diff --git a/doc/Description.pdf b/doc/Description.pdf index 0fb262b..7f85984 100644 Binary files a/doc/Description.pdf and b/doc/Description.pdf differ diff --git a/doc/Description.tex b/doc/Description.tex index a888b7d..03f567c 100644 --- a/doc/Description.tex +++ b/doc/Description.tex @@ -43,13 +43,13 @@ At a glance: \centering \begin{tabular}{|c|c|} \hline - Grid & 200x200 \\ \hline - Size & 1x1~m$^2$ \\ \hline - Timestep & 1000~s \\ \hline - Iterations & 50 \\ \hline - $\alpha_x, \alpha_y$ & heter., aniso. \\\hline - Species \# & 7 \\ \hline - Init & homog. \\ \hline + Grid & 200x200 \\ \hline + Size & 1x1~m$^2$ \\ \hline + Timestep & 1000~s \\ \hline + Iterations & 50 \\ \hline + $\alpha_x, \alpha_y$ & heter., aniso. \\\hline + Species \# & 7 \\ \hline + Init & homog. \\ \hline \end{tabular} \caption{Summary of parameters for the barite\_200 benchmark} \label{tab:b200} @@ -68,9 +68,9 @@ value of 0.1 molal \chem{BaCl_2}. All other boundaries are closed. \begin{table*}[!h] \centering \begin{tabular}{|r|r|r|r|r|r|r|r|}\hline - & H & O & Charge & Ba & Cl & S\_6\_ & Sr \\\hline - \textbf{IC} & 110.0124 & 55.5086 & -1.2163e-09 & 4.4553e-07 & 2.0e-12 & 6.1516e-5 & 6.1472e-5 \\\hline - \textbf{BC} & 111.0124 & 55.5062 & -3.3370e-08 & 0.1 & 0.2 & 0 & 0 \\\hline + & H & O & Charge & Ba & Cl & S\_6\_ & Sr \\\hline + \textbf{IC} & 110.0124 & 55.5086 & -1.2163e-09 & 4.4553e-07 & 2.0e-12 & 6.1516e-5 & 6.1472e-5 \\\hline + \textbf{BC} & 111.0124 & 55.5062 & -3.3370e-08 & 0.1 & 0.2 & 0 & 0 \\\hline \end{tabular} \caption{Initial and boundary values of all transported variables in the \texttt{barite\_200} benchmark.} @@ -87,8 +87,8 @@ for $\alpha_x$ and $\alpha_y$ respectively: \begin{equation*} \begin{cases} - \displaystyle \alpha_x & \displaystyle = 10^{-7} + 10^{-6} \frac{\mathcal{F}-\min{(\mathcal{F})}}{\max{(\mathcal{F})}}\\ - \alpha_y & \displaystyle = 10^{-7} + 10^{-7} \frac{\mathcal{F}-\min{(\mathcal{F})}}{\max{(\mathcal{F})}} + \displaystyle \alpha_x & \displaystyle = 10^{-7} + 10^{-6} \frac{\mathcal{F}-\min{(\mathcal{F})}}{\max{(\mathcal{F})}} \\ + \alpha_y & \displaystyle = 10^{-7} + 10^{-7} \frac{\mathcal{F}-\min{(\mathcal{F})}}{\max{(\mathcal{F})}} \end{cases} \end{equation*} @@ -111,7 +111,7 @@ benchmark. \end{figure} -This benchmarks runs in $\sim$11~s on 8 CPUs on my desktop. +This benchmarks runs in $\sim$ 1.8~s on 18 CPUs on a System @ PERFACCT. \clearpage @@ -128,13 +128,13 @@ At a glance: \centering \begin{tabular}{|c|c|} \hline - Grid & 1000x1000 \\ \hline - Size & 10x10~m \\ \hline - Timestep & 100~s \\ \hline - Iterations & 50 \\ \hline + Grid & 1000x1000 \\ \hline + Size & 10x10~m \\ \hline + Timestep & 100~s \\ \hline + Iterations & 50 \\ \hline $\alpha$ & homog. 1E-6 \\\hline - Species \# & 7 \\ \hline - Init & heter. \\ \hline + Species \# & 7 \\ \hline + Init & heter. \\ \hline \end{tabular} \caption{Summary of parameters for the \texttt{barite\_large} benchmark} \label{tab:blarge} @@ -181,7 +181,7 @@ record. The non-rounded values are read from file \texttt{barite\_200} benchmark\label{fig:blarge}} \end{figure} -This benchmark runs in $\sim$30~s on my desktop using 8 CPUs. +This benchmark runs in $\sim$6.4~s on my desktop using 18 CPUs. \clearpage @@ -197,7 +197,7 @@ glance: \centering \begin{tabular}{|c|c|} \hline - Grid & 200x100 \\ \hline + Grid & 200x100 \\ \hline Size & 0.02x0.01~m \\ \hline Timestep & 3600~s (1~h) \\ \hline Iterations & 20 \\ \hline @@ -216,28 +216,28 @@ boundaries are set to constant \textbf{BC} values. \textbf{Initial \begin{table*}[!h] \centering \begin{tabular}{|l|r|r|}\hline - & \textbf{IC} & \textbf{BC} \\ \hline - H & 1.11e+02 & 120.0 \\ \hline - O & 5.55e+01 & 55.1 \\ \hline - Charge & -2.0e-13 & 8.0e-17 \\ \hline - C & 2.0e-16 & 2.0e-15 \\ \hline - CH4 & 2.0e-03 & 0.2 \\ \hline - Ca & 2.0e-01 & 0.03 \\ \hline - Cl & 3.0e-01 & 0.5 \\ \hline - Fe2 & 1.4e-04 & 0.0002 \\ \hline - Fe3 & 1.3e-09 & 2.0e-08 \\ \hline - H0 & 6.0e-12 & 2.0e-11 \\ \hline - K & 2.0e-03 & 1.0e-05 \\ \hline - Mg & 1.0e-02 & 0.2 \\ \hline - Na & 2.0e-01 & 0.3 \\ \hline - HS2 & 5.9e-10 & 0 \\ \hline - S2 & 8.3e-15 & 8.3e-12 \\ \hline - S4 & 2.1e-14 & 5.1e-14 \\ \hline - S6 & 1.6e-02 & 0.026 \\ \hline - Sr & 4.5e-04 & 0.045 \\ \hline - U4 & 2.5e-09 & 2.5e-08 \\ \hline - U5 & 1.6e-10 & 1.6e-10 \\ \hline - U6 & 2.3e-07 & 1.0e-05 \\ \hline + & \textbf{IC} & \textbf{BC} \\ \hline + H & 1.11e+02 & 120.0 \\ \hline + O & 5.55e+01 & 55.1 \\ \hline + Charge & -2.0e-13 & 8.0e-17 \\ \hline + C & 2.0e-16 & 2.0e-15 \\ \hline + CH4 & 2.0e-03 & 0.2 \\ \hline + Ca & 2.0e-01 & 0.03 \\ \hline + Cl & 3.0e-01 & 0.5 \\ \hline + Fe2 & 1.4e-04 & 0.0002 \\ \hline + Fe3 & 1.3e-09 & 2.0e-08 \\ \hline + H0 & 6.0e-12 & 2.0e-11 \\ \hline + K & 2.0e-03 & 1.0e-05 \\ \hline + Mg & 1.0e-02 & 0.2 \\ \hline + Na & 2.0e-01 & 0.3 \\ \hline + HS2 & 5.9e-10 & 0 \\ \hline + S2 & 8.3e-15 & 8.3e-12 \\ \hline + S4 & 2.1e-14 & 5.1e-14 \\ \hline + S6 & 1.6e-02 & 0.026 \\ \hline + Sr & 4.5e-04 & 0.045 \\ \hline + U4 & 2.5e-09 & 2.5e-08 \\ \hline + U5 & 1.6e-10 & 1.6e-10 \\ \hline + U6 & 2.3e-07 & 1.0e-05 \\ \hline \end{tabular} \caption{\texttt{surfex} benchmark, homogeneous initial conditions \textbf{IC} and boundary values \textbf{BC}} @@ -260,7 +260,7 @@ boundaries are set to constant \textbf{BC} values. \textbf{Initial benchmark\label{fig:bsurf}} \end{figure} -This benchmark runs in $\sim$7~s on my desktop using 8 CPUs. +This benchmark runs in $\sim$1.1~s on my desktop using 18 CPUs. \clearpage @@ -314,7 +314,7 @@ equivalent): \begin{equation} \label{eq:GMAQ} \text{Geometric Mean of Absolute Quotients} = \left(\prod - \left|\frac{\hat{y}_{i}}{y_i}\right|\right)^{\frac {1}{N}} + \left|\frac{\hat{y}_{i}}{y_i}\right|\right)^{\frac {1}{N}} \end{equation} The geometric mean of the quotients would be 1 if the two variables @@ -325,7 +325,7 @@ of the terms: \begin{equation} \label{eq:5} \exp \left[{\frac {1}{N}}\sum\log a_{i}\right]= \left(\prod - a_{i}\right)^{\frac {1}{N}} + a_{i}\right)^{\frac {1}{N}} \end{equation} So the \chem{MAE_{log}} is the logarithm of the actual geometric mean @@ -337,9 +337,9 @@ error $\alpha_i$ as: \label{eq:relalpha} \alpha_i = \begin{cases} - \displaystyle \frac{ y_i-\hat{y_i}}{y_i} & \text{if~} \hspace{0.1cm} y_i,\hat{y}_i \neq 0 \\ - 1 & \text{if~} \hspace{0.1cm} y_i=0 \text{\hspace{0.1cm} and \hspace{0.1cm}} \hat{y}_i \neq 0 \\ - 0 & \text{if~} \hspace{0.1cm} y_i=0 \text{\hspace{0.1cm} and \hspace{0.1cm}} \hat{y}_i = 0 \\ + \displaystyle \frac{ y_i-\hat{y_i}}{y_i} & \text{if~} \hspace{0.1cm} y_i,\hat{y}_i \neq 0 \\ + 1 & \text{if~} \hspace{0.1cm} y_i=0 \text{\hspace{0.1cm} and \hspace{0.1cm}} \hat{y}_i \neq 0 \\ + 0 & \text{if~} \hspace{0.1cm} y_i=0 \text{\hspace{0.1cm} and \hspace{0.1cm}} \hat{y}_i = 0 \\ \end{cases} \end{equation} @@ -351,12 +351,12 @@ Absolute Percentage Error (\textbf{MAPE}) and Relative RMSE \begin{equation} \label{eq:MAPE} - \text{MAPE} = \frac{100\%}{N}\sum \left| \alpha_i \right| + \text{MAPE} = \frac{100\%}{N}\sum \left| \alpha_i \right| \end{equation} \begin{equation} \label{eq:RRMSE} - \text{RRMSE} = \sqrt{\frac{1}{N}\sum \left( \alpha_i\right)^2} + \text{RRMSE} = \sqrt{\frac{1}{N}\sum \left( \alpha_i\right)^2} \end{equation} These relative measures account for discrepancies across all