commit 457096e32269f911dd8f8d30f1aad8d487633f52
parent 3923e4b5593c42c7c003efbc9859e05b24388286
Author: Ivan Gankevich <igankevich@ya.ru>
Date: Fri, 28 Jun 2019 19:19:55 +0300
slides
Diffstat:
11 files changed, 343 insertions(+), 146 deletions(-)
diff --git a/Makefile b/Makefile
@@ -22,6 +22,8 @@ build/$(NAME).pdf: main.tex
@echo " LATEX $<"
@-$(LATEXMK) $(FLAGS) -f $<
+build/$(SLIDES).pdf: build/openmp-slides.eps
+build/$(SLIDES).pdf: build/histogram-slides.eps
build/$(SLIDES).pdf: slides.tex
@echo " LATEX $<"
@-$(LATEXMK) $(FLAGS) -xelatex -f $<
@@ -35,6 +37,12 @@ build/openmp.svg: build/*.openmp.dat gnuplot/openmp.gnuplot gnuplot/style.gnuplo
build/histogram.svg: build/*.histogram.dat gnuplot/histogram.gnuplot gnuplot/style.gnuplot
./gnuplot/histogram.gnuplot
+build/openmp-slides.svg: build/*.openmp.dat gnuplot/openmp-slides.gnuplot gnuplot/style.gnuplot
+ ./gnuplot/openmp-slides.gnuplot
+
+build/histogram-slides.svg: build/*.histogram.dat gnuplot/histogram-slides.gnuplot gnuplot/style.gnuplot
+ ./gnuplot/histogram-slides.gnuplot
+
build/%.eps: build/%.svg
inkscape -z --export-eps=$@ $<
diff --git a/gnuplot/histogram-slides.gnuplot b/gnuplot/histogram-slides.gnuplot
@@ -0,0 +1,43 @@
+#!/usr/bin/gnuplot -d
+
+set terminal svg size 1920/6,1080/6 dynamic round font 'Open Sans, 10' lw 0.5
+set key Left reverse outside
+set key autotitle columnheader
+set ylabel 'Time, ms' offset 2,0
+set xtics rotate by -45
+set ytics 0,20
+
+load 'gnuplot/style.gnuplot'
+
+set style histogram rowstacked title
+set style data histograms
+set style fill solid border -1
+set boxwidth 0.75
+set xlabel offset 0,1
+set output 'build/histogram-slides.svg'
+plot \
+ newhistogram "Storm", \
+ 'build/sphere.storm.histogram.dat' \
+ using 'waves':xtic(1) ls 1, \
+ '' using 'velocity' ls 2, \
+ '' using 'wetted' ls 3, \
+ '' using 'clamp' ls 4, \
+ '' using 'pressure' ls 5, \
+ '' using 'exchange' ls 6, \
+ newhistogram "GPUlab", \
+ 'build/sphere.gpulab1.histogram.dat' \
+ using 'waves':xtic(1) ls 1 notitle, \
+ '' using 'velocity' ls 2 notitle, \
+ '' using 'wetted' ls 3 notitle, \
+ '' using 'clamp' ls 4 notitle, \
+ '' using 'pressure' ls 5 notitle, \
+ '' using 'exchange' ls 6 notitle, \
+ newhistogram "Capybara", \
+ 'build/sphere.capybara1.histogram.dat' \
+ using 'waves':xtic(1) ls 1 notitle, \
+ '' using 'velocity' ls 2 notitle, \
+ '' using 'wetted' ls 3 notitle, \
+ '' using 'clamp' ls 4 notitle, \
+ '' using 'pressure' ls 5 notitle, \
+ '' using 'exchange' ls 6 notitle
+
diff --git a/gnuplot/openmp-slides.gnuplot b/gnuplot/openmp-slides.gnuplot
@@ -0,0 +1,27 @@
+#!/usr/bin/gnuplot -d
+
+set terminal svg size 1920/8*0.9,2.3*1080/6*0.7 dynamic round font 'Open Sans, 10' lw 0.5 enhanced
+set key right Left reverse width -2
+set xlabel 'No. of parallel threads' offset 0,1
+set ylabel 'Time, ms' offset 3,0
+set xtics offset 0,0.5
+set ytics 0,20,80 offset 0.5,0
+set xrange [0:10]
+load 'gnuplot/style.gnuplot'
+set output 'build/openmp-slides.svg'
+set multiplot layout 2,1
+plot \
+ 'build/sphere.storm.openmp.dat' with linespoints ls 1 lw 4 smooth csplines title 'Storm', \
+ 'build/sphere.gpulab1.openmp.dat' with linespoints ls 2 lw 4 smooth csplines title 'GPUlab', \
+ 'build/sphere.capybara1.openmp.dat' with linespoints ls 3 lw 4 smooth csplines title 'Capybara'
+
+set ylabel 'Speedup' offset 3,0
+set ytics 0,2 offset 0.5,0
+set yrange [0:10]
+set key left Left reverse height -2
+plot \
+ 'build/sphere.storm.openmp.dat' using 1:3 with linespoints ls 1 lw 4 smooth csplines title 'Storm', \
+ 'build/sphere.gpulab1.openmp.dat' using 1:3 with linespoints ls 2 lw 4 smooth csplines title 'GPUlab', \
+ 'build/sphere.capybara1.openmp.dat' using 1:3 with linespoints ls 3 lw 4 smooth csplines title 'Capybara', \
+ x with lines lw 4 lc 'gray' dt 3 notitle
+
diff --git a/graphics/aurora-real.jpg b/graphics/aurora-real.jpg
Binary files differ.
diff --git a/graphics/aurora-vsl.png b/graphics/aurora-vsl.png
Binary files differ.
diff --git a/graphics/ship-velocity-waves.png b/graphics/ship-velocity-waves.png
Binary files differ.
diff --git a/graphics/ship.png b/graphics/ship.png
Binary files differ.
diff --git a/graphics/waves-velocity.png b/graphics/waves-velocity.png
Binary files differ.
diff --git a/graphics/waves.png b/graphics/waves.png
Binary files differ.
diff --git a/preamble.tex b/preamble.tex
@@ -24,6 +24,18 @@
arrows={-Triangle[length=0.25cm,width=0.125cm]},
draw=spbuDarkGray
]
+\tikzstyle{Dashed} = [
+ very thick,
+ draw=spbuDarkGray2,
+ dashed
+]
+\tikzstyle{Label} = [
+ align=center,
+ font=\scriptsize\linespread{1}\selectfont,
+ fill=none,
+ baseline,
+ anchor=south
+]
\definecolor{markRed}{HTML}{E5C6C5}
diff --git a/slides.tex b/slides.tex
@@ -1,4 +1,4 @@
-\documentclass[aspectratio=169]{beamer}
+\documentclass[aspectratio=169,xcolor=table]{beamer}
\usepackage{polyglossia}
\setdefaultlanguage{english}
\usetheme{SaintPetersburg}
@@ -9,6 +9,9 @@
\usepackage{tikz}
\usetikzlibrary{arrows.meta}
\setlength{\tabcolsep}{4pt}
+\definecolor{opencl}{RGB}{200,255,200}
+\definecolor{openmp}{RGB}{255,255,200}
+
%\setbeamertemplate{footline}[frame number]
@@ -55,12 +58,12 @@ A.\:Grigorev%
\begin{column}{0.33\textwidth}
\centering
\includegraphics[height=4cm]{graphics/supercomputer.jpg}
- Supercomputers are scarce.
+ Supercomputers have command line interface (mostly).
\end{column}
\begin{column}{0.33\textwidth}
\centering
\includegraphics[height=4cm]{graphics/gpu.jpg}\linebreak
- GPUs are not.
+ GPUs are easy to get and powerfull.
\end{column}
\end{columns}
\pause
@@ -68,88 +71,169 @@ A.\:Grigorev%
{\Large How much performance can we gain using GPUs?}
\end{frame}
-\begin{frame}{Velocity potential equations}
- \footnotesize
- \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 for }z=\zeta(x,y,t)
- \\
- & D\zeta = \nabla \phi \cdot \vec{n}
- & \text{kinematic BC for }z=\zeta(x,y,t)\\
- \end{align*}%
- \vspace{-2.5\baselineskip}%
- \end{beamercolorbox}%
- %
- \pause%
- %
- \spbuArrow{}%
- \vspace{-0.2cm}%
- %
- \begin{beamercolorbox}[colsep*=.75ex,vmode]{block body}%
- \vspace{-\baselineskip}%
- \begin{align*}%
- & \phi_{xx} + \phi_{yy} + \phi_{zz} = 0\\
- & \zeta_t
- = \underbrace{\fillrectemph{f1}{\left(\FracSqrtZetaXY{\zeta_x} - \zeta_x\right)}}_{f_1} \phi_x
- + \underbrace{\fillrectemph{f2}{\left(\FracSqrtZetaXY{\zeta_y} - \zeta_y\right)}}_{f_2} \phi_y
- - \underbrace{\fillrectemph{f3}{\FracSqrtZetaXY{1}}}_{f_3} \phi_z \\
- \end{align*}%
- \vspace{-2.7\baselineskip}%
- \end{beamercolorbox}%
- %
- \pause%
-\vspace{-0.5\baselineskip}%
-\spbuArrow{}%
-\vspace{-\baselineskip}%
-\begingroup%
-\setlength\abovedisplayskip{1mm}%
-\begin{beamercolorbox}[colsep*=.75ex,vmode]{block body}%
-Solution:\vspace{-0.5\baselineskip}%
-\begin{equation*}%
- \phi(x,y,z,t)
- =
- \mathcal{W}_2(x,y,z)
- \mathrel{*}
-% \frac{\zeta_t(x,y,t)}{i f_1(x,y,t) + i f_2(x,y,t) - f_3(x,y,t)}
- \frac{\zeta_t(x,y,t)}{F\left(f_1, f_2, f_3\right)}
-% & \mathcal{W}_1 \approx \mathcal{W}_2
-\end{equation*}%
-\vspace{-0.5\baselineskip}%
-\end{beamercolorbox}%
-\endgroup%
+\begin{frame}{Wavy surface}
+ \begin{columns}[T]
+ \begin{column}{0.49\textwidth}
+ \includegraphics[width=\textwidth]{graphics/waves.png}
+ \end{column}
+ \begin{column}{0.49\textwidth}
+ \begin{itemize}
+ \item Stokes waves (without vorticity).
+ \end{itemize}
+ \end{column}
+ \end{columns}
+\end{frame}
+
+\begin{frame}{Velocity potential}
+ \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}%
+ \begin{equation*}%
+ \phi(x,y,z,t)
+ =
+ \mathcal{W}(x,y,z)
+ \mathrel{*}
+ \frac{\zeta_t(x,y,t)}{F\left(f_1, f_2, f_3\right)}
+ \end{equation*}%
+ \vspace{-0.5\baselineskip}%
+ \end{beamercolorbox}%
+ \end{column}
+ \end{columns}
\end{frame}
\begin{frame}{Wave pressure}
- 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:
- \begin{equation*}
- F(x,y,z,t) = -p S \vec{n}
- \end{equation*}
+ \begin{columns}[T]
+ \begin{column}{0.49\textwidth}
+ \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:
+ \begin{equation*}
+ F(x,y,z,t) = -p(x,y,z,t) S \vec{n}
+ \end{equation*}
+ \end{column}
+ \end{columns}
+\end{frame}
+
+\begin{frame}{Ship motions}
+ \begin{columns}[T]
+ \begin{column}{0.49\textwidth}
+ \includegraphics[width=\textwidth]{graphics/ship.png}
+ \end{column}
+ \begin{column}{0.49\textwidth}
+ \begin{equation*}
+ \frac{d}{dt}\left[
+ \begin{array}{c}
+ x(t)\\
+ q(t)\\
+ P(t)\\
+ L(t)
+ \end{array}
+ \right] = \left[
+ \begin{array}{c}
+ v(t)\\
+ \frac{1}{2}\omega(t)q(t)\\
+ F(t)\\
+ \tau(t)
+ \end{array}
+ \right]
+ \end{equation*}
+ \begin{equation*}
+ P(t) = mv(t) \qquad
+ L(t) = I(t)\omega(t)
+ \end{equation*}
+ \begin{equation*}
+ I(t) = R(q(t)) \, I_{\text{body}} \, R(q(t))^{T}
+ \end{equation*}
+ \vfill
+ \footnotesize
+ Classic reference:
+ \begin{itemize}
+ \item
+ David Baraff \textit{An Introduction to Physically Based Modeling:
+ Rigid Body Simulation}, 1997.
+ \end{itemize}
+ \end{column}
+ \end{columns}
+\end{frame}
+
+\begin{frame}{Digitised three-dimensional ship hull models}
+ \begin{columns}[T]
+ \begin{column}{0.49\textwidth}
+ \begin{tikzpicture}
+ \node[anchor=north west,inner sep=0] (image) at (0,0) {%
+ \includegraphics[width=\textwidth]{graphics/aurora-vsl.png}};
+ \node[anchor=north west,spbuWhite1,font={\large}] at (0,0)
+ {Aurora in Virtual testbed};
+ \end{tikzpicture}
+ \end{column}
+ \begin{column}{0.49\textwidth}
+ \begin{tikzpicture}
+ \node[anchor=north west,inner sep=0] (image) at (0,0)
+ {\includegraphics[width=\textwidth]{graphics/aurora-real.jpg}};
+ \node[anchor=north west,spbuWhite1,font={\large}] at (0,0)
+ {Aurora in Saint-Petersburg};
+ \end{tikzpicture}
+ \end{column}
+ \end{columns}
+ \vfill
+ Ship hull database is registered in~FIPS:
+ \footnotesize
+ \begin{itemize}
+ \item
+ A.\:Bogdanov, V.\:Khramushin
+ \textit{Vessel: Blueprints for the
+ analysis of hydrostatic characteristics, stability and
+ propulsion of the ship}, 2015, FIPS \#2015621368
+ (in Russian).
+ \item
+ V.\:Khramushin \textit{Analytic ship hull shape
+ construction, wave resistance
+ calculations, theoretical blueprint feature curve
+ calculations, and ship stability diagrams}, 2010, FIPS \#2010615849
+ (in Russian).
+ \end{itemize}
\end{frame}
\begin{frame}
- \frametitle{Main loop}
+ \frametitle{The anatomy of a simulation step}
\centering
\begin{tikzpicture}[x=2.2cm,y=-1.4cm]
- \node[Block] (s1) at (0,0) {\strut{}Wavy surface};
+ % nodes
+ \node[Block,fill=markRed] (s1) at (0,0) {\strut{}Wavy surface};
\node[Block] (s2) at (1,0) {\strut{}Autoreg. model};
\node[Block] (s3) at (2,0) {\strut{}Wave numbers};
- \node[Block] (s4) at (3,0) {\strut{}Velocity potential};
- \node[Block] (s5) at (4,0) {\strut{}Wave pressure};
- \node[Block] (s6) at (4,1) {\strut{}Wetted surface};
- \node[Block] (s7) at (3,1) {\strut{}Elevation deriv.};
- \node[Block] (s8) at (2,1) {\strut{}Pressure force};
+ \node[Block,fill=markRed] (s4) at (3,0) {\strut{}Velocity potential};
+ \node[Block,fill=markRed] (s5) at (4,0) {\strut{}Wave pressure};
+ \node[Block,fill=markRed] (s6) at (4,1) {\strut{}Wetted surface};
+ \node[Block,fill=markRed] (s7) at (3,1) {\strut{}Elevation deriv.};
+ \node[Block,fill=markRed] (s8) at (2,1) {\strut{}Pressure force};
\node[Block] (s9) at (1,1) {\strut{}Ship velocities};
+ % solid edges
\path[Arrow] (s1) -- (s2);
\path[Arrow] (s2) -- (s3);
\path[Arrow] (s3) -- (s4);
@@ -159,85 +243,108 @@ Solution:\vspace{-0.5\baselineskip}%
\path[Arrow] (s7) -- (s8);
\path[Arrow] (s8) -- (s9);
\path[Arrow] (s9) -| (s1);
+ % labels
+ \node[Label,anchor=south,above=of s1]
+ (lblWavySurface)
+ {Linear models};
+ \node[Label,anchor=north,above=of s4,text width=3.0cm]
+ (lblVelocityPotential)
+ {Convolution (4\(\times\)FFT), derivatives};
+ \node[Label,anchor=north,above=2cm of s5,text width=3.0cm]
+ (lblPressure)
+ {Geometric transformations, derivatives};
+ \node[Label,anchor=south,below=of s6,text width=4cm]
+ (lblGeometry)
+ {Geometric transformations};
+ \node[Label,anchor=south,below=1.5cm of s8,text width=3cm]
+ (lblInterpolation)
+ {Linear\\interpolation};
+ \node[Label,anchor=south,below=of s9,text width=4.0cm]
+ (lblShipMotion)
+ {Runge---Khutta---Fehlberg (or Euler)};
+ % dashed edges
+ \path[Dashed] (s1.north -| lblWavySurface.south) -- (lblWavySurface.south);
+ \path[Dashed] (s4.north -| lblVelocityPotential.south) -- (lblVelocityPotential.south);
+ \path[Dashed] (s5.north -| lblPressure.south) -- (lblPressure.south);
+ \path[Dashed] (lblGeometry.north -| s6.south) -- (s6.south);
+ \path[Dashed] (lblInterpolation.north -| s8.south) -- (s8.south);
+ \path[Dashed] (lblShipMotion.north -| s9.south) -- (s9.south);
\end{tikzpicture}
\end{frame}
\begin{frame}
- \frametitle{3-D ship models}
- \centering
- \includegraphics[width=0.5\textwidth]{build/aurora.eps}\hfill
- \includegraphics[width=0.5\textwidth]{build/micw.eps}
- \vfill
- \begin{tabular}{lrrr}
- \toprule
- & Aurora & MICW & Sphere \\
- \midrule
- Length, m & 126.5 & 260 & 100 \\
- Beam, m & 16.8 & 32 & 100 \\
- Depth, m & 14.5 & 31 & 100 \\
- No. of panels & 29306 & 10912 & 5120 \\
- \bottomrule
- \end{tabular}
-\end{frame}
-
-\begin{frame}
- \frametitle{Best median performance}
- \centering
- \begin{tabular}{lrrrlrrrlrrrl}
- \toprule
- & \multicolumn{4}{c}{Sphere}
- & \multicolumn{4}{c}{Aurora}
- & \multicolumn{4}{c}{MICW} \\
- \cmidrule(r){2-5}
- \cmidrule(r){6-9}
- \cmidrule(r){10-13}
- Node & \(t\), ms & \(m\) & \(n\) & ver.
- & \(t\), ms & \(m\) & \(n\) & ver.
- & \(t\), ms & \(m\) & \(n\) & ver. \\
- \midrule
- Storm & 16 & 64 & 1 & CL
- & 14 & 72 & 1 & CL
- & 29 & 34 & 1 & CL \\
- GPUlab & 10 & 104 & 1 & CL
- & 9 & 112 & 1 & CL
- & 18 & 55 & 1 & CL \\
- Capybara & 12 & 85 & 10 & MP
- & 15 & 66 & 10 & MP
- & 19 & 51 & 10 & MP \\
- \bottomrule
- \end{tabular}
-\end{frame}
-
-\begin{frame}
- \frametitle{Hardware configuration}
- \centering
- \begin{tabular}{lllrr}
- \toprule
- & & & \multicolumn{2}{c}{GPU GFLOPS} \\
- \cmidrule(r){4-5}
- Node & CPU & GPU & Single & Double \\
- \midrule
- Storm & Intel Q9550 & Radeon R7 360 & 1613 & 101 \\
- GPUlab & AMD FX-8370 & NVIDIA GTX1060 & 4375 & 137 \\
- Capybara & Intel E5-2630 v4 & NVIDIA P5000 & 8873 & 277 \\
- \bottomrule
- \end{tabular}
-\end{frame}
-
-\begin{frame}
- \frametitle{OpenMP performance}
- \centering
- \includegraphics{build/openmp.eps}
-\end{frame}
-
-\begin{frame}
- \frametitle{Overall performance}
- \centering
- \includegraphics{build/histogram.eps}
+ \small
+ \begin{columns}[T]
+ \begin{column}{0.56\textwidth}%
+ \centering%
+ \begin{block}{\small{}Detailed performance (sphere)\strut{}}%
+ \includegraphics{build/histogram-slides.eps}%
+ \end{block}%
+ \vspace{-1.5\baselineskip}
+ \begin{block}{\small{}Workstations\strut{}}
+ \centering\tiny
+ \begin{tabular}{lllrr}
+ \toprule
+ & & & \multicolumn{2}{c}{GPU GFLOPS} \\
+ \cmidrule(r){4-5}
+ Workstation & CPU & GPU & Single & Double \\
+ \midrule
+ Storm & Intel Q9550 & Radeon R7 360 & 1613 & 101 \\
+ GPUlab & AMD FX-8370 & NVIDIA GTX1060 & 4375 & 137 \\
+ Capybara & Intel E5-2630 v4 & NVIDIA P5000 & 8873 & 277 \\
+ \bottomrule
+ \end{tabular}
+ \end{block}
+ \end{column}%
+ \begin{column}{0.40\textwidth}%
+ \begin{block}{\small{}Best median performance\strut{}}%
+ \centering%
+ \scriptsize%
+ \begin{tabular}{lrrr}%
+ \toprule
+ & \multicolumn{3}{c}{Simulation step time, ms} \\
+ \cmidrule(r){2-4}
+ Workstation & Sphere & Aurora & MICW \\
+ \midrule
+ Storm & \cellcolor{opencl}16 & \cellcolor{opencl}14 & \cellcolor{opencl}29 \\
+ GPUlab & \cellcolor{opencl}10 & \cellcolor{opencl}9 & \cellcolor{opencl}18 \\
+ Capybara & \cellcolor{openmp}12 & \cellcolor{openmp}15 & \cellcolor{openmp}19 \\
+ \bottomrule
+ \end{tabular}
+ \vskip0.5\baselineskip
+ \begin{tabular}{cc}
+ \cellcolor{opencl}OpenCL &
+ \cellcolor{openmp}OpenMP \\
+ \end{tabular}
+ \end{block}%
+ \vspace{-1.5\baselineskip}
+ \begin{block}{\small{}Ship hulls\strut{}}
+ \centering%
+ \scriptsize
+ \begin{tabular}{lrrr}
+ \toprule
+ & Aurora & MICW & Sphere \\
+ \midrule
+ Length, m & 126.5 & 260 & 100 \\
+ Beam, m & 16.8 & 32 & 100 \\
+ Depth, m & 14.5 & 31 & 100 \\
+ No. of panels & 29306 & 10912 & 5120 \\
+ \bottomrule
+ \end{tabular}
+ \end{block}
+ \end{column}%
+ \end{columns}%
\end{frame}
\begin{frame}
- \frametitle{Results}
+ \frametitle{Conclusion}
+ \begin{itemize}
+ \item Moving computations to data (and not vice versa) is beneficial
+ for iterative programmes.
+ \item Computationally efficient mathematical models (rewriting formulae
+ using FFT) are needed for large performance gains.
+ \item Can not get away without GPU-specialised algorithms (derivatives).
+ \end{itemize}
\end{frame}
\begin{frame}
