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% XLiFE++ is an extended library of finite elements written in C++
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When the {\bf structured mesh generator} is chosen (mg = {\tt\_structured}), one can create a mesh of order~1:
\begin{itemize}
\item of a segment,
\item of a parallelogram with triangles or quadrangles,
\item of a parallelepiped with hexahedra, prisms or pyramids.
\end{itemize}
One has to declare an object of type {\class Geometry}, more precisely of one of its derived type {\class Segment}, {\class Parallelogram}, {\class Rectangle}, {\class Square}, {\class Parallelepiped}, {\class Cuboid} or {\class Cube} using one of these constructors, that allow in particular to specifiy the mesh refinement by setting the number of points (nodes) on each edge, including the two endpoints.

\medskip

Example 1.

\begin{lstlisting}
Strings sn(2);
sn[0] = "Sigma_1";
Mesh mesh1dP1(Segment(_xmin=0, _xmax=1, _nnodes=11, _side_names=sn), 1, _structured, "P1 mesh of [0,1], step=0.1");
\end{lstlisting}
This builds a mesh of the interval $[0,1]$ with 10 subintervals. The boundary domain Sigma\_1, corresponding to the lower bound $0$ of the interval, will be created ; the other one will not be created since it has no name. The second argument is the mesh order ; in the case of a structured mesh, the only possible value is 1.
\par
It can be noticed that the segment may have been defined by two points in the plane or in the space as well.

\medskip

Example 2.

\begin{lstlisting}
Strings sn(4);
sn[0] = "Gamma_1"; sn[2] = "Gamma_2";
Mesh mesh2dP1(Rectangle(_xmin=0, _xmax=1, _ymin=1, _ymax=3, _nnodes=Numbers(3, 5), _side_names=sn), _triangle, 1, _structured, "P1 mesh of [0,1]x[1,3]");
\end{lstlisting}
This builds a mesh of the rectangle $[0,1]\times[1,3]$ with triangles. The interval $[0,1]$ is subdivided into 2 subintervals; the interval $[1,3]$ is subdivided into 4 subintervals. Only the two domains Gamma\_1 and Gamma\_2 will be created.
For a rectangle $[a,b]\times[c,d]$, the correspondence of the sidenames is the following:\par
sideNames[0] is $[a,b]\times{c}$, sideNames[1] is ${b}\times[c,d]$,\par
sideNames[2] is $[a,b]\times{d}$, sideNames[3] is ${a}\times[c,d]$.

\medskip

Example 3.

\begin{lstlisting}
Strings sn(4);
sn[0] = "Sigma_1"; sn[1] = "Sigma_2";
Mesh mesh2dQ1(Rectangle(_xmin=1, _xmax=2, _ymin=1, _ymax=3, _nnodes=Numbers(3, 5), _side_names=sn), _quadrangle, 1, _structured, "Q1 mesh of [1,2]x[1,3]");
\end{lstlisting}
This builds a mesh of the rectangle $[1,2]\times[1,3]$ with quadrangles. Only the two domains Sigma\_1 and Sigma\_2 will be created.
See example 2 for other commentaries.

\medskip

Example 4.

\begin{lstlisting}
Strings sn( "z=1", "z=5", "y=1", "y=3", "x=0", "x=1");
Mesh mesh3dQ1(Cuboid(_xmin=0, _xmax=1, _ymin=1, _ymax=3, _zmin=1, _zmax=5, _nnodes=Numbers(3, 5, 9), _side_names=sn), _hexahedron, 1, _structured, "Q1 mesh of [0,1]x[1,3]x[1,5]");
\end{lstlisting}
This builds a mesh of the parallelepiped $[0,1]\times[1,3]\times[1,5]$ with hexahedra. The interval $[0,1]$ is subdivided into 2 subintervals ; the interval $[1,3]$ is subdivided into 4 subintervals ; the interval $[1,5]$ is subdivided into 8 subintervals. The 6 boundary domains will be created with their corresponding names.
For a parallelepiped $[a,b]\times[c,d]\times[e,f]$, the correspondence of the sidenames is the following:\par
  sideNames[0] is $[a,b]\times[c,d]\times{e}$, sideNames[1] is $[a,b]\times[c,d]\times{f}$,\par
  sideNames[2] is $[a,b]\times{c}\times[e,f]$, sideNames[3] is $[a,b]\times{d}\times[e,f]$,\par
  sideNames[4] is ${a}\times[c,d]\times[e,f]$, sideNames[5] is ${b}\times[c,d]\times[e,f]$.