diff --git a/imgs/black_hole_excision_mesh.png b/imgs/black_hole_excision_mesh.png new file mode 100644 index 0000000..ea10f1d Binary files /dev/null and b/imgs/black_hole_excision_mesh.png differ diff --git a/imgs/moving_puncture_init.png b/imgs/moving_puncture_init.png new file mode 100644 index 0000000..00dc662 Binary files /dev/null and b/imgs/moving_puncture_init.png differ diff --git a/imgs/moving_puncture_penrose.png b/imgs/moving_puncture_penrose.png new file mode 100644 index 0000000..ad154e3 Binary files /dev/null and b/imgs/moving_puncture_penrose.png differ diff --git a/imgs/moving_puncture_stable.png b/imgs/moving_puncture_stable.png new file mode 100644 index 0000000..aef6ee3 Binary files /dev/null and b/imgs/moving_puncture_stable.png differ diff --git a/mystyle_beamer.tex b/mystyle_beamer.tex index a0f762e..0cfdec5 100644 --- a/mystyle_beamer.tex +++ b/mystyle_beamer.tex @@ -20,14 +20,14 @@ %\usepackage{fancyvrb}%能用颜文字卖萌了，2333 %\usepackage{siunitx}%生成标准格式的国际单位 \usepackage{tensor} -% \usepackage{tikz} +\usepackage{tikz} %\usepackage{listings} %\usepackage{fontspec} %\usepackage{minted} %\usepackage{pifont} \usepackage{bm} % \usepackage{nomencl} -% \usepackage[style=gb7714-2015,backref=true]{biblatex} +\usepackage[backref=true]{biblatex} \hypersetup{ colorlinks=true, diff --git a/ref.bib b/ref.bib new file mode 100644 index 0000000..3c57300 --- /dev/null +++ b/ref.bib @@ -0,0 +1,25 @@ +@article{Hemberger_2013, + title={Dynamical excision boundaries in spectral evolutions of binary black hole spacetimes}, + volume={30}, + ISSN={1361-6382}, + url={http://dx.doi.org/10.1088/0264-9381/30/11/115001}, + DOI={10.1088/0264-9381/30/11/115001}, + number={11}, + journal={Classical and Quantum Gravity}, + publisher={IOP Publishing}, + author={Hemberger, Daniel A and Scheel, Mark A and Kidder, Lawrence E and Szilágyi, Béla and Lovelace, Geoffrey and Taylor, Nicholas W and Teukolsky, Saul A}, + year={2013}, + month=apr, pages={115001} } + +@article{Hannam_2008, + title={Wormholes and trumpets: Schwarzschild spacetime for the moving-puncture generation}, + volume={78}, + ISSN={1550-2368}, + url={http://dx.doi.org/10.1103/PhysRevD.78.064020}, + DOI={10.1103/physrevd.78.064020}, + number={6}, + journal={Physical Review D}, + publisher={American Physical Society (APS)}, + author={Hannam, Mark and Husa, Sascha and Ohme, Frank and Brügmann, Bernd and Ó Murchadha, Niall}, + year={2008}, + month=sep } diff --git a/report.tex b/report.tex index 3982101..38478cf 100644 --- a/report.tex +++ b/report.tex @@ -2,10 +2,19 @@ \input{mystyle_beamer.tex} +\usetikzlibrary{arrows.meta} +\usetikzlibrary{decorations.pathmorphing} + +\tikzset{zigzag/.style={decorate, decoration=zigzag}} +\def \L {2.} + + \title{Towards Moving Picture Simulations in a Discontinuous Galerkin Framework} \author{Yingjie Wang} \institute{FAU} +\addbibresource{ref.bib} + \begin{document} \maketitle @@ -40,8 +49,83 @@ \end{itemize} \end{frame} + \begin{frame}{Methods on evolving black holes} + \subsection{Methods on evolving black holes} + There are two main methods to evolve black holes in numerical relativity: + \begin{itemize} + \item Excision method: excise the black hole interior from the computational domain, and impose boundary conditions on the excision surface + \item Moving puncture method: evolve the black hole as a puncture, and use a suitable gauge condition to avoid the singularity. + \end{itemize} + \end{frame} + + \begin{frame}{Methods on evolving black holes: excision} + \begin{figure} + \centering + \includegraphics[width=0.7\textwidth]{imgs/black_hole_excision_mesh.png} + \caption{An example mesh using excision method from \cite{Hemberger_2013}.} + \end{figure} + \end{frame} + + \begin{frame}{Methods on evolving black holes} + \begin{tikzpicture}[>=Latex, line cap=round, line join=round] + % causal diamond + \draw[thick,red,zigzag] (-\L,\L) coordinate(stl) -- (\L,\L) coordinate (str); + \draw[thick,black] (\L,-\L) coordinate (sbr) + -- (0,0) coordinate (bif) -- (stl); + \draw[thick,black,fill=blue, fill opacity=0.2,text opacity=1] + (bif) -- (str) -- (2*\L,0) node[right] (io) {$i^0$} -- (sbr); + + % null labels + \draw[black] (1.4*\L,0.7*\L) node[right] (scrip) {$\mathcal{I}^+$} + (1.5*\L,-0.6*\L) node[right] (scrip) {$\mathcal{I}^-$} + (0.2*\L,-0.6*\L) node[right] (scrip) {$\mathcal{H}^-$} + (0.5*\L,0.85*\L) node[right] (scrip) {$\mathcal{H}^+$}; + + % singularity label + \draw[thick,red,<-] (0,1.05*\L) + -- (0,1.2*\L) node[above] {\color{red} singularity}; + % % Scwharzschild surface + % \draw[thick,blue] (bif) .. controls (1.*\L,-0.35*\L) .. (2*\L,0); + % \draw[thick,blue,<-] (1.75*\L,-0.1*\L) -- (1.9*\L,-0.5*\L) + % -- (2*\L,-0.5*\L) node[right,align=left] + % {$t=$ constant\\in Schwarzschild\\coordinates}; + % excision surface + \draw[thick,dashed,red] (-0.3*\L,0.3*\L) -- (0.4*\L,\L); + \draw[thick,red,<-] (-0.33*\L,0.3*\L) + -- (-0.5*\L,0.26*\L) node[left,align=right] {excision\\surface}; + % Kerr-Schild surface + \draw[green,thick] (0.325*\L,0.325*\L) .. controls (\L,0) .. (2*\L,0); + \draw[green,dashed,thick] (0.325*\L,0.325*\L) -- (-0.051*\L,0.5*\L); + % Kerr-Schild label + \draw[green,thick,<-] (0.95*\L,0.15*\L) -- (1.2*\L,0.5*\L) + -- (2*\L,0.5*\L) node[right,align=left] + {time slice}; + \end{tikzpicture} + \end{frame} + + \begin{frame}{Methods on evolving black holes: moving puncture} + \begin{figure} + \centering + \includegraphics[width=0.42\textwidth]{imgs/moving_puncture_init.png} + \includegraphics[width=0.45\textwidth]{imgs/moving_puncture_stable.png} + \caption{The embedding of the initial slice (left) and the final slice (right) in the moving puncture method, from \cite{Hannam_2008}.} + \end{figure} + \end{frame} + + \begin{frame}{Methods on evolving black holes: moving puncture} + \begin{figure} + \centering + \includegraphics[width=0.7\textwidth]{imgs/moving_puncture_penrose.png} + \caption{The numerical time slices in the moving puncture method in the Penrose diagram, from \cite{Hannam_2008}.} + \end{figure} + \end{frame} + \begin{frame}{Discontinuous Galerkin method and \texttt{nmesh}} \subsection{Discontinuous Galerkin method and \texttt{nmesh}} \end{frame} + \begin{frame}{References} + \printbibliography + \end{frame} + \end{document} \ No newline at end of file