115 lines
4 KiB
TeX
115 lines
4 KiB
TeX
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\documentclass[unicode,11pt,a4paper,oneside,numbers=endperiod,openany]{scrartcl}
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\usepackage{graphicx}
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\usepackage{subcaption}
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\usepackage{amsmath}
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\input{assignment.sty}
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\usepackage{pgfplots}
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\pgfplotsset{compat=newest}
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\usetikzlibrary{plotmarks}
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\usetikzlibrary{arrows.meta}
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\usepgfplotslibrary{patchplots}
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\usepackage{grffile}
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\usepackage{amsmath}
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\usepackage{subcaption}
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\hyphenation{PageRank}
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\hyphenation{PageRanks}
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\begin{document}
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\setassignment
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\setduedate{Wednesday, 4 November 2020, 11:55 PM}
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\serieheader{Numerical Computing}{2020}{Student: Claudio Maggioni}{Discussed with: --}{Solution for Project 3}{}
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\newline
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\assignmentpolicy
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Install METIS 5.0.2, and the corresponding Matlab mex interface}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Implement various graph partitioning algorithms \punkte{60}}
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I summarize the various benchmark results in table \ref{table:bisection}. Please note that this table
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can be generated at will with the script \texttt{ex2\_bisection\_table.m}.
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\section{Visualize the Fiedler eigenvector\punkte{10}}
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In figure \ref{fig:run1} there are graph outputs respectively from \textit{Grid9}, \textit{Small}, and \textit{Eppstein}.
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\begin{figure}[h]
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\begin{subfigure}{0.5\textwidth}
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\centering
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\includegraphics[trim=50 200 50 200,clip,width=\textwidth]{ex3_grid9.pdf}
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\caption{Plot for \textit{Grid9}}
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\end{subfigure}
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\begin{subfigure}{0.5\textwidth}
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\centering
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\includegraphics[trim=50 200 50 200,clip,width=\textwidth]{ex3_small.pdf}
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\caption{Plot for \textit{Small}}
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\end{subfigure}
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\begin{subfigure}{0.5\textwidth}
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\includegraphics[trim=50 200 50 200,clip,width=\textwidth]{ex3_eppstein.pdf}
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\caption{Plot for \textit{Eppstein}}
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\end{subfigure}
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\caption{Graph outputs for the 3 adjacency matrices.}
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\label{fig:run1}
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\end{figure}
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\section{Recursively bisecting meshes \punkte{20}}
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Summarize your results in table \ref{table:Rec_bisection}.
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\section{Compare recursive bisection to direct $k$-way partitioning\punkte{10}}
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Summarize your results in table \ref{table:Compare_Metis}.
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\begin{table}[h]
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\caption{Bisection results}
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\centering
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\begin{tabular}{|l|r|r|r|r|} \hline\hline
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Mesh & Coordinate & Metis 5.0.2 & Spectral & Inertial \\ \hline
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grid5rect(10,100)& 10 & 10 & 10 & 10 \\
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grid5rect(100,10)& 10 & 10 & 10 & 10 \\
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grid5recRotate(100,10,-45)& 18 & 10 & 10 & 10 \\
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gridt(40) & 58 & 58 & 58 & 58 \\
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grid9(30) & 88 & 92 & 104 & 88 \\
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Smallmesh & 25 & 13 & 12 & 30 \\
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Tapir & 55 & 34 & 18 & 49 \\
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Eppstein & 42 & 48 & 45 & 45 \\ \hline \hline
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\end{tabular}
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\label{table:bisection}
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\end{table}
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\begin{table}[h]
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\caption{Edge-cut results for recursive bi-partitioning.}
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\centering
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\begin{tabular}{|l|r|r|r|r|r|} \hline\hline
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Case & Spectral & Metis 5.0.2 & Coordinate & Inertial \\ \hline
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mesh3e1 & & & & \\
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airfoil1 & & & & \\
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3elt & & & & \\
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barth4 & & & & \\
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crack & & & & \\ \hline \hline
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\end{tabular}
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\label{table:Rec_bisection}
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\end{table}
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\begin{table}[h]
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\caption{Comparing the number of cut edges for recursive bisection and direct multiway partitioning in Metis 5.0.2.}
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\centering
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\begin{tabular}{|l|r|r|r|r|} \hline\hline
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Partitions & crack & airfoil1 \\ \hline
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16 & & \\
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32 & & \\ \hline \hline
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\end{tabular}
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\label{table:Compare_Metis}
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\end{table}
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\end{document}
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