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[svn:einsteintoolkit] Workshop_Spring_2012/example_wavetoy/ (Rev. 52)
by roland.haas＠physics.gatech.edu 04 Apr '12

04 Apr '12

User: rhaas Date: 2012/04/04 12:35 PM Modified: /example_wavetoy/ example_wavetoy.tex Log: add energy exercise to wavetoy File Changes: Directory: /example_wavetoy/ ============================ File [modified]: example_wavetoy.tex Delta lines: +7 -0 =================================================================== --- example_wavetoy/example_wavetoy.tex 2012-04-04 17:34:23 UTC (rev 51) +++ example_wavetoy/example_wavetoy.tex 2012-04-04 17:35:10 UTC (rev 52) @@ -659,6 +659,13 @@ \end{itemize} } +\frame{\frametitle{Exercise: compute wave energy} +\begin{itemize} +\item compute energy density $\rho_E = \phi^2 \, \mathrm{d}x \, \mathrm{d}y \, \mathrm{d}z$ +\item compute integral as '\texttt{sum}' reduction of \texttt{IOScalar::out\_reductions} during output +\end{itemize} +} + %\frame[containsverbatim]{ \frametitle{WaveToy Thorn} % \begin{enumerate} % \item Define a new variable in \verb|interface.ccl|, and allocate storage

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[svn:einsteintoolkit] Workshop_Spring_2012/ (Rev. 51)
by roland.haas＠physics.gatech.edu 04 Apr '12

04 Apr '12

User: rhaas Date: 2012/04/04 12:34 PM Added: /example_wavetoy/ example_wavetoy.pdf Log: add example_wavetoy slides Directory Changes: Directory: /svn:mime-type/ ========================== + application/octet-stream File Changes: Directory: /example_wavetoy/ ============================ File [added]: example_wavetoy.pdf Delta lines: +0 -0 =================================================================== (Binary files differ) Property changes on: example_wavetoy/example_wavetoy.pdf ___________________________________________________________________

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New changesets in Carpet Mercurial
by Carpet mercurial repositories 04 Apr '12

04 Apr '12

changeset: 3506:cd3d378c628a tag: tip user: Erik Schnetter <schnetter(a)gmail.com> date: Wed Apr 04 13:10:45 2012 -0400 summary: CarpetIOASCII: Declare function prototype

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[svn:einsteintoolkit] Workshop_Spring_2012/ (Rev. 50)
by jfaber＠einsteintoolkit.org 04 Apr '12

04 Apr '12

User: jfaber Date: 2012/04/04 12:05 PM Added: /genrel/ subtle.png Modified: /genrel/ genrel.aux, genrel.log, genrel.nav, genrel.pdf, genrel.tex Log: Typo fixes Directory Changes: Directory: /svn:mime-type/ ========================== + application/octet-stream File Changes: Directory: /genrel/ =================== File [modified]: genrel.aux Delta lines: +7 -5 =================================================================== --- genrel/genrel.aux 2012-04-04 16:54:47 UTC (rev 49) +++ genrel/genrel.aux 2012-04-04 17:05:53 UTC (rev 50) @@ -59,8 +59,10 @@ \@writefile{nav}{\headcommand {\beamer@framepages {22}{22}}} \@writefile{nav}{\headcommand {\slideentry {0}{0}{23}{23/23}{}{0}}} \@writefile{nav}{\headcommand {\beamer@framepages {23}{23}}} -\@writefile{nav}{\headcommand {\beamer@partpages {1}{23}}} -\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{23}}} -\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{23}}} -\@writefile{nav}{\headcommand {\beamer@documentpages {23}}} -\@writefile{nav}{\headcommand {\def \inserttotalframenumber {23}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{24}{24/24}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {24}{24}}} +\@writefile{nav}{\headcommand {\beamer@partpages {1}{24}}} +\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{24}}} +\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{24}}} +\@writefile{nav}{\headcommand {\beamer@documentpages {24}}} +\@writefile{nav}{\headcommand {\def \inserttotalframenumber {24}}} File [modified]: genrel.log Delta lines: +50 -52 =================================================================== --- genrel/genrel.log 2012-04-04 16:54:47 UTC (rev 49) +++ genrel/genrel.log 2012-04-04 17:05:53 UTC (rev 50) @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009) (format=pdflatex 2009.11.7) 4 APR 2012 08:50 +This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009) (format=pdflatex 2009.11.7) 4 APR 2012 13:05 entering extended mode \write18 enabled. %&-line parsing enabled. @@ -1144,108 +1144,106 @@ {/usr/local/texlive/2009/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] [2 -] -LaTeX Font Info: Try loading font information for U+msa on input line 40. +] <subtle.png, id=77, 702.625pt x 1055.945pt> +File: subtle.png Graphic file (type png) + <use subtle.png> [3 + + <./subtle.png>] +LaTeX Font Info: Try loading font information for U+msa on input line 47. (/usr/local/texlive/2009/texmf-dist/tex/latex/amsfonts/umsa.fd File: umsa.fd 2009/06/22 v3.00 AMS symbols A ) -LaTeX Font Info: Try loading font information for U+msb on input line 40. +LaTeX Font Info: Try loading font information for U+msb on input line 47. (/usr/local/texlive/2009/texmf-dist/tex/latex/amsfonts/umsb.fd File: umsb.fd 2009/06/22 v3.00 AMS symbols B -) [3 +) [4 -] [4 +] [5 ] -<edmb.png, id=136, 1028.84375pt x 908.39375pt> +<edmb.png, id=165, 1028.84375pt x 908.39375pt> File: edmb.png Graphic file (type png) <use edmb.png> -Overfull \vbox (0.88663pt too high) detected at line 58 +Overfull \vbox (0.88663pt too high) detected at line 65 [] -[5 +[6 - <./edmb.png (PNG copy)>] <timedilate.png, id=163, 905.3825pt x 478.78876pt> + <./edmb.png (PNG copy)>] <timedilate.png, id=192, 905.3825pt x 478.78876pt> File: timedilate.png Graphic file (type png) -<use timedilate.png> [6 +<use timedilate.png> [7 - <./timedilate.png>] [7 + <./timedilate.png>] [8 -] [8 +] [9 ] -<lortrans.png, id=247, 501.875pt x 488.82625pt> +<lortrans.png, id=275, 501.875pt x 488.82625pt> File: lortrans.png Graphic file (type png) <use lortrans.png> -Overfull \vbox (61.71777pt too high) detected at line 106 +Overfull \vbox (61.71777pt too high) detected at line 113 [] -[9 +[10 - <./lortrans.png>] [10 + <./lortrans.png>] [11 -] <elevator.png, id=301, 347.2975pt x 236.885pt> +] <elevator.png, id=329, 347.2975pt x 236.885pt> File: elevator.png Graphic file (type png) -<use elevator.png> <orbits.png, id=302, 701.62125pt x 440.64626pt> +<use elevator.png> <orbits.png, id=330, 701.62125pt x 440.64626pt> File: orbits.png Graphic file (type png) <use orbits.png> -Overfull \hbox (19.05467pt too wide) in paragraph at lines 121--121 +Overfull \hbox (19.05467pt too wide) in paragraph at lines 128--128 [][] [] -[11 +[12 - <./elevator.png (PNG copy)> <./orbits.png (PNG copy)>] [12 + <./elevator.png (PNG copy)> <./orbits.png (PNG copy)>] [13 -] [13 - ] [14 +] [15 + ] Package amsmath Warning: Foreign command \over; (amsmath) \frac or \genfrac should be used instead -(amsmath) on input line 193. +(amsmath) on input line 200. -[15 +[16 -] <covderiv.png, id=435, 180.675pt x 130.4875pt> +] <covderiv.png, id=463, 180.675pt x 130.4875pt> File: covderiv.png Graphic file (type png) <use covderiv.png> -<curvtens.png, id=436, 226.8475pt x 155.58125pt> +<curvtens.png, id=464, 226.8475pt x 155.58125pt> File: curvtens.png Graphic file (type png) - <use curvtens.png> [16 + <use curvtens.png> [17 - <./covderiv.png (PNG copy)> <./curvtens.png (PNG copy)>] [17 + <./covderiv.png (PNG copy)> <./curvtens.png (PNG copy)>] [18 -] [18 - ] [19 +] [20 + ] -<lapseshift.png, id=542, 245.91875pt x 140.525pt> +<lapseshift.png, id=570, 245.91875pt x 140.525pt> File: lapseshift.png Graphic file (type png) - <use lapseshift.png> [20 + <use lapseshift.png> [21 - <./lapseshift.png (PNG copy)>] [21 + <./lapseshift.png (PNG copy)>] [22 -] +] [23 -LaTeX Warning: Command \d invalid in math mode on input line 282. - - -LaTeX Warning: Command \d invalid in math mode on input line 282. - -[22 - -] <gwpol.png, id=620, 803.0pt x 401.5pt> +] <gwpol.png, id=648, 803.0pt x 401.5pt> File: gwpol.png Graphic file (type png) - <use gwpol.png> [23 +<use gwpol.png> [24 + <./gwpol.png (PNG copy)>] \tf@nav=\write6 \openout6 = `genrel.nav'. @@ -1263,10 +1261,10 @@ ) Here is how much of TeX's memory you used: - 15014 strings out of 493848 - 276863 string characters out of 3149207 + 15023 strings out of 493848 + 276967 string characters out of 3149207 358008 words of memory out of 3000000 - 17808 multiletter control sequences out of 15000+200000 + 17814 multiletter control sequences out of 15000+200000 11753 words of font info for 43 fonts, out of 3000000 for 9000 718 hyphenation exceptions out of 8191 47i,16n,57p,830b,534s stack positions out of 5000i,500n,10000p,200000b,50000s @@ -1284,9 +1282,9 @@ al/texlive/2009/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy6.pfb></usr/local /texlive/2009/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy8.pfb></usr/local/t exlive/2009/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb> -Output written on genrel.pdf (23 pages, 2422055 bytes). +Output written on genrel.pdf (24 pages, 3113109 bytes). PDF statistics: - 703 PDF objects out of 1000 (max. 8388607) - 47 named destinations out of 1000 (max. 500000) - 102 words of extra memory for PDF output out of 10000 (max. 10000000) + 732 PDF objects out of 1000 (max. 8388607) + 49 named destinations out of 1000 (max. 500000) + 107 words of extra memory for PDF output out of 10000 (max. 10000000) File [modified]: genrel.nav Delta lines: +7 -5 =================================================================== --- genrel/genrel.nav 2012-04-04 16:54:47 UTC (rev 49) +++ genrel/genrel.nav 2012-04-04 17:05:53 UTC (rev 50) @@ -45,8 +45,10 @@ \headcommand {\beamer@framepages {22}{22}} \headcommand {\slideentry {0}{0}{23}{23/23}{}{0}} \headcommand {\beamer@framepages {23}{23}} -\headcommand {\beamer@partpages {1}{23}} -\headcommand {\beamer@subsectionpages {1}{23}} -\headcommand {\beamer@sectionpages {1}{23}} -\headcommand {\beamer@documentpages {23}} -\headcommand {\def \inserttotalframenumber {23}} +\headcommand {\slideentry {0}{0}{24}{24/24}{}{0}} +\headcommand {\beamer@framepages {24}{24}} +\headcommand {\beamer@partpages {1}{24}} +\headcommand {\beamer@subsectionpages {1}{24}} +\headcommand {\beamer@sectionpages {1}{24}} +\headcommand {\beamer@documentpages {24}} +\headcommand {\def \inserttotalframenumber {24}} File [modified]: genrel.pdf Delta lines: +0 -0 =================================================================== (Binary files differ) File [modified]: genrel.tex Delta lines: +11 -4 =================================================================== --- genrel/genrel.tex 2012-04-04 16:54:47 UTC (rev 49) +++ genrel/genrel.tex 2012-04-04 17:05:53 UTC (rev 50) @@ -23,9 +23,16 @@ \item Linearized gravity and gravitational radiation \end{itemize} -For a very nice treatment of GR available freely online, I suggest Sean Carroll's notes: gr-qc/9712019. } +\frame{\frametitle{Other sources} +For a very nice treatment of GR available freely online, I suggest Sean Carroll's notes: gr-qc/9712019. + +For the best scientific biography of Einstein, including a discussion of the divergenceless of various tensors with full equations, I suggest {\em Subtle is the Lord}, by Abraham Pais. + +\includegraphics[width=1in]{subtle} +} + \frame{\frametitle{Space and time in Newtonian physics} \begin{itemize} \item In Newtonian physics, there is space, and there is time, and they are different.\\ @@ -81,7 +88,7 @@ 0&0&0&1\end{array}\right) ; ~~(x')^{\mu'} = \left[\sum_{\nu=0}^3\right] \Lambda^{\mu'}{}_\nu x^\nu \end{equation} -where $\phi = \tanh\beta$. +where $\phi = \tanh^{-1}\beta$. } \frame{\frametitle{Special relativity: Invariants} @@ -270,8 +277,8 @@ The most familiar black hole solution, for an uncharged BH without any angular momentum, is the Schwarzschild solution: \begin{equation} - ds^2 = -\left(1-{{2GM}\over r}\right)\d t^2 + - \left(1-{{2GM}\over r}\right)^{-1}\d r^2 + ds^2 = -\left(1-{{2GM}\over r}\right)d t^2 + + \left(1-{{2GM}\over r}\right)^{-1}dr^2 + r^2 d\Omega^2 \end{equation} where $d\Omega^2 = d\theta^2+\sin^2\theta d\phi^2$. This is a stationary solution to Einstein's equations. At $r=2M$, we have a singularity, since there is no change in distance in time, and the radial term goes to infinity. This is the BH horizon. While indeed light cannot escape from the horizon, the singularity is an artifact of the coordinates we chose. If we let $R = \frac{1}{2}(r-M+\sqrt{r(r-2M)})$, we find the metric takes the isotropic form: File [added]: subtle.png Delta lines: +0 -0 =================================================================== (Binary files differ) Property changes on: genrel/subtle.png ___________________________________________________________________

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[svn:einsteintoolkit] Workshop_Spring_2012/ (Rev. 49)
by bcmsma＠astro.rit.edu 04 Apr '12

04 Apr '12

User: bmundim Date: 2012/04/04 11:54 AM Added: /numerical_relativity/movies/ DiagShock2D_rho.mpg, DiagShock2D_rho_570.jpg Modified: /numerical_relativity/ numerical_relativity.tex Log: Shocktube test movie Directory Changes: Directory: /svn:mime-type/ ========================== + application/octet-stream File Changes: Directory: /numerical_relativity/movies/ ======================================== File [added]: DiagShock2D_rho.mpg Delta lines: +0 -0 =================================================================== (Binary files differ) Property changes on: numerical_relativity/movies/DiagShock2D_rho.mpg ___________________________________________________________________ File [added]: DiagShock2D_rho_570.jpg Delta lines: +0 -0 =================================================================== (Binary files differ) Property changes on: numerical_relativity/movies/DiagShock2D_rho_570.jpg ___________________________________________________________________ Directory: /numerical_relativity/ ================================= File [modified]: numerical_relativity.tex Delta lines: +11 -0 =================================================================== --- numerical_relativity/numerical_relativity.tex 2012-04-04 16:45:17 UTC (rev 48) +++ numerical_relativity/numerical_relativity.tex 2012-04-04 16:54:47 UTC (rev 49) @@ -685,7 +685,18 @@ \begin{figure} \includegraphics[width=10cm]{all_waves.pdf} \end{figure} +} +\frame{\frametitle{Shocktube Test} +\begin{figure} +% \hspace{1.0cm} + \href{run:movies/DiagShock2D_rho.mpg}{ + \includegraphics[width=6cm]{movies/DiagShock2D_rho_570.jpg} + } + \caption{Diagonal shock along xy-plane: final $\rho$ profile.} +\end{figure} + + }

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[svn:einsteintoolkit] Workshop_Spring_2012/numerical_relativity/ (Rev. 48)
by bcmsma＠astro.rit.edu 04 Apr '12

04 Apr '12

User: bmundim Date: 2012/04/04 11:45 AM Modified: /numerical_relativity/ numerical_relativity.tex Log: algorithm overview. File Changes: Directory: /numerical_relativity/ ================================= File [modified]: numerical_relativity.tex Delta lines: +32 -0 =================================================================== --- numerical_relativity/numerical_relativity.tex 2012-04-04 16:29:55 UTC (rev 47) +++ numerical_relativity/numerical_relativity.tex 2012-04-04 16:45:17 UTC (rev 48) @@ -658,4 +658,36 @@ \end{figure} } + +\frame{\frametitle{Algorithm Overview} +\begin{itemize} +\item Set boundary conditions or ghost zone values \pause +\item Calculate numerical flux at every cell interface by +solving an approximate Riemann problem \pause + \begin{itemize} + \item Reconstruct the primitive variables $p_l$ and $p_r$ at the +cell interfaces (by using slope limiters for example). \pause + \item Find the conservative variables $q_l$ and $q_r$ by using their +definition \pause + \item Calculate the fluxes $f(q_l)$ and $f(q_r)$ \pause + \item Calculate $A$, $r_{\alpha}$, $\lambda_{\alpha}$ and use them to +find $\omega_{\alpha}$ \pause + \item Calculate the Roe formula for the numerical flux: $F^{\rm Roe}_{i+1/2} +$ \pause + \end{itemize} + \item Evaluate the sources $\Psi(q)$. \pause + \item Update the average quantities $Q^n_i$ using method of lines. +\end{itemize} + +} + +\frame{\frametitle{Algorithm Overview} +\begin{figure} + \includegraphics[width=10cm]{all_waves.pdf} +\end{figure} + +} + + + \end{document}

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[svn:einsteintoolkit] Workshop_Spring_2012/numerical_relativity/ (Rev. 47)
by bcmsma＠astro.rit.edu 04 Apr '12

04 Apr '12

User: bmundim Date: 2012/04/04 11:29 AM Added: /numerical_relativity/figs/ minmod.eps, minmod.pdf Modified: /numerical_relativity/ numerical_relativity.tex Log: slope limiters File Changes: Directory: /numerical_relativity/figs/ ====================================== File [added]: minmod.eps Delta lines: <Unavailable> File [added]: minmod.pdf Delta lines: <Unavailable> Directory: /numerical_relativity/ ================================= File [modified]: numerical_relativity.tex Delta lines: <Unavailable>

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[svn:einsteintoolkit] Workshop_Spring_2012/numerical_relativity/ (Rev. 46)
by bcmsma＠astro.rit.edu 04 Apr '12

04 Apr '12

User: bmundim Date: 2012/04/04 11:13 AM Modified: /numerical_relativity/ numerical_relativity.tex Log: approximate riemann solvers, an example. File Changes: Directory: /numerical_relativity/ ================================= File [modified]: numerical_relativity.tex Delta lines: +24 -0 =================================================================== --- numerical_relativity/numerical_relativity.tex 2012-04-04 15:55:15 UTC (rev 45) +++ numerical_relativity/numerical_relativity.tex 2012-04-04 16:13:46 UTC (rev 46) @@ -609,7 +609,31 @@ \includegraphics[width=6cm]{rarefaction.pdf} \end{figure} +} +\frame{\frametitle{Approximate Riemann Solvers} +Usually the exact solution of the Riemann problem is computationally +very expensive. \pause + +Fortunately we can obtain very good approximation for the solutions +by approximating the conservation law as a quasi-linear system: +\begin{equation} +q_t + A q_x = 0 +\end{equation} \pause +where $A$ is a diagonalizable matrix given by: +\begin{equation} +A(q_l,q_r) = \left. \frac{\partial f}{\partial q} \right|_{q=1/2(q_l+q_R)} +\end{equation} \pause +Roe solver: +\begin{equation} +F^{\rm Roe}_{i+1/2}=\frac{1}{2} \left[f(q^r_{i+1/2})+f(q^l_{i-1/2}) +-\sum_{\alpha} |\lambda_{\alpha}| \omega_{\alpha} r_{\alpha} \right] +\end{equation} +where $\lambda_{\alpha}$ are the characteristics speeds, $\omega_{\alpha}$ +the jumps in the characteristics and $r_{\alpha}$ the right eigenvector +of $A$. } + + \end{document}

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[svn:einsteintoolkit] Workshop_Spring_2012/numerical_relativity/ (Rev. 45)
by bcmsma＠astro.rit.edu 04 Apr '12

04 Apr '12

User: bmundim Date: 2012/04/04 10:55 AM Modified: /numerical_relativity/ numerical_relativity.tex Log: burgers eqn File Changes: Directory: /numerical_relativity/ ================================= File [modified]: numerical_relativity.tex Delta lines: +21 -0 =================================================================== --- numerical_relativity/numerical_relativity.tex 2012-04-04 15:40:22 UTC (rev 44) +++ numerical_relativity/numerical_relativity.tex 2012-04-04 15:55:15 UTC (rev 45) @@ -591,4 +591,25 @@ } +\frame{\frametitle{Example: Burgers Equation} +\begin{equation} +u_t + f(u)_x = 0, \qquad f(u)=\frac{1}{2}u^2 +\end{equation} +with +\[ +u(x,0) = \left\{ \begin{array}{ll} + u_l & \mbox{if $x<0$}\\ + u_r & \mbox{if $x>0$} + \end{array} + \right. +\]\pause + +\begin{figure} + \includegraphics[width=6cm]{shock.pdf} + \includegraphics[width=6cm]{rarefaction.pdf} +\end{figure} + + +} + \end{document}

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[svn:einsteintoolkit] Workshop_Spring_2012/numerical_relativity/ (Rev. 44)
by bcmsma＠astro.rit.edu 04 Apr '12

04 Apr '12

User: bmundim Date: 2012/04/04 10:40 AM Added: /numerical_relativity/figs/ riemann.eps, riemann.pdf Modified: /numerical_relativity/ Makefile, numerical_relativity.tex Log: update... not ready yet... File Changes: Directory: /numerical_relativity/figs/ ====================================== File [added]: riemann.eps Delta lines: <Unavailable> File [added]: riemann.pdf Delta lines: <Unavailable> Directory: /numerical_relativity/ ================================= File [modified]: Makefile Delta lines: <Unavailable> File [modified]: numerical_relativity.tex Delta lines: <Unavailable>

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