Commit 79f8e95a by 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); ... ...
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment