Development of a Technique for the Practical Implementation of Higher Order Perturbation Methods

1990 ◽  
Vol 105 (2) ◽  
pp. 160-173 ◽  
Author(s):  
John R. White ◽  
Glenn A. Swanbon
Keyword(s):  
Perturbation Methods ◽  
Higher Order ◽  
Order Perturbation ◽  
Practical Implementation

Higher Order Perturbation Analysis of Stochastic Thermal Systems With Correlated Uncertain Properties

2000 ◽  
Vol 123 (2) ◽  
pp. 390-398 ◽  
Author(s):  
A. F. Emery
Keyword(s):  
Standard Deviation ◽  
Boundary Conditions ◽  
Perturbation Analysis ◽  
Perturbation Methods ◽  
Higher Order ◽  
Order Perturbation ◽  
Thermal Systems ◽  
The Mean ◽  
Almost All ◽  
Correlated Parameters

How the behavior of thermal systems depends on uncertainties in properties and boundary conditions is an important aspect of simulation. This dependence is usually judged by the statistics of the response, i.e., the mean response and its standard deviation which are often determined by perturbation methods, ranging from 1st to 3rd order. The aim of this paper is to be a tutorial for those interested in estimating uncertainties by summarizing the author’s experience in using higher order perturbation analysis for thermal problems, detailing the underlying assumptions, and presenting several examples. Problems involving correlated parameters, which occur in almost all thermal experiments, are also treated. It is shown that the scale of correlation has a strong effect upon the statistics of the response and that such correlation should not be ignored. It is recommended that the 1st order estimates of the standard deviation and 2nd order estimates of the mean response be used when characterizing thermal systems with random variables, regardless of the degree of correlation.

An algorithm of higher-order perturbation variables satisfying the additivity for system operators

2001 ◽  
Vol 28 (13) ◽  
pp. 1313-1328 ◽  
Author(s):  
Yaqi Wang ◽  
Zhengpei Luo ◽  
Fu Li ◽  
Wenfeng Liu
Keyword(s):  
Higher Order ◽  
Order Perturbation

Improving efficiency of semi‐direct møller–plesset second‐order perturbation methods through oversubscription on multiple nodes

2019 ◽  
Vol 40 (24) ◽  
pp. 2146-2157 ◽  
Author(s):  
Ellie L. Fought ◽  
Vaibhav Sundriyal ◽  
Masha Sosonkina ◽  
Theresa L. Windus
Keyword(s):  
Perturbation Methods ◽  
Second Order ◽  
Order Perturbation ◽  
Moller Plesset

scholarly journals Higher-order Lagrangian perturbative theory for the Cosmic Web

2014 ◽  
Vol 11 (S308) ◽  
pp. 119-120
Author(s):  
Takayuki Tatekawa ◽  
Shuntaro Mizuno
Keyword(s):  
Perturbation Theory ◽  
Fourth Order ◽  
Initial Conditions ◽  
Higher Order ◽  
Order Perturbation ◽  
Initial Condition ◽  
The Difference ◽  
Fifth Order ◽  
The Universe ◽  
Higher Order Lagrangian

AbstractZel'dovich proposed Lagrangian perturbation theory (LPT) for structure formation in the Universe. After this, higher-order perturbative equations have been derived. Recently fourth-order LPT (4LPT) have been derived by two group. We have shown fifth-order LPT (5LPT) In this conference, we notice fourth- and more higher-order perturbative equations. In fourth-order perturbation, because of the difference in handling of spatial derivative, there are two groups of equations. Then we consider the initial conditions for cosmological N-body simulations. Crocce, Pueblas, and Scoccimarro (2007) noticed that second-order perturbation theory (2LPT) is required for accuracy of several percents. We verify the effect of 3LPT initial condition for the simulations. Finally we discuss the way of further improving approach and future applications of LPTs.

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