The method, despite its simplicity, is shown to be more efficient on a set of test problems for certain values of the drop-off tolerance parameter than the partial elimination method.

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