manuscript-numapde-preprint.tex

% Generated by numapde-prepare-manuscript.py on 20210630-22:03:24
% numapde-prepare-manuscript.py

% A LaTeX template for the numapde-preprint class

% Prepend numapde-latex/ to input path if initialized
\makeatletter
\IfFileExists{./numapde-latex/numapde-packages.sty}{\providecommand*{\input@path}{}\edef\input@path{{./numapde-latex/}\input@path}}{}
\makeatother

% Load documentclass
\documentclass{numapde-preprint}

% Load standard packages
\RequirePackage[ruled,vlined]{algorithm2e}
\usepackage{numapde-semantic}
\usepackage{numapde-style}
\usepackage{numapde-local}

% Define the biblatex resources
\addbibresource{numapde-local.bib}
\IfFileExists{./numapde-bibliography/numapde.bib}{\addbibresource{./numapde-bibliography/numapde.bib}}{\addbibresource{numapde.bib}}

% Setup hyperref
\hypersetup{
	pdftitle={An Optimal Control Problem for Single-Spot Laser Pulse Welding},
	pdfauthor={Roland Herzog, Dmytro Strelnikov},
	pdfkeywords={optimal control, pulsed laser welding, solidification velocity, quasilinear heat equation, phase transition}
}

% Set the title and subtitle information
\title{An Optimal Control Problem for Single-Spot Laser Pulse Welding\thanks{This work was funded by the Federal Ministry for Economic Affairs and Energy (BMWi) of Germany through IGF grant 20.826~B (project OptiPuls), which is gratefully acknowledged.}}
\subtitle{}
\shorttitle{Optimal Control of Single-Spot Laser Pulse Welding}

% Set author information
\author{Roland Herzog\thanks{Interdisciplinary Center for Scientific Computing, Heidelberg University, 69120 Heidelberg, Germany (\email{roland.herzog@mathematik.tu-chemnitz.de}, \url{https://www.tu-chemnitz.de/mathematik/part_dgl/people/herzog}, \orcid{0000-0003-2164-6575}).}
\and
Dmytro Strelnikov\thanks{Technische Universität Chemnitz, Faculty of Mathematics, 09107 Chemnitz, Germany (\email{dmytro.strelnikov@mathematik.tu-chemnitz.de}, \url{https://www.tu-chemnitz.de/mathematik/part_dgl/people/strelnikov}, \orcid{0000-0002-7668-3640}).}}
\shortauthor{R. Herzog and D. Strelnikov}

% Set dedication information
\dedication{}

% Turn off hyperref colors in case the document has change marks
\IfFileExists{numapde-uncolorizeHyperrefIfChanges.sty}{\RequirePackage{numapde-uncolorizeHyperrefIfChanges}}{}

\begin{document}
\maketitle

% Insert abstract
\begin{abstract}
We consider an optimal control problem for a single-spot laser pulse welding problem.
The distribution of thermal energy is described by a quasilinear heat equation.
Our emphasis is on materials which tend to suffer from hot cracking, such as aluminum alloys.
A simple indicator for the occurrente of hot cracks is the velocity of the solidification front.
We therefore formulate an optimal control problem whose objective contains a term which penalizes excessive solidification velocities.
The control function to be optimized is the laser power over time, subject to pointwise lower and upper bounds.
We describe the finite element discretization of the problem and a projected gradient scheme for its solution.
Numerical experiments for material data representing \added[id=RH]{\textbf{a certain aluminum alloy}} exhibit interesting laser pulse patterns which perform significantly better than standard ramp-down patterns.\end{abstract}

% Insert keywords
\begin{keywords}
optimal control, pulsed laser welding, solidification velocity, quasilinear heat equation, phase transition\end{keywords}

% Insert Mathematics Subject Classification (MSC2010)
\begin{AMS}
\href{https://mathscinet.ams.org/msc/msc2010.html?t=49K20}{49K20}, \href{https://mathscinet.ams.org/msc/msc2010.html?t=35K59}{35K59}, \href{https://mathscinet.ams.org/msc/msc2010.html?t=49M05}{49M05}
\end{AMS}

% Insert document body
\input{main.tex}

% Insert bibliography
\printbibliography

\end{document}