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Commit e07a1ae8 authored by sfritschi's avatar sfritschi
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Updated thesis

parent 9524b285
This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019/Debian) (preloaded format=pdflatex 2021.4.27) 28 NOV 2021 11:32
This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019/Debian) (preloaded format=pdflatex 2021.4.27) 29 NOV 2021 23:00
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Output written on thesis.pdf (7 pages, 221300 bytes).
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\begin{equation}
j^* = \argmin_{j \in \mathcal{N}(i)}\Bigr| ||\mathbf{p}_i - \mathbf{p}_j||_2 - L_t \Bigr|
\end{equation}
Where $\mathcal{N}(i)$ is the set of all pores in adjacent cells to pore $i$. Finding $j^*$ for different pores is \emph{embarrassingly parallel} and can therefore be computed by a large number of threads, storing their results in shared memory. Each thread works on an even chunk of the pores located \emph{inside} the domain. Subsequently, these ideal matches are connected, while avoiding \textbf{conflicts} between different pores seeking the same neighbor. Finally we repeat the two steps from above, now only considering pores that still have throats left in \emph{random} order (for improved \textbf{load balancing}), until only a specified \textbf{fraction of total feasible throats} are left e.g. $1\%$. Empirically, this process converges very fast and consistently, for different target sizes of the full domain, after merely 3-4 iterations. The first iteration alone achieves $\approx 70\%$ of all possible throats, see Table ~\ref{table:iter}. The procedure is summarized as pseudo-code in Algorithm ~\ref{alg:connect}.
Where $\mathcal{N}(i)$ is the set of all pores in adjacent cells to pore $i$. Finding $j^*$ for different pores is \emph{embarrassingly parallel} and can therefore be computed by a large number of threads, storing their results in shared memory. Each thread works on an even chunk of the pores located \emph{inside} the domain. Subsequently, these ideal matches are connected, while avoiding \textbf{conflicts} of pores seeking a neighbor that is already fully-connected. Finally we repeat the two steps from above, now only considering pores that still have throats left in \emph{random} order (for improved \textbf{load balancing}), until only a specified \textbf{fraction of total feasible throats} are left e.g. $1\%$. Empirically, this process converges very fast and consistently, for different target sizes of the full domain, after merely 3-4 iterations. The first iteration alone leaves only $\approx 18\%$ of all possible throats left, see Table ~\ref{table:iter}. The procedure is summarized as pseudo-code in Algorithm ~\ref{alg:connect}.
\end{multicols}
\begin{table}[h]
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