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Averge scheme documented

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Documentation of the average scheme for species properties.
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Jorge Gonzalez 2022-12-16 19:27:10 +01:00
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doc/user-manual/bibliography.bib
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@ -51,4 +51,15 @@
howpublished = {\url{https://gmsh.info/}},
}
@Article{welford1962note,
author = {Welford, BP},
journal = {Technometrics},
title = {Note on a method for calculating corrected sums of squares and products},
year = {1962},
number = {3},
pages = {419--420},
volume = {4},
publisher = {Taylor \& Francis},
}
@Comment{jabref-meta: databaseType:bibtex;}

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doc/user-manual/fpakc_UserManual.pdf
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doc/user-manual/fpakc_UserManual.tex
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@ -1,4 +1,4 @@
\documentclass[10pt,a4paper,oneside]{book}
\documentclass[10pt,a4paper,twoside]{book}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
@ -22,6 +22,7 @@
Author = {Jorge Gonzalez}
}
}
\usepackage[margin=1in]{geometry} % Reduces margins of the document
% Allows breaking of URL in bibliography.
\setcounter{biburllcpenalty}{7000}
\setcounter{biburlucpenalty}{8000}
@ -260,6 +261,18 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Electromagnetic field}
WIP.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Average scheme}
Particle-in-cell codes has an intrinsic statistical noise associated with them.
Although this can be reduced by increasing the number of particles, this also increases the CPU requirements of the case.
It is quite common that most cases reach a quasi-steady state after a number of iterations and time-average results can be obtained after to improve analysis, plotting and restarting the case using these time-average results as new species backgrounds.
Although this is possible to do once the simulation is finished with post-processing tools, this is limited to the amount of iterations printed.
\Gls{fpakc} implements a simple average scheme that, after a start time provided by the user, scores a mean and standard deviation of all the main species properties, and the electromagnetic field.
This scheme is based on the Welford's online algorithm~\cite{welford1962note}.
The averaged data is written in the same format as the input mesh at the end of the simulation.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Installation}
@ -642,7 +655,7 @@ make
\item \textbf{initialTime}: Real.
Units of $\unit{s}$.
Initial simulation time.
If no value is provided, the initial time is set to $\unit[0]{s}$.
If no value is provided, the initial time is set to $\unit[0.0]{s}$.
\item \textbf{pusher}: Character.
Array dimension 'number of species'.
Indicates the type of pusher used for each species:
@ -684,6 +697,17 @@ make
File must be located at \textbf{output.path}.
\end{itemize}
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{average}
This object determines the use of an average scheme.
If this object exists in the input file, average will be written at the end of the simulation.
Acceptable values are:
\begin{itemize}
\item \textbf{startTime}: Real.
Units in $\unit{s}$.
Simulation physical time in which average scheme will start to compute the mean and standard validation.
If no value is provided, the initial time is set to $\unit[0.0]{s}$.
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{interactions}\label{ssec:input_interactions}
This object determine the different interactions among species.