Is Minimising the Convergence Rate a Good Choice for Efficient Optimized Schwarz Preconditioning in Heterogeneous Coupling? The Stokes-Darcy Case

2018 ◽  
pp. 233-241
Author(s):  
Marco Discacciati ◽  
Luca Gerardo-Giorda
Keyword(s):  
Convergence Rate ◽  
Good Choice ◽  
Heterogeneous Coupling

On the Choice of Design Points for Least Square Polynomial Approximations with Application to Uncertainty Quantification

2014 ◽  
Vol 16 (2) ◽  
pp. 365-381 ◽  
Author(s):  
Zhen Gao ◽  
Tao Zhou
Keyword(s):  
Monte Carlo ◽  
Convergence Rate ◽  
Uncertainty Quantification ◽  
Good Choice ◽  
Least Square ◽  
Design Matrix ◽  
Numerical Comparison ◽  
Convergence Properties ◽  
Stability Point ◽  
The Stability

AbstractIn this work, we concern with the numerical comparison between different kinds of design points in least square (LS) approach on polynomial spaces. Such a topic is motivated by uncertainty quantification (UQ). Three kinds of design points are considered, which are the Sparse Grid (SG) points, the Monte Carlo (MC) points and the Quasi Monte Carlo (QMC) points. We focus on three aspects during the comparison: (i) the convergence properties; (ii) the stability, i.e. the properties of the resulting condition number of the design matrix; (iii) the robustness when numerical noises are present in function values. Several classical high dimensional functions together with a random ODE model are tested. It is shown numerically that (i) neither the MC sampling nor the QMC sampling introduce the low convergence rate, namely, the approach achieves high order convergence rate for all cases provided that the underlying functions admit certain regularity and enough design points are used; (ii)The use of SG points admits better convergence properties only for very low dimensional problems (say d ≤ 2); (iii)The QMC points, being deterministic, seem to be a good choice for higher dimensional problems not only for better convergence properties but also in the stability point of view.

Environmental cell studies of deformation and fracture

1990 ◽  
Vol 48 (4) ◽  
pp. 516-517
Author(s):  
H. K. Birnbaum ◽  
I. M. Robertson
Keyword(s):  
National Laboratory ◽  
Argonne National Laboratory ◽  
Damage Threshold ◽  
Chromatic Aberration ◽  
Good Choice ◽  
Point Of View ◽  
Deformation And Fracture ◽  
Environmental Cell ◽  
Gas Molecules ◽  
The University

Studies of the effects of hydrogen environments on the deformation and fracture of fcc, bcc and hep metals and alloys have been carried out in a TEM environmental cell. The initial experiments were performed in the environmental cell of the HVEM facility at Argonne National Laboratory. More recently, a dedicated environmental cell facility has been constructed at the University of Illinois using a JEOL 4000EX and has been used for these studies. In the present paper we will describe the general design features of the JEOL environmental cell and some of the observations we have made on hydrogen effects on deformation and fracture.The JEOL environmental cell is designed to operate at 400 keV and below; in part because of the available accelerating voltage of the microscope and in part because the damage threshold of most materials is below 400 keV. The gas pressure at which chromatic aberration due to electron scattering from the gas molecules becomes excessive does not increase rapidly with with accelerating voltage making 400 keV a good choice from that point of view as well. A series of apertures were placed above and below the cell to control the pressures in various parts of the column.

Is the Free Sensate Deltoid Flap a Good Choice for Phalloplasty?

2006 ◽  
Vol 22 (03) ◽  
Author(s):  
Satoru Yamaguchi ◽  
Ako Takamatsu ◽  
Takao Harashina
Keyword(s):  
Good Choice ◽  
Deltoid Flap

Convergence of Finite Fifference Method for Parabolic Problem

2003 ◽  
Vol 3 (1) ◽  
pp. 45-58 ◽  
Author(s):  
Dejan Bojović
Keyword(s):  
Convergence Rate ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Parabolic Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variable Coefficients ◽  
Rate Estimate ◽  
Convergence Rate Estimate ◽  
Initial Boundary Value

Abstract In this paper we consider the first initial boundary-value problem for the heat equation with variable coefficients in a domain (0; 1)x(0; 1)x(0; T]. We assume that the solution of the problem and the coefficients of the equation belong to the corresponding anisotropic Sobolev spaces. Convergence rate estimate which is consistent with the smoothness of the data is obtained.

On the approximation of $ \ exp (-x) $ on the half-axis by spline functions in three-point rational interpolants

2019 ◽  
pp. 32-37
Author(s):  
Abdul-Rashid Ramazanov ◽  
V.G. Magomedova
Keyword(s):  
Convergence Rate ◽  
Spline Functions ◽  
Rational Spline ◽  
Rational Interpolants ◽  
Half Axis

For the function $f(x)=\exp(-x)$, $x\in [0,+\infty)$ on grids of nodes $\Delta: 0=x_0<x_1<\dots $ with $x_n\to +\infty$ we construct rational spline-functions such that $R_k(x,f, \Delta)=R_i(x,f)A_{i,k}(x)\linebreak+R_{i-1}(x, f)B_{i,k}(x)$ for $x\in[x_{i-1}, x_i]$ $(i=1,2,\dots)$ and $k=1,2,\dots$ Here $A_{i,k}(x)=(x-x_{i-1})^k/((x-x_{i-1})^k+(x_i-x)^k)$, $B_{i,k}(x)=1-A_{i,k}(x)$, $R_j(x,f)=\alpha_j+\beta_j(x-x_j)+\gamma_j/(x+1)$ $(j=1,2,\dots)$, $R_j(x_m,f)=f(x_m)$ при $m=j-1,j,j+1$; we take $R_0(x,f)\equiv R_1(x,f)$. Bounds for the convergence rate of $R_k(x,f, \Delta)$ with $f(x)=\exp(-x)$, $x\in [0,+\infty)$, are found.

Stability Analysis of the Nanjung Water Diversion Twin Tunnels based on Convergence Measurement

2019 ◽  
Vol 1 (1) ◽  
pp. 49-60
Author(s):  
Simon Heru Prassetyo ◽  
Ganda Marihot Simangunsong ◽  
Ridho Kresna Wattimena ◽  
Made Astawa Rai ◽  
Irwandy Arif ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Convergence Rate ◽  
Critical Strain ◽  
Convergence Rates ◽  
Strain Analysis ◽  
Water Diversion ◽  
Tunnel Face ◽  
Tunnel Stability ◽  
The Stability ◽  
Twin Tunnels

This paper focuses on the stability analysis of the Nanjung Water Diversion Twin Tunnels using convergence measurement. The Nanjung Tunnel is horseshoe-shaped in cross-section, 10.2 m x 9.2 m in dimension, and 230 m in length. The location of the tunnel is in Curug Jompong, Margaasih Subdistrict, Bandung. Convergence monitoring was done for 144 days between February 18 and July 11, 2019. The results of the convergence measurement were recorded and plotted into the curves of convergence vs. day and convergence vs. distance from tunnel face. From these plots, the continuity of the convergence and the convergence rate in the tunnel roof and wall were then analyzed. The convergence rates from each tunnel were also compared to empirical values to determine the level of tunnel stability. In general, the trend of convergence rate shows that the Nanjung Tunnel is stable without any indication of instability. Although there was a spike in the convergence rate at several STA in the measured span, that spike was not replicated by the convergence rate in the other measured spans and it was not continuous. The stability of the Nanjung Tunnel is also confirmed from the critical strain analysis, in which most of the STA measured have strain magnitudes located below the critical strain line and are less than 1%.

Recent Trends in Development of Nanomaterials Based Green Analytical Methods for Environmental Remediation

2020 ◽  
Vol 16 ◽  
Author(s):  
Sidra Amin ◽  
Amber R. Solangi ◽  
Dilawar Hassan ◽  
Nadir Hussain ◽  
Jamil Ahmed ◽  
...  
Keyword(s):  
Optical Sensors ◽  
Environmental Remediation ◽  
Environmental Chemistry ◽  
Limit Of Detection ◽  
Environmental Pollutants ◽  
Toxic Metal ◽  
Electrochemical Analysis ◽  
Good Choice ◽  
Nano Materials ◽  
Limit Of Quantification

Background: In recent years, the occurrence and fate of environmental pollutants has been recognized as one of the emerging issues in environmental chemistry. A survey documented about a wide variety of these pollutants, which are often detected in our environment and these are major cause of shortened life spans and the global warming. These pollutants include toxic metal, pesticides, fertilizers, drugs and dyes released into soil and major water bodies. The presence of these contaminants causes major disturbance in eco-system’s balance. To tackle these issues many technological improvements are made to detect minute contaminations. The latest issue being answered by the scientists is the use of green nano materials as sensors which are economical, instant and give much better results at low concentrations and can be used for the field measurements resulting in no dangerous by-product that could lead to more environmental contamination. Nano materials are known for their wide band gap, enhanced physical and optical properties with option of tuneablity as per need, by optimizing certain parameters. They are proved to be good choice for analytical/optical sensors with high sensitivity. Objective: This review holds information about multiple methods that use green nanomaterials for the analytical assessment of environmental pollutants. UV-Vis spectrophotometry and electrochemical analysis using green and reproducible nanomaterials are the major focus of this review article. To date, there are number of spectrophotometric and electro chemical methods available that have been used for the detection of environmental pollutants such as toxic metals, pesticides and dyes. Conclusion: The use of nanomaterials can drastically change the detection limits due to having large surface area, strong catalytic properties, and tunable possibility. With the use of nano materials, lower than the marked limit of detection and limit of quantification were seen when compared with previously reported work. The used nano-materials could be washed, dried, and reused, which makes the methods more proficient, cost effective and environmentally friendly.

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