scholarly journals Numerical Solution of Sine-Gordon Equation with the Local Kriging Meshless Method

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Pengfei Guo ◽  
Ariunkhishig Boldbaatar ◽  
Dutao Yi ◽  
Pengxiang Dai
Keyword(s):  
Meshless Method ◽  
Gordon Equation ◽  
Numerical Solutions ◽  
Interpolation Method ◽  
Time Discretization ◽  
Delta Function ◽  
Kriging Interpolation ◽  
Sine Gordon Equation ◽  
Field Function ◽  
Kriging Interpolation Method

This paper develops a local Kriging meshless solution to the nonlinear 2 + 1-dimensional sine-Gordon equation. The meshless shape function is constructed by Kriging interpolation method to have Kronecker delta function property for the two-dimensional field function, which leads to convenient implementation of imposing essential boundary conditions. Based on the local Petrov–Galerkin formulation and the center difference method for time discretization, a system of nonlinear discrete equations is obtained. The numerical examples are presented and the numerical solutions are found to be in good agreement with the results in the literature to validate the ability of the present meshless method to handle the 2 + 1-dimensional sine-Gordon equation related problems.

Numerical Investigation of the Identifiability of Elastomer Mechanical Properties by Nano-Indentation and Shape-Manifold Approach

2021 ◽  
Author(s):  
Oumaima Ezzaamari ◽  
Guénhaël Le Quilliec ◽  
Florian Lacroix ◽  
Stéphane Méo
Keyword(s):  
Numerical Study ◽  
Interpolation Method ◽  
Structural Characteristics ◽  
Numerical Approach ◽  
Kriging Interpolation ◽  
Nano Indentation ◽  
Kriging Interpolation Method ◽  
Elastomeric Materials ◽  
Hyper Elastic ◽  
Characterization Test

ABSTRACT Various research is covering instrumented nano-indentation in the literature. However, studies on this characterization test remain limited when it comes to the local mechanical behavior of elastomeric materials. The application of nano-indentation on these materials is a difficult task given their complex mechanical and structural characteristics. We try to overcome these experimental limitations and find an effective numerical approach for local mechanical characterization of hyper-elastic materials. For such needs, we carried out a numerical study based on model reduction and shape manifold approach to investigate the parameters identification of different hyper-elastic constitutive laws by using instrumented indentation. Similarly, we studied the influence of the indenter geometry, the friction coefficient variation, and finally the indented material height effect. To this end, we constructed a reduced order model through a design of experiments by proper orthogonal decomposition combined with the kriging interpolation method.

scholarly journals Estimation of Ice Thickness and the Features of Subglacial Media Detected by Ground Penetrating Radar at the Baishui River Glacier No. 1 in Mt. Yulong, China

2020 ◽  
Vol 12 (24) ◽  
pp. 4105
Author(s):  
Jing Liu ◽  
Shijin Wang ◽  
Yuanqing He ◽  
Yuqiang Li ◽  
Yuzhe Wang ◽  
...  
Keyword(s):  
Ground Penetrating Radar ◽  
Interpolation Method ◽  
Kriging Interpolation ◽  
Ice Thickness ◽  
Grid Data ◽  
Differential Gps ◽  
Landsat Images ◽  
Kriging Interpolation Method ◽  
Bedrock Surface ◽  
Ground Penetrating

Using ground-penetrating radar (GPR), we measured and estimated the ice thickness of the Baishui River Glacier No. 1 of Yulong Snow Mountain. According to the position of the reflected media from the GPR image, combined with the radar waveform amplitude and polarity change information, the ice thickness and the changing medium position at the bottom of this temperate glacier were identified. Water paths were found in the measured ice, including ice caves and crevasses. A debris-rich ice layer was found at the bottom of the glacier, which produces strong abrasion and ploughing action at the bedrock surface. This results in the formation of different detrital layers stagnated at the ice-bedrock interface and numerous crevasses on the bedrock surface. Based on the obtained ice thickness and differential GPS data, combined with Landsat images, the kriging interpolation method was used to obtain grid data. The average ice thickness was 52.48 m and between 4740 and 4890 m above sea level, with a maximum depth of 92.83 m. The bedrock topography map of this area was drawn using digital elevation model from the Shuttle Radar Topography Mission. The central part of the glacier was characterized by small ice basins with distributed ice steps and ice ridges at the upper and lower parts.

Numerical Modeling of Fracture Process Using Element-Free Method

2013 ◽  
Vol 427-429 ◽  
pp. 146-149
Author(s):  
Cheng Fan
Keyword(s):  
Interpolation Method ◽  
Kriging Interpolation ◽  
Computational Accuracy ◽  
Simple Method ◽  
Solution Domain ◽  
Kriging Interpolation Method ◽  
Finite Covers ◽  
Crack Problems ◽  
Cover Systems ◽  
Element Free

A new element-free formulation of Kriging interpolation procedure based on finite covers technique and Kriging interpolation method which integrates the flexibilities of the manifold method in dealing with discontinuity and the element-free features of the moving Kriging interpolation. Two cover systems are employed in this method. Mathematical cover of the solution domain under consideration are used to construct shape function and physical cover is used to reproduce the geometry of the solution domain. The mathematical covers can take any types of shape and is much easily formed compared with those in the conventional MM. The presented method can overcome some difficulties in conventional element-free Galerkin methods in treating discontinuous crack problems. The fundamental theory of this procedure is illustrated and numerical analyses of examples show that the proposed procedure is an effective and simple method with higher computational accuracy.

Integration of statistical and spatial methods for distributing precipitation in tropical areas

2012 ◽  
Vol 44 (6) ◽  
pp. 982-994 ◽  
Author(s):  
Mandana Abedini ◽  
Md Azlin Md Said ◽  
Fauziah Ahmad
Keyword(s):  
Multivariate Regression ◽  
Interpolation Method ◽  
Rainfall Data ◽  
Environmental Research ◽  
Kriging Interpolation ◽  
Slope Aspect ◽  
Annual Average ◽  
Rain Gauges ◽  
Kriging Interpolation Method ◽  
Topographical Factors

The high spatial resolution of precipitation distribution is a major concern for experts in environmental research and planning. This paper establishes a combination of multivariate regression algorithm and spatial analysis to predict distribution of precipitation, considering the four topographical factors of altitude, slope, aspect and location. Annual average and seasonal rainfall data were collected in nine rain gauges in Ulu Kinta Catchment in East Malaysia from 1974 to 2010. To examine records and fill gaps from long-term rain gauges, homogeneity analysis was performed using the double-mass curve method. Estimated missing rainfall data were also tested using index gauges from network rainfall stations. Multivariate regression analysis was conducted to propose an empirical equation for the study area. Topographical factors were considered from a 90 m resolution digital elevation model. The multivariate regression model was found to clarify 74% of spatial variability of precipitation on annual average and 78% during wet season. However, the correlation coefficient for the dry season decreased sharply to 63%. By using the kriging interpolation method, the estimated annual average improved to 78.4%; the average improved to 65.2 and 80.3% in the dry and wet seasons, respectively. This confirms the efficiency and significance of the model and its potential for use in other tropical catchments.

The Flow Units Study Based on Reservoir Architecture

2011 ◽  
Vol 361-363 ◽  
pp. 66-69
Author(s):  
Cong Jun Feng ◽  
Zhi Dong Bao ◽  
Ying Wang
Keyword(s):  
Oil Recovery ◽  
Interpolation Method ◽  
Flow Unit ◽  
Kriging Interpolation ◽  
Empirical Formulas ◽  
Reservoir Architecture ◽  
Flow Units ◽  
Kriging Interpolation Method ◽  
The Relationship

In the case of Fourth Member of Quantou Formation (K1q4) in Well X5-16 of Fuyu Oilfield, it integrates the theory of reservoir architecture and methodology for flow-unit analysis to characterize the architectural units and their permeable features in reservoirs. As the research found, point bars are very developed in low-sinuosity meandering distributary channels. Therefore, parameter modeling for reservoirs, confined by reservoir architecture is firstly constructed from empirical formulas and integrating the data from closely-spaced wells in dense pattern area. At this basis, clustering analysis with optimized reservoir parameters help demarcate the classification of flow units and further the Kriging interpolation method is introduced for interwell flow unit prediction. Besides, the study also illustrates the relationship between the lateral accretion and the flow unit. Finally, the research achievements were confirmed by successfully matching the production data, so as to predict how the remaining oil distributes, or to adjust the development plan, as well as enhance the oil recovery.

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