scholarly journals Using quadratic simplicial elements for hierarchical approximation and visualization

2002 ◽  
Author(s):  
David F. Wiley ◽  
Henry R. Childs ◽  
Bernd Hamann ◽  
Kenneth I. Joy ◽  
Nelson Max
Keyword(s):  
Hierarchical Approximation

RENORMALIZATION GROUP METHODS IN CONSTRUCTIVE FIELD THEORIES

2000 ◽  
Vol 14 (12n13) ◽  
pp. 1363-1398
Author(s):  
HIROSHI WATANABE
Keyword(s):  
Renormalization Group ◽  
Group Analysis ◽  
Group Method ◽  
Coupling Region ◽  
Renormalization Group Analysis ◽  
New Approach ◽  
Group Methods ◽  
Technical Details ◽  
Hierarchical Approximation

Mathematical construction of quantum field theory is reviewed with emphasis on the conceptual structure of the construction and on the role of rigorous renormalization group analysis without technical details. After explaining a rigorous formulation of a renormalization group method in a weak coupling region, a new approach in a strong coupling region is proposed in the context of the hierarchical approximation. An idea of proving triviality in d≥4 dimensions utilizing this new proposal concludes this review.

scholarly journals REMARKS CONCERNING POLYAKOV’S CONJECTURE FOR THE 3D ISING MODEL AND THE HIERARCHICAL APPROXIMATION

1992 ◽  
Vol 07 (35) ◽  
pp. 3331-3336 ◽  
Author(s):  
YANNICK MEURICE
Keyword(s):  
Renormalization Group ◽  
Ising Model ◽  
Hierarchical Model ◽  
Continuum Limit ◽  
Group Transformation ◽  
New Variables ◽  
String Models ◽  
Hierarchical Approximation ◽  
The Continuum ◽  
3D Ising Model

We consider the possibility of using the hierarchical approximation to understand the continuum limit of a reformulation of the 3D Ising model initiated by Polyakov. We introduce several new formulations of the hierarchical model using dual or fermionic variables. We discuss several aspects of the renormalization group transformation in terms of these new variables. We mention a reformulation of the model closely related to string models proposed by Zabrodin.

Wavelet interpolation networks for hierarchical approximation

1999 ◽  
Author(s):  
Christophe P. Bernard ◽  
Stephane G. Mallat ◽  
Jean-Jeacques E. Slotine
Keyword(s):  
Hierarchical Approximation

Identification of Crack Damage with Wavelet Finite Element

2005 ◽  
Vol 293-294 ◽  
pp. 63-70
Author(s):  
Xue Feng Chen ◽  
Zheng Jia He ◽  
Qiang Gao ◽  
Yanyang Zi
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Experimental Studies ◽  
Transient Signal ◽  
Crack Identification ◽  
Crack Location ◽  
Good Ability ◽  
Wavelet Finite Element ◽  
Elastic Fracture ◽  
Hierarchical Approximation

An improved method to identify the crack location and size is presented which takes advantages of wavelet finite element (WFE). The important property of wavelet analysis is the capability to represent functions in a dynamic multiscale manner, so solution with WFE enables a hierarchical approximation to the exact solution. WFE has good ability in modal analysis for singularity problems like a cracked beam. The crack in a beam is modeled with WFE and represented as a rotational spring. The additional flexibility caused by crack in its vicinity is evaluated according to linear and elastic fracture mechanics theory. The WFE stiffness matrix of the crack is constructed and the algorithm for crack identification through the use of vibration-based inspection (VBI) is developed. With the accurate natural frequencies obtained from the transient signal measured, graphs of crack equivalent stiffness versus crack location are plotted, by providing the first three natural frequencies as an input. The intersection of the three curves gives the crack location and size. Experimental studies of cracked shafts are presented to demonstrate the accuracy of the method. The error in identification of crack location and size are both less than 2%. This study provides the new method for the diagnosis of incipient small crack.

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