correct

[book_gpu.git] / BookGPU / Chapters / chapter7 / ch7.tex

diff --git a/BookGPU/Chapters/chapter7/ch7.tex b/BookGPU/Chapters/chapter7/ch7.tex
index 401f132aea15bd79801faeeb035002c23a068cf1..45fc4537654456483c5e1dc70d7bc7f6d816e1f8 100644 (file)
--- a/BookGPU/Chapters/chapter7/ch7.tex
+++ b/BookGPU/Chapters/chapter7/ch7.tex
@@ -9,7 +9,7 @@
 
 \begin{figure}[!htb]
 \centering
 
 \begin{figure}[!htb]
 \centering

-\includegraphics[width=0.95\textwidth]{Chapters/chapter7/figures/figSeries60CB06Type7StedaySnapshot.eps}
+\includegraphics[width=0.95\textwidth]{Chapters/chapter7/figures/figSeries60CB06Type7StedaySnapshot-eps-converted-to.pdf}

 %\caption{Snapshot of steady state wave field generated by a Series 60 ship hull.}
 \end{figure}
 
 %\caption{Snapshot of steady state wave field generated by a Series 60 ship hull.}
 \end{figure}
 


@@ -313,19 +313,19 @@ Similar results were reported for the first time in the context of high-order Bo
 \centering
 \subfigure[Grid scaling, $x=(1-a)\xi^3+a\xi$.]{
 % MainLaplace2D_ex03.m
 \centering
 \subfigure[Grid scaling, $x=(1-a)\xi^3+a\xi$.]{
 % MainLaplace2D_ex03.m

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/scalingNx25.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/scalingNx25-eps-converted-to.pdf}

 }
 \subfigure[High-order spatial discretisation and stable explicit time-stepping with large time steps for a nonlinear standing wave. Scaling based on $a=0$. ]{
 % MainLaplace2D_ex03.m
 }
 \subfigure[High-order spatial discretisation and stable explicit time-stepping with large time steps for a nonlinear standing wave. Scaling based on $a=0$. ]{
 % MainLaplace2D_ex03.m

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/standingwaveglozman.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/standingwaveglozman-eps-converted-to.pdf}

 }
 \subfigure[Uniform grid ($a=1$).]{
 % MainLaplace2D_ex035_nonlinearLaplace.m
 }
 \subfigure[Uniform grid ($a=1$).]{
 % MainLaplace2D_ex035_nonlinearLaplace.m

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/SFwaves_snapshots_uniform.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/SFwaves_snapshots_uniform-eps-converted-to.pdf}

 }
 \subfigure[Clustered grid ($a=0.05$).]{
 % MainLaplace2D_ex035_nonlinearLaplace.m
 }
 \subfigure[Clustered grid ($a=0.05$).]{
 % MainLaplace2D_ex035_nonlinearLaplace.m

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/SFwaves_snapshots_clustered.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/SFwaves_snapshots_clustered-eps-converted-to.pdf}

 }
 \caption{Numerical experiments to assess stability properties of numerical wave model. In three cases, computed snapshots are taken of the wave elevation over one wave period of time. In a) the grid distribution of nodes in a one-parameter mapping for the grid is illustrated. Results from changes in wave elevation are illustrated for b) a mildly nonlinear standing wave on a highly clustered grid, c) regular stream function wave of medium steepness in shallow water $(kh,H/L)=(0.5,0.0292)$ on a uniform grid ($N_x=80$) and d) for a nonuniform grid with a minimal grid spacing 20 times smaller(!). In every case the step size remains fixed at $\Delta t = T/160$ s corresponding to a Courant number $C_r=c\tfrac{\Delta t}{\Delta x}=0.5$ for the uniform grid. A 6'$th$ order scheme and explicit EKR4 time-stepping is used in each test case.}
 \label{ch7:numexp}
 }
 \caption{Numerical experiments to assess stability properties of numerical wave model. In three cases, computed snapshots are taken of the wave elevation over one wave period of time. In a) the grid distribution of nodes in a one-parameter mapping for the grid is illustrated. Results from changes in wave elevation are illustrated for b) a mildly nonlinear standing wave on a highly clustered grid, c) regular stream function wave of medium steepness in shallow water $(kh,H/L)=(0.5,0.0292)$ on a uniform grid ($N_x=80$) and d) for a nonuniform grid with a minimal grid spacing 20 times smaller(!). In every case the step size remains fixed at $\Delta t = T/160$ s corresponding to a Courant number $C_r=c\tfrac{\Delta t}{\Delta x}=0.5$ for the uniform grid. A 6'$th$ order scheme and explicit EKR4 time-stepping is used in each test case.}
 \label{ch7:numexp}


@@ -376,12 +376,12 @@ The profiles can be reversed by a change of coordinate, i.e. $\Gamma(1-x)$, and
 \centering
 \subfigure[Wave generation, reflection and absorption of small-amplitude waves.]{
 % Script : MainLaplace2D_ex03penalityLINEAR_REFLECTEDWAVES.m
 \centering
 \subfigure[Wave generation, reflection and absorption of small-amplitude waves.]{
 % Script : MainLaplace2D_ex03penalityLINEAR_REFLECTEDWAVES.m

-\includegraphics[width=0.98\textwidth]{Chapters/chapter7/figures/standingwavespenalty.eps}
+\includegraphics[width=0.98\textwidth]{Chapters/chapter7/figures/standingwavespenalty-eps-converted-to.pdf}

 % Nx = 480, 6th order, vertical clustering, Nz=6;
 }
 \subfigure[Wave generation and absorption of steep finite-amplitude waves.]{
 % Script : MainLaplace2D_ex03penalityNONLINEAR_GENERATEWAVES.m
 % Nx = 480, 6th order, vertical clustering, Nz=6;
 }
 \subfigure[Wave generation and absorption of steep finite-amplitude waves.]{
 % Script : MainLaplace2D_ex03penalityNONLINEAR_GENERATEWAVES.m

-\includegraphics[width=0.98\textwidth]{Chapters/chapter7/figures/nonlinearwavespenalty.eps}
+\includegraphics[width=0.98\textwidth]{Chapters/chapter7/figures/nonlinearwavespenalty-eps-converted-to.pdf}

 % Nx = 540, 6th order, vertical clustering, Nz=6;
 }
 \caption{Snapshots at intervals $T/8$ over one wave period in time of computed a) small-amplitude $(kh,kH)=(0.63,0.005)$ and b) finite-amplitude $(kh,kH)=(1,0.41)$ stream function waves elevations having reached a steady state after transient startup. Combined wave generation and absorption zones in the western relaxation zone of both a) and b). In b) an absorption zone is positioned next to the eastern boundary and causes minor visible reflections. }
 % Nx = 540, 6th order, vertical clustering, Nz=6;
 }
 \caption{Snapshots at intervals $T/8$ over one wave period in time of computed a) small-amplitude $(kh,kH)=(0.63,0.005)$ and b) finite-amplitude $(kh,kH)=(1,0.41)$ stream function waves elevations having reached a steady state after transient startup. Combined wave generation and absorption zones in the western relaxation zone of both a) and b). In b) an absorption zone is positioned next to the eastern boundary and causes minor visible reflections. }


@@ -535,7 +535,8 @@ __global__ void laplace_sigma_transformed(
        {                       
                size_type offset_i = i < alpha ? 2*alpha-i : i >= Ns-alpha ? Ns-1-i : alpha;
                size_type row_i    = offset_i*rank;
        {                       
                size_type offset_i = i < alpha ? 2*alpha-i : i >= Ns-alpha ? Ns-1-i : alpha;
                size_type row_i    = offset_i*rank;

-               size_type offset_j = alpha;  // Always centered stencils in x-dir
+    // Always centered stencils in x-dir
+               size_type offset_j = alpha;  

                size_type row_j    = alpha*rank;
                        
                value_type dhdx    = hx[j];
                size_type row_j    = alpha*rank;
                        
                value_type dhdx    = hx[j];


@@ -681,10 +682,11 @@ where $m$ is one of the scalar functions $\phi,u,w$ describing kinematics, $c$ i
 \begin{figure}[!htb]
 \begin{center}
 \subfigure[Uniform vertical grid.]{
 \begin{figure}[!htb]
 \begin{center}
 \subfigure[Uniform vertical grid.]{

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/lineardispersion_Nx30-HL90-p6-vergrid0_Linear.eps}
+%\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/lineardispersion_Nx30-HL90-p6-vergrid0_Linear.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/lineardispersion_Nx30-HL90-p6-vergrid0_Linear-eps-converted-to.pdf}

 }
 \subfigure[Cosine-clustered vertical grid.]{
 }
 \subfigure[Cosine-clustered vertical grid.]{

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/lineardispersion_Nx30-HL90-p6_Linear.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/lineardispersion_Nx30-HL90-p6_Linear-eps-converted-to.pdf}

 }
 \end{center}
 \caption{The accuracy in phase celerity $c$ determined by \eqref{ch7:errdisp} for small-amplitude (linear) wave.
 }
 \end{center}
 \caption{The accuracy in phase celerity $c$ determined by \eqref{ch7:errdisp} for small-amplitude (linear) wave.


@@ -696,16 +698,16 @@ $N_z\in[6,12]$. Sixth order scheme.}
 \begin{figure}[!htb]
 \begin{center}
 \subfigure[Linear]{
 \begin{figure}[!htb]
 \begin{center}
 \subfigure[Linear]{

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/kinematicsPHI_Nx30-HL90-p6_Linear.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/kinematicsPHI_Nx30-HL90-p6_Linear-eps-converted-to.pdf}

 }
 \subfigure[Linear]{
 }
 \subfigure[Linear]{

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/kinematicsW_Nx30-HL90-p6_Linear.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/kinematicsW_Nx30-HL90-p6_Linear-eps-converted-to.pdf}

 }
 \subfigure[Nonlinear]{
 }
 \subfigure[Nonlinear]{

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/kinematicsPHI_Nx30-HL90-p6_Nonlinear.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/kinematicsPHI_Nx30-HL90-p6_Nonlinear-eps-converted-to.pdf}

 }
 \subfigure[Nonlinear]{
 }
 \subfigure[Nonlinear]{

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/kinematicsW_Nx30-HL90-p6_Nonlinear.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/kinematicsW_Nx30-HL90-p6_Nonlinear-eps-converted-to.pdf}

 }
 \end{center}
 \caption{Assessment of kinematic error is presented in terms of the depth-averaged error determined by \eqref{ch7:errkin} for a) scalar velocity potential and b) vertical velocity for a small-amplitude (linear) wave, and c) scalar velocity potential and d) vertical velocity for a finite-amplitude (nonlinear) wave with wave height $H/L=90\%(H/L)_\textrm{max}$.
 }
 \end{center}
 \caption{Assessment of kinematic error is presented in terms of the depth-averaged error determined by \eqref{ch7:errkin} for a) scalar velocity potential and b) vertical velocity for a small-amplitude (linear) wave, and c) scalar velocity potential and d) vertical velocity for a finite-amplitude (nonlinear) wave with wave height $H/L=90\%(H/L)_\textrm{max}$.


@@ -730,10 +732,10 @@ Previously reported performance results for the wave model can be taken a step f
 \begin{center}
 % MainLaplace2D_ex025nonlinearLaplaceSINGLE.m
 \subfigure[Single precision.]{
 \begin{center}
 % MainLaplace2D_ex025nonlinearLaplaceSINGLE.m
 \subfigure[Single precision.]{

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/PrecisionSINGLE.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/PrecisionSINGLE-eps-converted-to.pdf}

 }
 \subfigure[Double precision.]{
 }
 \subfigure[Double precision.]{

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/PrecisionDOUBLE.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/PrecisionDOUBLE-eps-converted-to.pdf}

 }
 \end{center}
 \caption{Comparison between convergence histories for single and double precision computations using a PDC method for the solution of the transformed Laplace problem. Very steep nonlinear stream function wave in intermediate water $(kh,H/L)=(1,0.0903)$. Discretizaiton based on $(N_x,N_z)=(15,9)$ with 6'$th$ order stencils.}
 }
 \end{center}
 \caption{Comparison between convergence histories for single and double precision computations using a PDC method for the solution of the transformed Laplace problem. Very steep nonlinear stream function wave in intermediate water $(kh,H/L)=(1,0.0903)$. Discretizaiton based on $(N_x,N_z)=(15,9)$ with 6'$th$ order stencils.}


@@ -758,16 +760,16 @@ Results from numerical experiments are presented in figure \ref{ch7:filtering} a
 \begin{center}
 % DriverWavemodelDecomposition.m
 \subfigure[Direct solve without filter.]{
 \begin{center}
 % DriverWavemodelDecomposition.m
 \subfigure[Direct solve without filter.]{

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/ComparisonLUNoFiltering.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/ComparisonLUNoFiltering-eps-converted-to.pdf}

 }
 \subfigure[Direct solve with filter.]{
 }
 \subfigure[Direct solve with filter.]{

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/ComparisonLUWithFiltering.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/ComparisonLUWithFiltering-eps-converted-to.pdf}

 } \\
 \subfigure[Iterative PDC solve without filter.]{
 } \\
 \subfigure[Iterative PDC solve without filter.]{

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/ComparisonDCNoFiltering.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/ComparisonDCNoFiltering-eps-converted-to.pdf}

 }
 \subfigure[Iterative PDC solve with filter.]{
 }
 \subfigure[Iterative PDC solve with filter.]{

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/ComparisonDCWithFiltering.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/ComparisonDCWithFiltering-eps-converted-to.pdf}

 }
 \end{center}
 \caption{Comparison between accuracy as a function of time for double precision calculations vs. single precision with and without filtering. The double precision result are unfiltered in each comparison and shows to be less sensitive to roundoff-errors. Medium steep nonlinear stream function wave in intermediate water $(kh,H/L)=(1,0.0502)$. Discretization is based on $(N_x,N_z)=(30,6)$, A courant number of $C_r=0.5$ and 6'$th$ order stencils.}
 }
 \end{center}
 \caption{Comparison between accuracy as a function of time for double precision calculations vs. single precision with and without filtering. The double precision result are unfiltered in each comparison and shows to be less sensitive to roundoff-errors. Medium steep nonlinear stream function wave in intermediate water $(kh,H/L)=(1,0.0502)$. Discretization is based on $(N_x,N_z)=(30,6)$, A courant number of $C_r=0.5$ and 6'$th$ order stencils.}


@@ -818,10 +820,12 @@ Ideally, the ratio $\mathcal{C}_\mathcal{G}/\mathcal{C}_\mathcal{F}$ is small an
     \setlength\figureheight{0.35\textwidth}
     \setlength\figurewidth{0.37\textwidth}
     \subfigure[Performance scaling]{
     \setlength\figureheight{0.35\textwidth}
     \setlength\figurewidth{0.37\textwidth}
     \subfigure[Performance scaling]{

-        {\small\input{Chapters/chapter7/figures/PararealScaletestGTX590.tikz}}
+%        {\small\input{Chapters/chapter7/figures/PararealScaletestGTX590.tikz}}
+      \includegraphics[width=0.5\textwidth]{Chapters/chapter7/figures/PararealScaletestGTX590_conv.pdf}

     }
     \subfigure[Speedup]{
     }
     \subfigure[Speedup]{

-        {\small\input{Chapters/chapter7/figures/PararealSpeedupGTX590.tikz}}
+       % {\small\input{Chapters/chapter7/figures/PararealSpeedupGTX590.tikz}}
+ \includegraphics[width=0.5\textwidth]{Chapters/chapter7/figures/PararealSpeedupGTX590_conv.pdf}

     }
     \end{center}
     \caption{(a) Parareal absolute timings for an increasingly number of water waves traveling one wave length, each wave resolution is ($33\times 9$). (b) Parareal speedup for two to sixteen compute nodes compared to the purely sequential single GPU solver. Notice how insensitive the parareal scheme is to the size of the problem solved. Test environment 2.}\label{ch7:fig:DDPA_SPEEDUP}
     }
     \end{center}
     \caption{(a) Parareal absolute timings for an increasingly number of water waves traveling one wave length, each wave resolution is ($33\times 9$). (b) Parareal speedup for two to sixteen compute nodes compared to the purely sequential single GPU solver. Notice how insensitive the parareal scheme is to the size of the problem solved. Test environment 2.}\label{ch7:fig:DDPA_SPEEDUP}


@@ -894,10 +898,10 @@ The modified numerical model can still be based on flexible-order finite differe
 \begin{figure}[!htb]
 \begin{center}
 \subfigure[Hydrodynamic force calculations.]{
 \begin{figure}[!htb]
 \begin{center}
 \subfigure[Hydrodynamic force calculations.]{

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/figSeries60CB06Type7Resistance.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/figSeries60CB06Type7Resistance-eps-converted-to.pdf}

 }
 \subfigure[Kelvin pattern.]{
 }
 \subfigure[Kelvin pattern.]{

-\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/figSeries60CB06Type7kelvin.eps}
+\includegraphics[width=0.45\textwidth]{Chapters/chapter7/figures/figSeries60CB06Type7kelvin-eps-converted-to.pdf}

 }
 \end{center}
 \caption{Computed results. Comparison with experiments for hydrodynamics force calculations confirming engineering accuracy for low Froudes numbers.}
 }
 \end{center}
 \caption{Computed results. Comparison with experiments for hydrodynamics force calculations confirming engineering accuracy for low Froudes numbers.}