Commit 79f8e95a authored by Dennis Gläser's avatar Dennis Gläser

[doc][handbook] each matrix entry is related to control volume

parent 42a4f9a8
......@@ -50,8 +50,8 @@ direction of maximum growth $\textbf{x}^i$ until our approximated solution becom
\subsection{Structure of matrix and vectors}
To understand the meaning of an entry in the matrix or the vector of the linear system, we have
to define their structure. Both have a blocking structure. Each block contains the degrees of
freedom (also called variable or unknown) for a sub-control volume. The equation index is used
to order of the degrees of freedom. For each sub-control volume we have one block. The mapper is
freedom (also called variable or unknown) for a control volume. The equation index is used
to order of the degrees of freedom. For each control volume we have one block. The mapper is
used to order the blocks.
\begin{figure}[htbp]
......@@ -59,23 +59,23 @@ used to order the blocks.
\begin{tikzpicture}[fill=dumuxBlue]
%% blocking structure
% matrix
\node at (0.3,4.2){\footnotesize 1. SCV};
\node at (1.7,4.2){\footnotesize 2. SCV};
\node at (3.5,4.2){\footnotesize $n$. SCV};
\node at (0.3,4.2){\footnotesize 1. CV};
\node at (1.7,4.2){\footnotesize 2. CV};
\node at (3.5,4.2){\footnotesize $n$. CV};
\draw (0,0) rectangle (4,4);
\fill (0.1,3.1) rectangle (0.9,3.9);
\fill (1.1,3.1) rectangle (1.9,3.9);
\node at (2.5,3.5) {$\dots$};
\fill (3.1,3.1) rectangle (3.9,3.9);
\node at (4,3.5) [right]{\footnotesize 1. SCV};
\node at (4,3.5) [right]{\footnotesize 1. CV};
\fill (0.1,2.1) rectangle (0.9,2.9);
\fill (1.1,2.1) rectangle (1.9,2.9);
\node at (2.5,2.5) {$\dots$};
\fill (3.1,2.1) rectangle (3.9,2.9);
\node at (4,2.5) [right]{\footnotesize 2. SCV};
\node at (4,2.5) [right]{\footnotesize 2. CV};
\node at (0.5,1.5) {$\vdots$};
\node at (1.5,1.5) {$\vdots$};
......@@ -86,7 +86,7 @@ used to order the blocks.
\fill (1.1,0.1) rectangle (1.9,0.9);
\node at (2.5,0.5) {$\dots$};
\fill (3.1,0.1) rectangle (3.9,0.9);
\node at (4,0.5) [right]{\footnotesize $n$. SCV};
\node at (4,0.5) [right]{\footnotesize $n$. CV};
% vector
\draw (5.5,0) rectangle (5.9,4);
......@@ -94,19 +94,19 @@ used to order the blocks.
\fill (5.6,2.1) rectangle (5.8,2.9);
\node at (5.7,1.5) {$\vdots$};
\fill (5.6,0.1) rectangle (5.8,0.9);
%% intra-block structure
\fill (8.1,2.1) rectangle (8.9,2.9);
\draw (9,2.8) -- (9.6,3.4);
\draw (9,2.6) -- (9.6,2.8);
\draw (9,2.2) -- (9.3,1.6);
\node at (10,4) {${eqIdx}$};
\node at (10,3.4) {$0$};
\node at (10,2.8) {$1$};
\node at (10,2.2) {$\vdots$};
\node at (10,1.6) {$m-1$};
\fill (11.1,2.1) rectangle (11.3,2.9);
\draw (11,2.8) -- (10.4,3.4);
\draw (11,2.6) -- (10.4,2.8);
......
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