commit 2c9d425cf37a798122b5428de4ef10486b573e16 Author: Yingjie Wang Date: Mon Apr 6 16:16:53 2026 -0400 init diff --git a/Makefile b/Makefile new file mode 100644 index 0000000..04bdc60 --- /dev/null +++ b/Makefile @@ -0,0 +1,13 @@ +main = report +latexmk = latexmk -pdflatex + +.PHONY : main clean cleanall + +main: $(main).tex + $(latexmk) $< + +clean: + $(latexmk) -c $(main).tex + +cleanall: + $(latexmk) -C $(main).tex diff --git a/mystyle_beamer.tex b/mystyle_beamer.tex new file mode 100644 index 0000000..a0f762e --- /dev/null +++ b/mystyle_beamer.tex @@ -0,0 +1,270 @@ +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{mathtools} +% \usepackage{esint} +\usepackage{amsthm} +\usepackage{framed} +\usepackage{mathrsfs} %定义了类似铜版体的\mathscr +%\usepackage{upgreek} +%\usepackage{textcomp} +\usepackage{physics} +\usepackage{cancel} +% \usepackage{geometry} +%\usepackage{tabularx} +\usepackage{hyperref} +% \usepackage[amsmath,hyperref,thmmarks,framed]{ntheorem} +%\usepackage{bookmark} +\usepackage{xcolor} +%\usepackage{graphicx} +% \usepackage{enumitem} +%\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{listings} +%\usepackage{fontspec} +%\usepackage{minted} +%\usepackage{pifont} +\usepackage{bm} +% \usepackage{nomencl} +% \usepackage[style=gb7714-2015,backref=true]{biblatex} + +\hypersetup{ + colorlinks=true, + linkcolor=blue, + % pdftitle={Notes on Loop Quantum Gravity}, + pdfauthor={Yingjie Wang} +} + +% { +% \theoremstyle{plain} +% \theoremsymbol{\ensuremath{\clubsuit}} +% \theoremseparator{.} +% \theoremprework{\bigskip\hrule\smallskip} +% \theorempostwork{\smallskip\hrule\bigskip} +% \newtheorem{Definition}{定义} +% } +% { +% \theoremstyle{plain} +% \theoremheaderfont{\normalfont\bfseries} +% \theorembodyfont{\slshape} +% \theoremsymbol{\ensuremath{\diamondsuit}} +% \theoremseparator{.} +% % \theoremprework{\bigskip\hrule} +% % \theorempostwork{\hrule\bigskip} +% \newtheorem{Theorem}{定理} +% } +% { +% \theoremclass{Theorem} +% \theoremstyle{plain} +% % \theoremheaderfont{\normalfont\bfseries} +% % \theorembodyfont{\slshape} +% % \theoremsymbol{\ensuremath{\diamondsuit}} +% % \theoremseparator{.} +% % \theoremprework{\bigskip\hrule} +% % \theorempostwork{\hrule\bigskip} +% \newframedtheorem{fTheorem}{Theorem} +% } +% { +% \theoremstyle{plain} +% \theorembodyfont{\slshape} +% \theoremsymbol{\ensuremath{\diamondsuit}} +% \theoremseparator{.} +% % \theoremprework{\bigskip\hrule} +% % \theorempostwork{\hrule\bigskip} +% \newtheorem{Property}{命题}[section] +% } +% { +% \theoremstyle{plain} +% \theorembodyfont{\slshape} +% \theoremsymbol{\ensuremath{\diamondsuit}} +% \theoremseparator{.} +% \theoremprework{\bigskip\hrule} +% \theorempostwork{\hrule\bigskip} +% \newtheorem{lProperty}{Property} +% } +% { +% \theoremclass{Property} +% \theoremstyle{plain} +% \newframedtheorem{fProperty}{Property} +% } +% { +% \theoremstyle{plain} +% % \theoremsymbol{\ensuremath{\heartsuit}} +% \theoremindent0.5cm +% % \theoremnumbering{greek} +% \newtheorem{Lemma}{引理} +% } +% { +% \theoremindent0cm +% \theoremsymbol{\ensuremath{\spadesuit}} +% \theoremnumbering{arabic} +% \newtheorem{Corollary}[Theorem]{Corollary} +% } +% { +% \theoremstyle{change} +% \theorembodyfont{\upshape} +% \theoremsymbol{\ensuremath{\ast}} +% \theoremseparator{} +% \newtheorem{Example}{Example} +% } +% { +% \theoremheaderfont{\upshape\bfseries} +% \theorembodyfont{\mdseries\itshape} +% \theoremstyle{nonumberplain} +% \theoremseparator{} +% \theoremsymbol{\mbox{$\square$}} +% \newtheorem{Proof}{证明}[section] +% } +% { +% \theoremindent0cm +% \theoremsymbol{\ensuremath{\spadesuit}} +% \theoremnumbering{arabic} +% \theorembodyfont{\upshape} +% \newtheorem{Remark}{注} +% } + +\newcommand{\myvec}[1]{\vb*{#1}} %定制矢量格式 +\newcommand{\myvu}[1]{\vu*{#1}}%单位矢量 +%\providecommand{\dd}[0]{\mathrm{d}} +\newcommand{\qst}{\qq{s.t.}} +\newcommand{\qsts}{\qq*{s.t.}} +\newcommand{\tst}{\text{s.t.}} + +\newcommand{\RomanNumeralCaps}[1]{\textnormal{\MakeUppercase{\romannumeral #1}}} +\newcommand{\e}[1]{\mathrm{e}^{#1}} +\newcommand{\ii}{\mathrm{i}} +\newcommand{\nG}{\ensuremath{\mathrm{G}}} +\newcommand{\gkappa}{\upkappa} + +\newcommand{\dvt}[2][]{\dv[#1]{#2}{t}} +\newcommand{\pdvt}[2][]{\pdv[#1]{#2}{t}} +\newcommand{\pd}[1]{\pdv*{}{#1}} +\newcommand{\liej}[1]{\ensuremath{{#1}_1,\cdots,{#1}_n}} +\newcommand{\qqiff}{\qq{iff}} +\newcommand{\F}{\ensuremath{\mathscr{F}}} +\newcommand{\La}{\ensuremath{\mathscr{L}}} +\newcommand{\Lad}{\ensuremath{\tilde{\mathscr{L}}}} +\newcommand{\Laf}{\ensuremath{\form{L}}} +\newcommand{\Ha}{\ensuremath{\mathscr{H}}} +\newcommand{\Had}{\ensuremath{\tilde{\mathscr{H}}}} +\newcommand{\Ld}[1]{\ensuremath{\mathcal{L}\indices{_{#1}}}} +\newcommand{\spaceLd}[1]{\ensuremath{\tilde{\mathcal{L}}\indices{_{#1}}}} +\newcommand{\TT}{\ensuremath{\mathscr{T}}} +\newcommand{\I}{\ensuremath{\mathrm{I}}} +\newcommand{\II}{\ensuremath{I}} +\newcommand{\J}{\ensuremath{\mathrm{J}}} +% \newcommand{\hj}[2][-1bp]{\raisebox{#1}{\includegraphics[height=#2 bp]{hj}}} +% \newcommand{\wl}[2][-1bp]{\raisebox{#1}{\includegraphics[height=#2 bp]{wulian}}} + +\newcommand{\Nabla}[1]{\tensor{\nabla}{_{#1}}}%协变导数算符 +\newcommand{\tNabla}[1]{\tensor{{\tilde{\nabla}}}{_{#1}}}%另一个协变导数算符 +\newcommand{\spaceD}[1]{\tensor{D}{_{#1}}} +\newcommand{\Dc}[1]{\tensor{D}{_{#1}}} +\newcommand{\tDc}[1]{\tensor{\tilde{D}}{_{#1}}} +\newcommand{\AD}[1]{\tensor{\mathcal{D}}{_{#1}}} +\newcommand{\ADd}{\mathcal{D}} +\newcommand{\connection}[1]{\mathcal{#1}} +\newcommand{\Partial}[1]{\tensor{\partial}{_{#1}}}%普通导数算符 +\newcommand{\tPartial}[1]{\tensor{\tilde{\partial}}{_{#1}}} +\newcommand{\Fd}[2][\tau]{\ensuremath{\frac{\mathrm{D_F}#2}{\dd{#1}}}}%费米导数 +\newcommand{\Fdd}[2][\tau]{\ensuremath{\mathrm{D_F}#2/\dd{#1}}}%行内费米导数 +\newcommand{\Dd}[2][\tau]{\ensuremath{\frac{\mathrm{D}#2}{\dd{#1}}}}%协变导数 +\newcommand{\Ddd}[2][\tau]{\ensuremath{\mathrm{D}#2/\dd{#1}}}%行内协变导数 +\newcommand{\ChristoffelSymbol}[3]{\tensor{\Gamma}{^{#1}_{#2}_{#3}}} +\newcommand{\christoffelSymbol}[4]{\frac{1}{2} \tensor{g}{^{#1}^{#4}} \left( \tensor{g}{_{#4}_{#2}_{,#3}} + \tensor{g}{_{#3}_{#4}_{,#2}} - \tensor{g}{_{#2}_{#3}_{,#4}} \right) } +\newcommand{\riemannR}[5]{\tensor{\Gamma}{^{#4}_{#1}_{#3}_{,#2}}- \tensor{\Gamma}{^{#4}_{#2}_{#3}_{,#1}}+ \ChristoffelSymbol{#5}{#3}{#1} \ChristoffelSymbol{#4}{#2}{#5}- \ChristoffelSymbol{#5}{#3}{#2} \ChristoffelSymbol{#4}{#1}{#5}} +%\newcolumntype{Y}{>{\centering\arraybackslash}X} +%\newcommand{\tmu}{\mspace{2mu}} +%\newcommand{\mmacs}{\bfseries\ttfamily\itshape\color[RGB]{67,137,88}}%mma局部变量字体 +%\newcommand{\mmab}{\bfseries\ttfamily\color[RGB]{60,125,145}}%mma变量字体 +%\newcommand{\mmaundef}{\bfseries\ttfamily\color[RGB]{0,44,195}}%mma未定义 +%\newcommand{\mma}{\bfseries\ttfamily}%mma代码字体 + +\newcommand{\tensord}[2]{\tensor{\left( \dd{#1} \right)}{_{#2}}} +\newcommand{\tensorp}[2]{\tensor{\left( \pdv{#1} \right)}{^{#2}}} + +% \newcommand{\Rn}[1]{\ensuremath{\mathbb{R}^{#1}}} +\newcommand{\SO}[1]{\ensuremath{\mathrm{SO}\left(#1\right)}} +\newcommand{\SU}[1]{\ensuremath{\mathrm{SU}\left(#1\right)}} +\newcommand{\OO}[1]{\ensuremath{\mathrm{O}\left(#1\right)}} +\newcommand{\so}[1]{\ensuremath{\mathrm{so}\left( #1 \right)}} +\newcommand{\su}[1]{\ensuremath{\mathrm{su}\left( #1 \right)}} +\newcommand{\SL}[1]{\mathrm{SL}\left( #1 \right)} +\newcommand{\sll}[1]{\mathrm{sl}\left( #1 \right)} +\newcommand{\Ad}[1]{\mathrm{Ad}_{#1}} +\newcommand{\Hom}[2]{\mathrm{Hom}\left( #1,#2 \right)} +\newcommand{\Cyl}{\mathrm{Cyl}} + +\newcommand{\Lo}[1]{\ensuremath{\mathrm{Lor}\left(#1\right)}} +\newcommand{\Riem}[1]{\ensuremath{\mathrm{Riem}\left( #1 \right)}} +\newcommand{\superspace}[1]{\ensuremath{\mathcal{S}\left(#1\right)}} +\newcommand{\Diff}[1]{\ensuremath{\mathrm{Diff}\left(#1\right)}} +\newcommand{\definedby}{:=} + +\newcommand{\phasespace}[1]{\mathcal{#1}} +\newcommand{\configurationspace}[1]{\mathcal{#1}} +\newcommand{\extentedconfigurationspace}[1]{\bar{\configurationspace{#1}}} +\newcommand{\staralgebra}[1]{\mathfrak{#1}} +\newcommand{\Linear}[1]{\mathcal{L}\left( {#1} \right)} +\newcommand{\pathorder}{\hat{\mathcal{P}}} +\newcommand{\Dkin}{\mathcal{D}_{\text{kin}}} +\newcommand{\DDiff}{\mathcal{D}_{\text{Diff}}} +\newcommand{\Dphys}{\mathcal{D}_{\text{phys}}} +\newcommand{\Hil}{\mathcal{H}} +\newcommand{\Hkin}{\Hil_{\text{kin}}} +\newcommand{\HDiff}{\Hil_{\text{Diff}}} +\newcommand{\Hphys}{\Hil_{\text{phys}}} +\newcommand{\masterconstraint}[1]{\ensuremath{\bm{\mathsf{#1}}}} +\newcommand{\complex}[1]{\mathcal{#1}} +\newcommand{\amplitude}{A} + + +\newcommand{\form}[1]{\ensuremath{\bm{#1}}} +\newcommand{\Ric}{\ensuremath{R}} +\newcommand{\curR}{\ensuremath{{R}}} +\newcommand{\spacecurR}{\ensuremath{\mathcal{R}}} +\newcommand{\vol}{\ensuremath{\varepsilon}} +\newcommand{\nvol}{\ensuremath{\epsilon}} +\newcommand{\spc}{\ensuremath{\mathcal{S}}} +\newcommand{\setofcurve}{\mathcal{C}} +\newcommand{\setofpath}{\mathcal{P}} + +\newcommand{\TB}[2][{}]{\mathrm{T}_{#1}\!{#2}} +\newcommand{\TBx}[2][{}]{\mathrm{T}_{#1} {#2}} +\newcommand{\CTB}[2][{}]{\mathrm{T}^*_{#1}\!{#2}} +\newcommand{\FB}[2][{}]{\mathrm{F}_{#1}\!{#2}} +\newcommand{\Jet}[4][{}]{\ensuremath{\mathrm{Jet}_{#1}^{#2}\left( #3,#4 \right)}} +\newcommand{\Cinf}{\mathrm{C}^{\infty}} +\newcommand{\Vect}[1]{\Gamma\left(\TB{#1}\right)} + +\newcommand{\End}[1]{\mathrm{End}\left( #1 \right)} + +% \newcommand{\uphbar}{\mathchar'0026\mkern-9mu h} +\newcommand{\uphbar}{\hbar} + +%\renewcommand{\CancelColor}{\color{blue!70!red}} + +%\newcommand*{\circled}[1]{\lower.7ex\hbox{\tikz\draw (0pt, 0pt)circle (.5em) node {\makebox[1em][c]{\small #1}};}} +\newcommand{\card}[1]{\abs{#1}} +\newcommand{\setR}{\mathbb{R}} +\newcommand{\setC}{\mathbb{C}} +\newcommand{\setZ}{\mathbb{Z}} +\newcommand{\set}[2]{\left\{ #1 \,\middle|\, #2 \right\}} +\newcommand{\RP}[1]{\mathbb{RP}^{#1}} + +\newcommand{\myvaried}[1]{{\phantom{#1}\llap{\raisebox{0pt}[0pt][0pt]{\ensuremath{\mspace{3mu}\overset{\lambda}{#1}}}}}} + +\DeclareMathOperator{\ddiv}{div} +\DeclareMathOperator{\ggrad}{grad} +\DeclareMathOperator{\ccurl}{curl} +\DeclareMathOperator{\Exp}{Exp} +\DeclareMathOperator{\Span}{Span} +\DeclareMathOperator{\Inv}{Inv} +\DeclareMathOperator{\image}{im} + +% \usetheme{PaloAlto} +% \usetheme{AnnArbor} +%\usecolortheme{beaver} +\usetheme{Darmstadt} +\usefonttheme{professionalfonts} diff --git a/report.tex b/report.tex new file mode 100644 index 0000000..3982101 --- /dev/null +++ b/report.tex @@ -0,0 +1,47 @@ +\documentclass[10pt]{beamer} + +\input{mystyle_beamer.tex} + +\title{Towards Moving Picture Simulations in a Discontinuous Galerkin Framework} +\author{Yingjie Wang} +\institute{FAU} + +\begin{document} + \maketitle + + \begin{frame}{Contents} + \tableofcontents + \end{frame} + + \begin{frame}{Outline of the Project} + \section{Introduction} + \begin{enumerate} + \item A first order evolution system, to be named FOZ4c + \item An implementation in our discontinuous Galerkin code \texttt{nmesh} + \item Simulations of binary black holes with large mass ratio with the moving puncture gauge + \end{enumerate} + \end{frame} + + \begin{frame}{Final Goal: binary black holes with large mass ratio} + \subsection{binary black holes with large mass ratio} + + Why binary black holes? + + \begin{itemize} + \item Main sources of gravitational waves + \item Simplest two-body problem in general relativity + \item Connecting strong field GR with post-Newtonian approximations + \end{itemize} + + Why large mass ratio? + \begin{itemize} + \item LISA is able to detect extreme mass ratio inspirals (EMRIs) + \item Compare with perturbation theory + \end{itemize} + \end{frame} + + \begin{frame}{Discontinuous Galerkin method and \texttt{nmesh}} + \subsection{Discontinuous Galerkin method and \texttt{nmesh}} + \end{frame} + +\end{document} \ No newline at end of file