commit 2f567e38c8ecc5406c7089d63cef5177b585b517
parent 457096e32269f911dd8f8d30f1aad8d487633f52
Author: Ivan Gankevich <igankevich@ya.ru>
Date: Sat, 29 Jun 2019 13:44:01 +0300
More formulae.
Diffstat:
| Makefile | | | 4 | ++++ |
| graphics/roll.svg | | | 145 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| shell/profile | | | 10 | ++++++++++ |
| slides.tex | | | 107 | ++++++++++++++++++++++++++++++++++++++++++++----------------------------------- |
4 files changed, 218 insertions(+), 48 deletions(-)
diff --git a/Makefile b/Makefile
@@ -24,6 +24,7 @@ build/$(NAME).pdf: main.tex
build/$(SLIDES).pdf: build/openmp-slides.eps
build/$(SLIDES).pdf: build/histogram-slides.eps
+build/$(SLIDES).pdf: build/roll.eps
build/$(SLIDES).pdf: slides.tex
@echo " LATEX $<"
@-$(LATEXMK) $(FLAGS) -xelatex -f $<
@@ -46,6 +47,9 @@ build/histogram-slides.svg: build/*.histogram.dat gnuplot/histogram-slides.gnupl
build/%.eps: build/%.svg
inkscape -z --export-eps=$@ $<
+build/roll.eps: graphics/roll.svg
+ inkscape -z --export-eps=$@ $<
+
build:
@mkdir -p build
diff --git a/graphics/roll.svg b/graphics/roll.svg
@@ -0,0 +1,145 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<svg
+ xmlns:dc="http://purl.org/dc/elements/1.1/"
+ xmlns:cc="http://creativecommons.org/ns#"
+ xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
+ xmlns:svg="http://www.w3.org/2000/svg"
+ xmlns="http://www.w3.org/2000/svg"
+ xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+ xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+ version="1.1"
+ width="3.9097521cm"
+ height="3.440449cm"
+ id="svg2"
+ sodipodi:docname="roll.svg"
+ inkscape:version="0.92.3 (2405546, 2018-03-11)">
+ <metadata
+ id="metadata981">
+ <rdf:RDF>
+ <cc:Work
+ rdf:about="">
+ <dc:format>image/svg+xml</dc:format>
+ <dc:type
+ rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
+ <dc:title>Metacentric Height</dc:title>
+ </cc:Work>
+ </rdf:RDF>
+ </metadata>
+ <defs
+ id="defs979" />
+ <sodipodi:namedview
+ pagecolor="#ffffff"
+ bordercolor="#666666"
+ borderopacity="1"
+ objecttolerance="10"
+ gridtolerance="10"
+ guidetolerance="10"
+ inkscape:pageopacity="0"
+ inkscape:pageshadow="2"
+ inkscape:window-width="1920"
+ inkscape:window-height="1052"
+ id="namedview977"
+ showgrid="false"
+ fit-margin-top="0"
+ fit-margin-left="0"
+ fit-margin-right="0"
+ fit-margin-bottom="0"
+ units="cm"
+ inkscape:zoom="4.0785919"
+ inkscape:cx="43.964647"
+ inkscape:cy="57.069134"
+ inkscape:window-x="0"
+ inkscape:window-y="28"
+ inkscape:window-maximized="0"
+ inkscape:current-layer="svg2" />
+ <title
+ id="title918">Metacentric Height</title>
+ <style
+ type="text/css"
+ id="style920">
+ circle {fill:yellow;stroke:green;stroke-width:1}
+ </style>
+ <rect
+ id="rect924"
+ style="fill:#0080ff;stroke:#0000ff;stroke-width:0.2240504;fill-opacity:0.6036036"
+ y="51.747646"
+ x="0.1120252"
+ rx="0"
+ height="78.173042"
+ width="147.54611" />
+ <path
+ inkscape:connector-curvature="0"
+ id="path928"
+ style="fill:#ffffff;stroke:#000000;stroke-width:0.35928196px;stroke-linecap:square;stroke-linejoin:miter;stroke-opacity:1"
+ d="M 31.38784,0.23024814 146.1768,42.010012 116.6852,123.03751 C 111.76994,136.54209 -3.0190202,94.762325 1.8962439,81.257747 Z" />
+ <path
+ inkscape:connector-curvature="0"
+ id="path944"
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;stroke-miterlimit:4;stroke-dasharray:1, 2;stroke-dashoffset:10"
+ d="M 80.180603,19.603415 V 116.60953" />
+ <path
+ inkscape:connector-curvature="0"
+ id="path946"
+ style="display:inline;fill:none;stroke:#000000;stroke-width:1;stroke-linecap:square;stroke-linejoin:round;stroke-opacity:1;stroke-miterlimit:4;stroke-dasharray:1, 2;stroke-dashoffset:10"
+ d="M 88.167909,22.808202 56.218683,110.58799" />
+ <g
+ id="g1153"
+ transform="matrix(0.625,0,0,0.625,120.76586,56.594712)">
+ <circle
+ r="9.1943493"
+ cy="53.16795"
+ cx="-64.360443"
+ id="path1127"
+ style="fill:#d9dad9;fill-opacity:1;stroke:#000000;stroke-width:1.88999999;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1" />
+ <text
+ id="text1089"
+ y="58.16502"
+ x="-69.196869"
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:14px;line-height:25px;font-family:'Open Sans';-inkscape-font-specification:'Open Sans';letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+ xml:space="preserve"><tspan
+ y="58.16502"
+ x="-69.196869"
+ id="tspan1087"
+ sodipodi:role="line">B</tspan></text>
+ </g>
+ <g
+ id="g1158"
+ transform="matrix(0.625,0,0,0.625,113.79348,-2.1418544)">
+ <circle
+ r="9.1943493"
+ cy="74.376259"
+ cx="-53.204639"
+ id="path1127-3"
+ style="fill:#d9dad9;fill-opacity:1;stroke:#000000;stroke-width:1.88999999;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1" />
+ <text
+ id="text1089-3"
+ y="79.373329"
+ x="-59.527882"
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:14px;line-height:25px;font-family:'Open Sans';-inkscape-font-specification:'Open Sans';letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+ xml:space="preserve"><tspan
+ y="79.373329"
+ x="-59.527882"
+ id="tspan1087-6"
+ sodipodi:role="line">M</tspan></text>
+ </g>
+ <g
+ id="g1163"
+ transform="matrix(0.625,0,0,0.625,116.36791,10.760879)">
+ <circle
+ r="9.1943493"
+ cy="91.784218"
+ cx="-71.838516"
+ id="path1127-5"
+ style="fill:#d9dad9;fill-opacity:1;stroke:#000000;stroke-width:1.88999999;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1" />
+ <text
+ id="text1089-3-7"
+ y="96.784706"
+ x="-76.849258"
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:14px;line-height:25px;font-family:'Open Sans';-inkscape-font-specification:'Open Sans';letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+ xml:space="preserve"><tspan
+ y="96.784706"
+ x="-76.849258"
+ id="tspan1087-6-5"
+ sodipodi:role="line">G</tspan></text>
+ </g>
+</svg>
diff --git a/shell/profile b/shell/profile
@@ -122,3 +122,13 @@ WHERE node='$node' AND ship='$ship' AND total = (
" > build/$ship.$node.histogram.dat
done
done
+
+query "
+.mode csv
+.separator ' '
+SELECT nthreads,AVG(pressure)
+FROM profile
+WHERE node = 'capybara1' AND profile = 'openmp'
+GROUP BY nthreads
+ORDER BY nthreads ASC
+"
diff --git a/slides.tex b/slides.tex
@@ -3,6 +3,7 @@
\setdefaultlanguage{english}
\usetheme{SaintPetersburg}
+\usepackage{textcomp}
\usepackage{booktabs}
\usepackage{multicol}
\usepackage{pgfgantt}
@@ -66,9 +67,6 @@ A.\:Grigorev%
GPUs are easy to get and powerfull.
\end{column}
\end{columns}
- \pause
- \vfill
- {\Large How much performance can we gain using GPUs?}
\end{frame}
\begin{frame}{Wavy surface}
@@ -84,28 +82,21 @@ A.\:Grigorev%
\end{columns}
\end{frame}
-\begin{frame}{Velocity potential}
+\begin{frame}{Fluid motions}
\begin{columns}[T]
\begin{column}{0.49\textwidth}
\includegraphics[width=\textwidth]{graphics/waves-velocity.png}
\end{column}
\begin{column}{0.49\textwidth}
- \begin{beamercolorbox}[colsep*=.75ex,vmode]{block body}%
- \vspace{-\baselineskip}%
- \begin{align*}%
- & \nabla^2\phi = 0
- & \text{continuity equation}\\
- & \phi_t+\frac{1}{2} |\vec{\upsilon}|^2 + g\zeta=-\frac{p}{\rho}
- & \text{dynamic BC}\\
- & D\zeta = \nabla \phi \cdot \vec{n}
- & \text{kinematic BC}\\
- \end{align*}%
- \vspace{-2.5\baselineskip}%
- \end{beamercolorbox}
- \spbuArrow{}%
- \vspace{-0.2cm}%
- \begin{beamercolorbox}[colsep*=.75ex,vmode]{block body}%
- Solution:\vspace{-0.5\baselineskip}%
+ Equations of motion:
+ \begin{equation*}%
+ \begin{cases}
+ \nabla^2\phi = 0 \\
+ \phi_t+\frac{1}{2} |\vec{\upsilon}|^2 + g\zeta=-\frac{p}{\rho} \\
+ D\zeta = \nabla \phi \cdot \vec{n}
+ \end{cases}
+ \end{equation*}%
+ Solution in convolution form:
\begin{equation*}%
\phi(x,y,z,t)
=
@@ -113,8 +104,11 @@ A.\:Grigorev%
\mathrel{*}
\frac{\zeta_t(x,y,t)}{F\left(f_1, f_2, f_3\right)}
\end{equation*}%
- \vspace{-0.5\baselineskip}%
- \end{beamercolorbox}%
+ \footnotesize
+ \begin{itemize}
+ \item Describe conservation of mass and momentum for fluid.
+ \item Convolution theorem is used for fast computation.
+ \end{itemize}
\end{column}
\end{columns}
\end{frame}
@@ -125,16 +119,20 @@ A.\:Grigorev%
\includegraphics[width=\textwidth]{graphics/ship-velocity-waves.png}
\end{column}
\begin{column}{0.49\textwidth}
- Pressure:
- \begin{equation*}
- p(x,y,z,t) = -\rho\phi_t
- - \rho\frac{1}{2}\left( \phi_x^2 + \phi_y^2 + \phi_z^2 \right)
- - \rho g z
- \end{equation*}
- Pressure force:
+ For each ship hull panel:
\begin{equation*}
- F(x,y,z,t) = -p(x,y,z,t) S \vec{n}
+ \begin{aligned}
+ F &= \overbrace{
+ \rho\left(
+ \phi_t +
+ \frac{1}{2}\left( \phi_x^2 + \phi_y^2 + \phi_z^2 \right)
+ \right)
+ S \vec{n}}^{\text{Froude---Krylov force}} \\
+ & + \underbrace{\rho g z S \vec{n}}_{\text{Archimedes' force}}
+ \end{aligned}
\end{equation*}
+ \centering
+ \includegraphics{build/roll.eps}
\end{column}
\end{columns}
\end{frame}
@@ -145,37 +143,37 @@ A.\:Grigorev%
\includegraphics[width=\textwidth]{graphics/ship.png}
\end{column}
\begin{column}{0.49\textwidth}
+ Equations of motion (Newton's second law):
\begin{equation*}
\frac{d}{dt}\left[
\begin{array}{c}
- x(t)\\
+ \vec{x}(t)\\
q(t)\\
- P(t)\\
- L(t)
+ \vec{P}(t)\\
+ \vec{L}(t)
\end{array}
\right] = \left[
\begin{array}{c}
- v(t)\\
- \frac{1}{2}\omega(t)q(t)\\
- F(t)\\
- \tau(t)
+ \vec{v}(t)\\
+ \frac{1}{2}\vec\omega(t)q(t)\\
+ \vec{F}(t)\\
+ \vec\tau(t)
\end{array}
- \right]
- \end{equation*}
- \begin{equation*}
- P(t) = mv(t) \qquad
- L(t) = I(t)\omega(t)
+ \right] \quad
\end{equation*}
\begin{equation*}
- I(t) = R(q(t)) \, I_{\text{body}} \, R(q(t))^{T}
+ \begin{aligned}
+ & \vec{P}(t) = m\vec{v}(t) \qquad \vec{L}(t) = I(t)\vec\omega(t) \\
+ & I(t) = R(q(t)) \, I_{\text{body}} \, R(q(t))^{T}
+ \end{aligned}
\end{equation*}
- \vfill
\footnotesize
- Classic reference:
\begin{itemize}
- \item
- David Baraff \textit{An Introduction to Physically Based Modeling:
- Rigid Body Simulation}, 1997.
+ \item Describe conservation of linear and angular momentum
+ for a ship.
+ \item Approachable reference: David Baraff \textit{An
+ Introduction to Physically Based Modeling: Rigid Body
+ Simulation}, 1997.
\end{itemize}
\end{column}
\end{columns}
@@ -354,4 +352,17 @@ A.\:Grigorev%
Thank you for attention!
\end{frame}
+\begin{frame}
+ \tiny\vfill
+ Copyright \textcopyright{} 2019 Ivan Gankevich
+ \texttt{\href{mailto:i.gankevich@spbu.ru}{i.gankevich@spbu.ru}}. \\
+ \vskip\baselineskip
+ Aurora Cruiser under CC BY-SA 4.0 by Vitaly V. Kuzmin, \url{http://vitalykuzmin.net/}. \\
+ Metacentric height under CC BY-SA 2.5 by Life of Riley, \url{https://commons.wikimedia.org/wiki/File:MetacentricHeight.svg}.\\
+ \vskip\baselineskip
+ This work is licensed under a \alert{Creative Commons Attribution-ShareAlike 4.0
+ International License}. The copy of the license is available at
+ \url{https://creativecommons.org/licenses/by-sa/4.0/}.
+\end{frame}
+
\end{document}
