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partialModels.tex
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\section{List of Partial Models}
\label{sec:partialModels}
\begin{align}
&\begin{aligned}
t_{K|act|T} \sim\; &\mathrm{poly(I(1/nprocs), 3, raw=T) + poly(ndoms, 3, raw=T)}\\
&+ \mathrm{poly(nDOF, 3, raw=T)}\\
&+ \mathrm{I(1/nprocs):poly(nDOF, 2, raw=T)}
\end{aligned}\\[10pt]
&\begin{aligned}
t_{Dir|act} \sim\; &\mathrm{poly(I(1/nprocs), 3, raw=T) + poly(nDOF, 3, raw=T)}\\
&+ \mathrm{poly(ndoms, 3, raw=T)}
\end{aligned}\\[10pt]
&\begin{aligned}
t_{Lump_|act} \sim\; &\mathrm{poly(I(1/nprocs), 3, raw=T)}\\
&+ \mathrm{poly(ndoms, 3, raw=T) + poly(nDOF, 3, raw=T)}\\
&+ \mathrm{I(1/nprocs):nDOF}
\end{aligned}\\[10pt]
&\begin{aligned}
t_{Dir|asm} \sim\; &\mathrm{poly(I(1/nprocs), 2, raw=T) + poly(nDOF, 4, raw=T)}\\
&+ \mathrm{poly(ndoms, 3, raw=T)}
\end{aligned}\\[10pt]
&\begin{aligned}
t_{K|asm} \sim\; &\mathrm{poly(I(1/nprocs), 2 ,raw=T) + poly(nDOF, 3, raw=T)}\\
&+ \mathrm{poly(ndoms, 3, raw=T)}\\
&+ \mathrm{I(1/nprocs):poly(ndoms, 2, raw=T)}
\end{aligned}\\[10pt]
&\begin{aligned}
t_{F|asm} \sim\; &\mathrm{poly(I(1/nprocs), 3, raw=T)}\\
&+ \mathrm{poly(ndoms, 3, raw=T)}\\
&+ \mathrm{poly(nDOF, 3, raw=T)}
\end{aligned}\\[10pt]
&\begin{aligned}
t_{K|fact} \sim\; &\mathrm{poly(I(1/nprocs), 2) + poly(nDOF, 3)}\\
&+ \mathrm{poly(ndoms, 3) + I(1/nprocs):poly(nDOF, 3)}
\end{aligned}\\[10pt]
&\begin{aligned}
t_{GG^T|asm|HT} \sim\; &\mathrm{poly(I(1/nprocs), 3, raw=T)}\\
&+ \mathrm{poly(nnodes, 3, raw=T) + poly(nDOF, 3, raw=T)}\\
&+ \mathrm{poly(ndoms, 3, raw=T)}\\
&+ \mathrm{poly(I(1/nprocs), 2, raw=T):ndoms + ndoms:nDOF}\\
&+ \mathrm{I(1/nprocs\,\widehat{}\,2):nnodes}
\end{aligned}\\[10pt]
&\begin{aligned}
t_{GG^T|asm|T} \sim\; &\mathrm{poly(nnodes, 3, raw=T) + poly(ndoms, 2, raw=T)}\\
&+ \mathrm{poly(nDOF, 3, raw=T)}\\
&+ \mathrm{poly(I(1/nprocs), 3, raw=T)}\\
&+ \mathrm{poly(nnodes, 3, raw=T):poly(nDOF, 3, raw=T)}\\
&+ \mathrm{poly(nDOF, 3, raw=T):poly(I(1/nprocs), 3, raw=T)}\\
&+ \mathrm{poly(nnodes, 3, raw=T):poly(I(1/nprocs), 3, raw=T)}
\end{aligned}\\[10pt]
&\begin{aligned}
t_{GG^T\: 1|asm|T} \sim\; &\mathrm{nnodes + poly(I(log(2*nnodes)), 3, raw=T)}\\
&+ \mathrm{poly(ndoms, 2, raw=T)}\\
&+ \mathrm{poly(nDOF, 3, raw=T)}\\
&+ \mathrm{I(log(2*nnodes)\,\widehat{}\,3):poly(nDOF, 2, raw=T)}
\end{aligned}\\[10pt]
&\begin{aligned}
t_{GG^T\: 2|asm|T} \sim\; &\mathrm{poly(nnodes, 3, raw=T) + poly(ndoms, 2, raw=T)}\\
&+ \mathrm{poly(nDOF, 3, raw=T)}\\
&+ \mathrm{poly(nnodes, 2, raw=T):poly(nDOF, 2, raw=T)}
\end{aligned}\\[10pt]
&\begin{aligned}
t_{GG^T|act|HT} \sim\; &\mathrm{poly(nDOF, 3, raw=T)+ I(ndoms\,\widehat{}\,2)}\\
&+ \mathrm{(poly(I(1/nprocs), 2, raw=T)}\\
&+ \mathrm{poly(nnodes, 2, raw=T))\,\widehat{}\,2}\\
&+ \mathrm{I(1/nprocs):nDOF}\\
&+ \mathrm{(poly(nnodes, 2, raw=T) + ndoms)\,\widehat{}\,2}\\
&+ \mathrm{nnodes:nDOF + nDOF:ndoms}
\end{aligned}\\[10pt]
&\begin{aligned}
t_{GG^T|act|T} \sim\; &\mathrm{poly(nnodes, 3, raw=T) + poly(I(1/nprocs), 3, raw=T)}\\
&+ \mathrm{poly(ndoms, 3, raw=T) + poly(nDOF, 2, raw=T)}\\
&+ \mathrm{poly(nnodes, 3, raw=T):nDOF + nnodes:ndoms}
\end{aligned}\\[10pt]
&\begin{aligned}
t_{S_\alpha|asm} \sim\; &\mathrm{nDOF + poly(I(1/nprocs), 3, raw=T)}\\
&+ \mathrm{poly(ndoms, 2, raw=T)}\\
&+ \mathrm{poly(nDOF, 3, raw=T):poly(I(1/nprocs), 3, raw=T)}
\end{aligned}
\end{align}