A Convergence Test and a Remainder Theorem

1933 ◽  
Vol 40 (4) ◽  
pp. 216
Author(s):  
W. F. Libby
Keyword(s):  
Convergence Test

scholarly journals Characteristics of saccades during the near point of convergence test

2021 ◽  
Vol 187 ◽  
pp. 27-40
Author(s):  
Clara Mestre ◽  
Harold E. Bedell ◽  
Fernando Díaz-Doutón ◽  
Jaume Pujol ◽  
Josselin Gautier
Keyword(s):  
Convergence Test

scholarly journals Verification of Convergence Rates of Numerical Solutions for Parabolic Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Darae Jeong ◽  
Yibao Li ◽  
Chaeyoung Lee ◽  
Junxiang Yang ◽  
Yongho Choi ◽  
...  
Keyword(s):  
Parabolic Equations ◽  
Convergence Rates ◽  
Numerical Solutions ◽  
Second Order ◽  
Order Convergence ◽  
Numerical Convergence ◽  
Verification Method ◽  
First Order ◽  
Convergence Test ◽  
Second Order Convergence

In this paper, we propose a verification method for the convergence rates of the numerical solutions for parabolic equations. Specifically, we consider the numerical convergence rates of the heat equation, the Allen–Cahn equation, and the Cahn–Hilliard equation. Convergence test results show that if we refine the spatial and temporal steps at the same time, then we have the second-order convergence rate for the second-order scheme. However, in the case of the first-order in time and the second-order in space scheme, we may have the first-order or the second-order convergence rates depending on starting spatial and temporal step sizes. Therefore, for a rigorous numerical convergence test, we need to perform the spatial and the temporal convergence tests separately.

DYNAMICS OF A2 FINGER PULLEY RUPTURE

2007 ◽  
Vol 07 (01) ◽  
pp. 75-87 ◽  
Author(s):  
MING A. TAN ◽  
FRANZ K. FUSS ◽  
GÜNTHER NIEGL
Keyword(s):  
Mechanical Properties ◽  
Mathematical Model ◽  
Initial Rate ◽  
Constant Force ◽  
Common Occurrence ◽  
Pulley System ◽  
Convergence Test ◽  
A2 Pulley ◽  
The Common ◽  
Rupture Mechanism

A mathematical model of the A2 pulley system will enable us to have a better understanding of the mechanics of the pulley-tendon system and provide us with insights of the pulley rupture mechanism. The A2 pulley was modeled based on parallel pulley fibers attached to a phalanx with a tendon passing them. Mechanical properties of the pulleys such as stiffness, strength and friction were included in the model. A convergence test was done to ensure the accuracy of the test. The model managed to show high loads on flexed finger may lead to pulley ruptures. Further studies on the rupture mechanism showed that pulley ruptures are self-propagating when a constant force is applied and the rate of rupture increases, as fewer intact fibers are present to support the load. The initial rate of propagation is much slower and this accelerates as more fibers are ruptured. This explains the common occurrence of partial pulley ruptures.

Numerical Simulation Study on the Recovery Process of Autonomous Underwater Vehicle

2021 ◽  
Author(s):  
Weigang Huang ◽  
Donglei Zhang ◽  
Jiawei Yu ◽  
Tao He ◽  
Xianzhou Wang
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Autonomous Underwater Vehicle ◽  
Flow Characteristics ◽  
Recovery Process ◽  
Underwater Vehicle ◽  
Hydrodynamic Performance ◽  
Time Step ◽  
Convergence Test ◽  
Motion Paths

Abstract AUV (Autonomous Underwater Vehicle) recovery is considerably influenced by the nearby flow field and simulations of AUV in different motion paths in the wake of a submarine with a propeller are presented in this paper. A commercial CFD solver STAR CCM+ has been used to research the motion and flow characteristics of AUV, which using the advanced computational continuum mechanics algorithms. The DARPA (Defense Advanced Research Projects Agency) SUBOFF Submarine (L1 = 4.356m) propelled with INSEAN (Italian Ship Model Basin) E1619 propeller is used in this study, and the self-propulsion characteristics of the propeller at an incoming flow velocity of 2.75m/s are obtained through numerical simulation and results are compared with the available experimental data to prove the accuracy of the chosen investigation methodology. A grid/time-step convergence test is performed for verification study. AUV (L2 = 0.4356m) is a smaller-scale SUBOFF without a sail, which approaches the submarine in different motion paths in the submarine wake at a relative speed combined with the dynamic overlapping grid technology. The hydrodynamic performance of the AUV when approaching the submarine and the velocity distribution of the surrounding flow field are analyzed, which provides a useful reference for underwater recovery of the AUV.

Relevance of Mesh Dimension Optimization, Geometry Simplification and Discretization Accuracy in the Study of Mechanical Behaviour of Bare Metal Stents

2011 ◽  
Vol 2 (1) ◽  
pp. 1-15
Author(s):  
Mariacristina Gagliardi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Bare Metal Stents ◽  
Nonlinear Finite Element ◽  
Metal Stents ◽  
Bare Metal ◽  
Nonlinear Finite Element Method ◽  
Convergence Test ◽  
Geometry Simplification

In this paper, the authors propose a set of analyses on the deployment of coronary stents by using a nonlinear finite element method. The goal is to propose a convergence test able to select the appropriate mesh dimension and a methodology to perform the simplification of structures composed of cyclically repeated units to reduce the number of degrees of freedom and the analysis run time. A systematic study, based on the analysis of seven meshes for each model, was performed, gradually reducing the element dimension. In addition, geometric models were simplified considering symmetries; adequate boundary conditions were applied and verified based on the results obtained from the analysis of the whole model.

scholarly journals Net Greenhouse Gas Emissions from Agriculture in China: Estimation, Spatial Correlation and Convergence

2019 ◽  
Vol 11 (18) ◽  
pp. 4817 ◽  
Author(s):  
Haoyue Wu ◽  
Hanjiao Huang ◽  
Jin Tang ◽  
Wenkuan Chen ◽  
Yanqiu He
Keyword(s):  
Greenhouse Gas ◽  
Spatial Correlation ◽  
Yangtze River ◽  
Regional Cooperation ◽  
Negative Impact ◽  
Ghg Emissions ◽  
Coastal Region ◽  
The Yangtze River ◽  
Agricultural Ecosystem ◽  
Convergence Test

The agricultural ecosystem has dual attributes of greenhouse gas (GHG) emission and absorption, which both influence the net amount of GHG. To have a clearer understanding of the net GHG effect, we linked up the emission and absorption of the agricultural ecosystem, estimated the net emissions of 30 provinces in China from 2007 to 2016, then explored the spatial correlation from global and local perspectives by Moran’s I, and finally tested the convergence of the net emissions by α convergence test, conditional β convergence test and spatial econometric methods. The results were: (1) The average of provincial agricultural net GHG emissions was around 4999.916 × 104 t, showing a fluctuating trend in the 10 years. Meanwhile, the gaps among provinces were gradually widening, as the provinces with high emissions were mainly agglomerated in the middle reaches of the Yangtze River, while those with less emissions mainly sat in the northwest. (2) The net emissions correlated spatially in close provinces. The agglomeration centers were located in the middle reaches of the Yangtze River and the northern coastal region, showing “high–high” and “low–low” agglomeration, respectively. (3) The net emissions did not achieve α convergence or conditional β convergence in the whole country, but the growth rate had a significant positive spillover effect among adjacent provinces, and two factors, the quantity of the labor force and the level of agricultural economy, had a negative impact on the rate. It is suggested that all provinces could strengthen regional cooperation to reduce agricultural net GHG emissions.

scholarly journals Usage of the convergence test of the residual norm in the Tsuno-Nodera version of the GMRES algorithm

2007 ◽  
Vol 49 (2) ◽  
pp. 293-308
Author(s):  
K. Moriya ◽  
T. Nodera
Keyword(s):  
Distribution Of Zeros ◽  
Numerical Examples ◽  
Convergence Test ◽  
New Variant ◽  
Residual Norm ◽  
Gmres Algorithm

AbstractTsuno and Nodera proposed a new variant of the GMRES(m) algorithm. Their algorithm is referred to as the GMRES(≤ mmax) algorithm and performs the restart process adaptively, considering the distribution of the zeros of the residual polynomial. However, unless the zeros of the residual polynomial are distributed uniformly, mass is always chosen and their algorithm becomes almost the same as the GMRES(m) algorithm with m = mmax. In this paper, we include a convergence test for the residual norm in the GMRES(≤ mmax) algorithm and propose a new restarting technique based on two criteria. Even if the distribution of zeros does not become uniform, the restart can be performed by using the convergence test of the residual norm. Numerical examples simulated on a Compaq Beowulf computer demonstrate that the proposed technique accelerates the convergence of the GMRES(≤ mmax) algorithm.

Sign in / Sign up

Export Citation Format

Share Document