scholarly journals Displacement Field Approximations for Force-Based Elements in Large Displacement Analyses

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
M. Vahidi ◽  
V. Jafari ◽  
M. H. Abyaneh ◽  
SH. Vahdani
Keyword(s):  
State Space ◽  
Displacement Field ◽  
Order Approximation ◽  
Computational Cost ◽  
Higher Order ◽  
Linear Displacement ◽  
Large Displacement ◽  
Approximation Techniques ◽  
Engineering Problems

This paper investigates different approximation techniques for planar beam column elements in force-based methods. The three fields, introduced in this review, are: curvature-based displacement interpolation (CBDI) used in matrix-based flexibility formulations, linear displacement approximation applied in state space, and higher-order displacement approximation utilized again in state space. Using these three approximation fields, the responses and their accuracies in some systems are compared in examples. Finally, focusing on the accuracy and regarding the performed analyses, it seems that the computational cost is reduced and accuracy of responses is elevated in many engineering problems using the higher-order approximation field in state space.

PoLIM: an open source 2D higher-order thermomechanically coupled mountain glacier flow model

2020 ◽  
Author(s):  
Yuzhe Wang ◽  
Tong Zhang
Keyword(s):  
Flow Model ◽  
Order Approximation ◽  
Water Pressure ◽  
Computational Cost ◽  
Higher Order ◽  
Thermomechanical Coupling ◽  
High Mountain ◽  
Climate Data ◽  
Mountain Glacier ◽  
Ice Flow

<p>The worldwide glacier is retreating and is expected to continue shrinking in a warming climate. Understanding the dynamics of glaciers is essential for the knowledge of sea-level rise, water resources in high mountain and arid regions, and the potential glacier hazards. Over the past decades, various 3D higher-order and full-Stokes ice flow models including thermomechanical coupling have been developed, and some have opened their source codes. However, such 3D modeling requires detailed datasets about surface and bedrock topography, variable climatic conditions, and high computational cost. Due to difficulties in measuring glacier thickness, only a small minority of glaciers around the globe have ice thickness observations. It is also a challenge to downscale the climate data (e.g., air temperature, precipitation) to the glacier surface, particularly, in rugged high-mountain terrains. In contrast to 3D models, flowline models only require inputs along the longitudinal profile and are thus computationally efficient. They continue to be useful tools for simulating the evolution of glaciers and studying the particular phenomena related to glacier dynamics. In this study, we present a two-dimensional thermomechanically coupled ice flow model named PoLIM (Polythermal Land Ice Model). The velocity solver of PoLIM is developed based on the higher-order approximation (Blatter-Pattyn type). It includes three critical features for simulating the dynamics of mountain glaciers: 1) an enthalpy-based thermal model to describe the heat transfer, which is particularly convenient to simulate the polythermal structures; 2) a drainage model to simulate the water transport in the temperate ice layer driven by gravity; 3) a subglacial hydrology model to simulate the subglacial water pressure for the coupling with the basal sliding law. We verify PoLIM with several standard benchmark experiments (e.g., ISMIP-HOM, enthalpy, SHMIP) in the glacier modeling community. PoLIM shows a good performance and agrees well with these benchmark results, indicating its reliable and robust capability of simulating the thermomechanical behaviors of glaciers.</p>

scholarly journals Analytical Solutions of Fractional Differential Equations Using the Convenient Adomian Series

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Xiang-Chao Shi ◽  
Lan-Lan Huang ◽  
Zhen-Guo Deng ◽  
Dan Liu
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Decomposition Method ◽  
Order Approximation ◽  
Adomian Decomposition Method ◽  
Higher Order ◽  
Nonlinear Fractional Differential Equation ◽  
Adomian Decomposition ◽  
Engineering Problems ◽  
Fractional Differential

Due to the memory trait of the fractional calculus, numerical or analytical solution of higher order becomes very difficult even impossible to obtain in real engineering problems. Recently, a new and convenient way was suggested to calculate the Adomian series and the higher order approximation was realized. In this paper, the Adomian decomposition method is applied to nonlinear fractional differential equation and the error analysis is given which shows the convenience.

Using the Multi-Parameter Fracture Mechanics for more Accurate Description of Stress/Displacement Crack Tip Fields

2013 ◽  
Vol 586 ◽  
pp. 237-240 ◽  
Author(s):  
Lucie Šestáková
Keyword(s):  
Stress Distribution ◽  
Fracture Mechanics ◽  
Boundary Conditions ◽  
Displacement Field ◽  
Singular Term ◽  
Crack Tip ◽  
Higher Order ◽  
Precise Description ◽  
Accurate Knowledge ◽  
Higher Order Terms

Most of fracture analyses often require an accurate knowledge of the stress/displacement field over the investigated body. However, this can be sometimes problematic when only one (singular) term of the Williams expansion is considered. Therefore, also other terms should be taken into account. Such an approach, referred to as multi-parameter fracture mechanics is used and investigated in this paper. Its importance for short/long cracks and the influence of different boundary conditions are studied. It has been found out that higher-order terms of the Williams expansion can contribute to more precise description of the stress distribution near the crack tip especially for long cracks. Unfortunately, the dependences obtained from the analyses presented are not unambiguous and it cannot be strictly derived how many of the higher-order terms are sufficient.

Efficient and High-Quality Seeded Graph Matching: Employing Higher-order Structural Information

2021 ◽  
Vol 15 (3) ◽  
pp. 1-31
Author(s):  
Haida Zhang ◽  
Zengfeng Huang ◽  
Xuemin Lin ◽  
Zhe Lin ◽  
Wenjie Zhang ◽  
...  
Keyword(s):  
Large Scale ◽  
Graph Matching ◽  
Structural Information ◽  
Experimental Studies ◽  
Higher Order ◽  
Personalized Pagerank ◽  
Matching Accuracy ◽  
Approximation Techniques ◽  
Order Of Magnitude ◽  
Matching Score

Driven by many real applications, we study the problem of seeded graph matching. Given two graphs and , and a small set of pre-matched node pairs where and , the problem is to identify a matching between and growing from , such that each pair in the matching corresponds to the same underlying entity. Recent studies on efficient and effective seeded graph matching have drawn a great deal of attention and many popular methods are largely based on exploring the similarity between local structures to identify matching pairs. While these recent techniques work provably well on random graphs, their accuracy is low over many real networks. In this work, we propose to utilize higher-order neighboring information to improve the matching accuracy and efficiency. As a result, a new framework of seeded graph matching is proposed, which employs Personalized PageRank (PPR) to quantify the matching score of each node pair. To further boost the matching accuracy, we propose a novel postponing strategy, which postpones the selection of pairs that have competitors with similar matching scores. We show that the postpone strategy indeed significantly improves the matching accuracy. To improve the scalability of matching large graphs, we also propose efficient approximation techniques based on algorithms for computing PPR heavy hitters. Our comprehensive experimental studies on large-scale real datasets demonstrate that, compared with state-of-the-art approaches, our framework not only increases the precision and recall both by a significant margin but also achieves speed-up up to more than one order of magnitude.

scholarly journals Higher Order Haar Wavelet Method for Solving Differential Equations

2020 ◽  
Author(s):  
Jüri Majak ◽  
Mart Ratas ◽  
Kristo Karjust ◽  
Boris Shvartsman
Keyword(s):  
Differential Equations ◽  
Computational Cost ◽  
Haar Wavelet ◽  
Higher Order ◽  
Wavelet Method ◽  
Haar Wavelet Method ◽  
Convergence Results ◽  
Key Characteristics ◽  
Parameter Values ◽  
Excellent Accuracy

The study is focused on the development, adaption and evaluation of the higher order Haar wavelet method (HOHWM) for solving differential equations. Accuracy and computational complexity are two measurable key characteristics of any numerical method. The HOHWM introduced recently by authors as an improvement of the widely used Haar wavelet method (HWM) has shown excellent accuracy and convergence results in the case of all model problems studied. The practical value of the proposed HOHWM approach is that it allows reduction of the computational cost by several magnitudes as compared to HWM, depending on the mesh and the method parameter values used.

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