diff --git a/doc/ng4.tex b/doc/ng4.tex new file mode 100644 index 00000000..d03926b3 --- /dev/null +++ b/doc/ng4.tex @@ -0,0 +1,1029 @@ +\documentclass[12pt]{book} +\usepackage{a4, epsf, graphicx} +\usepackage{html} + +\title{NETGEN - 4.X} +\author{Joachim Sch\"oberl} + + + +\unitlength=1cm + +\begin{document} +\maketitle +\tableofcontents + +\chapter{Getting Started} + + +WARNING: DOCUMENTATION IS NOT UP TO DATE + + +\section{What is NETGEN} +NETGEN is an automatic mesh generation tool for two and three +dimensions. Netgen is open source under the conditions of the LGPL. +It comes as stand alone programme with graphical user +interface, or as C++ library to be linked into an other application. +Netgen is available for Unix/Linux and Windows 98/NT. Netgen +generates triangular or quadrilateral meshes in 2D, and tetrahedral +meshes in 3D. The input for 2D is described by spline curves, and the +input for 3D problems is either defined by constructive solid +geometries (CSG), see Chapter \ref{chap_csg}, or by the standard STL +file format. NETGEN contains modules for mesh optimization and +hierarchical mesh refinement. Curved elements are supported of arbitrary +order. + + +\section{The history of NETGEN} +% +The NETGEN project was started 1994 in the master's programme of +Joachim Sch\"oberl, under supervision of Prof. Ulrich Langer, at the +Department of Computational Mathematics and Optimization, University +Linz, Austria. Its further development was supported by the Austrian +science Fund ``Fonds zur F\"orderung der wissenschaftlichen +Forschung'' (http://www.fwf.ac.at) under projects P 10643-TEC and SFB +1306. Starting from 2002, the development continued within the Start +project ``hp-FEM'' (http://www.hpfem.jku.at) granted by the FWF. In +2006, the Netgen development moved together with J.~Sch\"oberl to RWTH +Aachen Universtiy, Germany (http://www.mathcces.rwth-aachen.de/netgen). + + +\section{How to receive NETGEN} +% +The latest NETGEN source code release is available from sourceforge +\begin{center} +http://sourceforge.net/projects/netgen-mesher +\end{center} + +There are file releases, as well as a public SVN repository containing +the latest sources. + +The latest NETGEN Windows executable is available from +\begin{center} +http://www.mathcces.rwth-aachen.de/netgen +\end{center} + +\section{Installing NETGEN} + +THIS SECTION NEEDS UPDATE + +INFORMATION AVAILABLE AT http://netgen-mesher.wiki.sourceforge.net/ + +\subsection{Installing NETGEN for Unix/Linux} + +To install NETGEN on Unix/Linux you will download the source code and +compile it yourself. You need the following libraries: + +\begin{itemize} +\item +The 3D visualization library {\bf OpenGL}. +It comes with most systems with hardware graphics. The free +software version mesagl is available from +\htmladdnormallink{http://www.mesa3d.org}{http://www.mesa3d.org/}. +\item +The graphical toolkit {\bf TclTk} developed by John Ousterhout +(available from \htmladdnormallink{http://www.scriptics.com/}{http://www.scriptics.com/}) and its extension {\bf Tix} available from \htmladdnormallink{http://www.sourceforge.com}{http://www.sourceforge.com/}) by Iam Lan. +Netgen has been tested with version TclTk 8.0 - TclTk 8.4 and Tix 4.6. - Tix 8.2 +\end{itemize} +You can also download these packages from the Netgen site. + + +To install NETGEN please move into the directory ng4. +You set the Unix-variable MACHINE according to +your machine/operating system, e.g. +\begin{quote} +\tt +setenv MACHINE LINUX +\end{quote} +% +(in bash shell you type {\tt export MACHINE=LINUX}). +The Makefile includes the makefile-include +\begin{quote} +\tt + libsrc/makefile.mach.\$(MACHINE) +%$ +\end{quote} +Please create/modify the according file, +(e.g. copy makefile.mach.LINUX to makefile.mach.SUN). Then you enter +{\bf \tt make} to build the executable. + +\medskip + +To make NETGEN globally available you just copy the binary ``ng'' +to the global bin - directory. In difference to earlier versions, +it needs no additional files. + +\subsection{Installing NETGEN for Windows} + +NETGEN is available now for Windows in binary form. You download +the zip - archive {\tt ng4win.zip}. After unpacking it with winzip, +you can start the executable ``ng4.exe''. + +\subsection{Adding IGES/STEP file support via OpenCascade} +\label{subsec_occ} + +NETGEN is capable of importing IGES and STEP geometry files. If you want to use this functionality you have the add the OpenCascade library to your NETGEN distribution. + +OpenCascade is an open source 3D solid modeller library by OpenCASCADE S.A. You can obtain it from \htmladdnormallink{http://www.opencascade.org}{http://www.opencascade.org/} (Linux and Windows). + +To compile NETGEN with OpenCascade for Windows just choose the project settings ``Release (OCC)'' and adjust the proper search paths. + +For Linux adjust the directory search paths OCC\_DIR, OCCINC\_DIR and OCCLIB\_DIR in the Makefile and in libsrc/makefile.inc. Then add -DOCCGEOMETRY to the CPLUSPLUSFLAGS2 in libsrc/makefile.mach.\$(MACHINE). If you use OpenCascade version 5.2 also add -DOCC52 and -DHAVE\_IOSTREAM to the CPLUSPLUSFLAGS2. + +\subsection{Testing Netgen} +Please start Netgen by entering ``ng'' or clicking the ``ng.exe'' icon. + +A white window with menu items should appear. Please load a geometry +file by selecting "File {\tt ->} Load Geometry", choose e.g. +tutorials/cube.geo. Then press the button "Generate Mesh". By keeping +pressed the left, middle or right button of your mouse you can rotate, +move or zoom the object. With ``File {\tt->} Export Mesh'' you can +save the mesh file. + + +\chapter{Constructive Solid Geometry (CSG)} +\label{chap_csg} +% +The CSG input format is a useful geometry format for small and +medium size geometries. One defines the geometry by writing an +ASCII file in a text editor. + +The geometry is defined by the Eulerian operations (union, +intersection and complement) from primitives. A complete list of +availabe primitives is given in Section~\ref{sec_primitives}. + +The following input describes a cube: +\begin{quote} +\begin{verbatim} +# A cube +algebraic3d +solid cube = orthobrick (0, 0, 0; 1, 1, 1); +tlo cube; +\end{verbatim} +\end{quote} +Lines starting with $\#$ are comment lines. Every CSG file must contain the +keyword {\tt algebraic3d} before any non-comment line. +The keyword {\tt solid} defines a named solid, here the solid {\it cube} +is defined. A solid is defined by the Eulerian operations applied to +primitives. Here, the solid is just the primitve defined by {\tt orthobrick}. +This is a brick parallel to the axis, specified by the minimal $x$, $y$, and +$z$ coordinates, and the maximal $x$, $y$, and $z$ coordinates. The present +definition gives the cube $[0,1]^3$. Finally, the definition {\tt tlo cube} +declares the solid {\it cube} as a top-level-object, what is necessary for +meshing. + +Please start netgen with the geometry file above by entering +\begin{quote} +ng cube.geo +\end{quote} +Instead, you can also load the geometry from the file menu. You will +see a blue cube, which you can rotate by keeping the left mouse button +pressed. Pressing the big {\bf generate mesh} button will result in a +(very coarse) mesh of that cube. + +Instead of using the primitive {\tt orthobrick}, one can also specify +a cube by intersecting six halfspaces (called planes). Each primitive +{\tt plane} is given by an arbitrary point in the plane, and a outward +vector, not necessarily a unit vector. The six halfspaces are intersected +by the keyword {\tt and}. The following input gives an equivalent result: + +\begin{quote} +\begin{verbatim} +# A cube +algebraic3d +solid cube = plane (0, 0, 0; 0, 0, -1) + and plane (0, 0, 0; 0, -1, 0) + and plane (0, 0, 0; -1, 0, 0) + and plane (1, 1, 1; 0, 0, 1) + and plane (1, 1, 1; 0, 1, 0) + and plane (1, 1, 1; 1, 0, 0); +tlo cube; +\end{verbatim} +\end{quote} + +To drill a hole though the cube, we will intersect the cube +and the complement of a cylinder. A cylinder is defined by two points +on the central axis, and the radius. Please note, a cylinder is +understood as an infinitely long cylinder (although the visualization +may suggest a finite cylinder): +\begin{quote} +\begin{verbatim} +# cube with hole +algebraic3d +solid cubehole = orthobrick (0, 0, 0; 1, 1, 1) + and not cylinder (0.5, 0.5, 0; 0.5, 0.5, 1; 0.1); +tlo cubehole; +\end{verbatim} +\end{quote} + +Like {\tt and} denotes the intersection, {\tt or} denotes the union: +\begin{quote} +\begin{verbatim} +solid cubeball = orthobrick (0, 0, 0; 1, 1, 1) + or sphere (0, 0, 0; 0.5) -maxh = 0.2; +\end{verbatim} +\end{quote} +The flag {\tt -maxh=0.2} assignes the maximal mesh size of $0.2$ to +the solid. The current version, NG4.1, uses the mesh size assigned to +the main solid of the top-level-object for the domain. Future version +will contain more possibilities to define mesh-sizes for parts of a +domain. + +It is possible to define geometries with several sub-domains, simply +by declaring several tlos: +\begin{quote} +\begin{verbatim} +algebraic3d +solid cube = orthobrick (0, 0, 0; 1, 1, 1); +solid cyl = cylinder (0.5, 0.5, 0; 0.5, 0.5, 1; 0.1); +solid dom1 = cube and not cyl; +solid dom2 = cube and cyl; + +tlo dom1 -col=[0,0,1] -transparent; +tlo dom2 -col=[1,0,0]; +\end{verbatim} +\end{quote} +This example show also solid trees involving previously defined named +solids. Top-level-objects can be assigned a color specified by the +amount of red, green and blue (RGB) values. The flag {\tt + -transparent} makes the solid appear transparent. + + +It is possible to specify bounday condition numbers for individual +surfaces of a solid. The flag {\tt -bc} assignes the bc to all +surfaces of that solid-tree. If several flags are given the one closest +to the leaves of the tree dominates. The following file defines a +cube, with $bc=1$ at the bottom, $bc=2$ at the top, and $bc=3$ for +all other surfaces: + +\begin{quote} +\begin{verbatim} +algebraic3d + +solid bottom = plane (0, 0, 0; 0, 0, -1) -bc=1; +solid top = plane (1, 1, 1; 0, 0, 1) -bc=2; +solid cube = bottm and top + and plane (0, 0, 0; 0, -1, 0) + and plane (0, 0, 0; -1, 0, 0) + and plane (1, 1, 1; 0, 1, 0) + and plane (1, 1, 1; 1, 0, 0) -bc=3; + +tlo cube; +\end{verbatim} +\end{quote} + + + +\section{Curves} +For the construction of some of the primitives in the following section it is necessary to define 2D or +3D curves, which are given in terms of straight lines and of quadratic rational spline patches. A line is given +by the two endpoints, a spline patch by three d'Boor points. The patch is an elliptic arc from point 1 to point 3, +such that the lines 1--2 and 2--3 are tangents. + +A 2D curve is defined as +\begin{quote} +\samepage +\tt +\begin{tabbing} +aaa\=aaa\=aaa\=aaa\=aaa\=aaa\= \kill +curve2d $name$ = ($np$;\\ +\>\> $x_1$, $y_1$;\\ +\>\> \ldots\\ +\>\> $x_{np}$, $y_{np}$;\\ +\>\> $ns$;\\ +\>\> [ 2 | 3 ], $p_{1,1}$, $p_{1,2}$ [, $p_{1,3}$];\\ +\>\> \ldots\\ +\>\> [ 2 | 3 ], $p_{ns,1}$, $p_{ns,2}$ [, $p_{ns,3}$]); +\end{tabbing} +\end{quote} +The number of points is given by $np$, the number of segments by $ns$. Each point is +given by its coordinates, each segment by the number of points +(2 for line segments, 3 for spline patches) and the pointnumbers. + +The 3D curves are given analogously by +\begin{quote} +\samepage +\tt +\begin{tabbing} +aaa\=aaa\=aaa\=aaa\=aaa\=aaa\= \kill +curve3d $name$ = ($np$;\\ +\>\> $x_1$, $y_1$, $z_1$;\\ +\>\> \ldots\\ +\>\> $x_{np}$, $y_{np}$, $z_{np}$;\\ +\>\> $ns$;\\ +\>\> [ 2 | 3 ], $p_{1,1}$, $p_{1,2}$ [, $p_{1,3}$];\\ +\>\> \ldots\\ +\>\> [ 2 | 3 ], $p_{ns,1}$, $p_{ns,2}$ [, $p_{ns,3}$]); +\end{tabbing} +\end{quote} + + + +\section{Available Primitives} +\label{sec_primitives} +Netgen %4.1 +supports the following primitives: +\begin{enumerate} +\item A halfspace, i.e., a plane and everything on one side of it, + given by an arbitrary point~$p = (p_x, p_y, p_z)$ in the plane and + an outside normal vector~$n = (n_x, n_y, n_z)$, not necessarily a + unit vector: + \begin{quote} + \tt + plane ( $p_x$, $p_y$, $p_z$ ; $n_x$, $n_y$, $n_z$ ) + \end{quote} + +\item + A cylinder of infinite length, given by two points~$a=(a_x, a_y,a_z)$ + and $b=(b_x, b_y, b_z)$ on the central axis and the radius $r$: + \begin{quote} + \tt cylinder ( $a_x$, $a_y$, $a_z$ ; $b_x$, $b_y$, $b_z$ ; $r$ ) + \end{quote} + +\item + A sphere, given by the center~ $c=(c_x,c_y,c_z)$ and the radius~$r$: + \begin{quote} + \tt + sphere ( $c_x$, $c_y$, $c_z$ ; $r$ ) + \end{quote} + +\item + An elliptic cylinder, given by the point $c=(c_x, c_y, c_z)$ on the main axis, + and the vectors $v$ and $w$ of the long and short axis of the ellipse, respectively: + \begin{quote} + \tt + ellipticcylinder ($c_x$, $c_y$, $c_z$ ; $v_x$, $v_y$, $v_z$ ; $w_x$, $w_y$, $w_z$) + \end{quote} + +\item + An ellipsoid, given by the center $c=(c_x, c_y, c_z)$, + and the vectors $u$, $v$ and $w$ of the main axis of the ellipsoid: + \begin{quote} + \tt + ellipsoid ($c_x$, $c_y$, $c_z$ ; $u_x$, $u_y$, $u_z$; $v_x$, $v_y$, $v_z$ ; $w_x$, $w_y$, $w_z$) + \end{quote} + + +\item A cone is given by two points on the central axis and the two + corresponding radii. It is not possible to mesh the top of the cone + yet, it must be cut off. + \begin{quote} + \tt + cone ( $a_x$, $a_y$, $a_z$ ; $r_a$; $b_x$, $b_y$, $b_z$ ; $r_b$ ) + \end{quote} + +\item A orthobrick is a brick parallel to the coordinate axis. It is + specified by two opposite corner points $a = (a_x, a_y, a_z)$ and + $b = (b_x, b_y, b_z)$: + \begin{quote} + \tt + orthobrick ( $a_x$, $a_y$, $a_z$ ; $b_x$, $b_y$, $b_z$ ) + \end{quote} + +\item A polyhedron is defined by a set of triangles forming + a closed polyhedron. First, a set of points is defined, then + the triangles are given by point indices. The triangles must be + oriented counter-clockwise when looking onto the object. The + following polyhedron describes a tetrahedron: + \begin{quote} +\begin{verbatim} +algebraic3d +solid poly = polyhedron (0,0,0; 1,0,0; 0,1,0; 0,0,1 ;; + 1,3,2 ; 1,4,3; 1,2,4 ; 2,3,4 ); +tlo poly; +\end{verbatim} + \end{quote} + +\item A body of extrusion is defined by its profile +(which has to be a closed, \textit{clockwise} oriented 2D curve), by a path (a 3D curve) and a +vector $d$. It is constructed as follows. Take a point $p$ on the path and denote the (unit-) tangent of the path in this point by $t$. +If we cut the body by the plane given by $p$ and $t$ as normal vector, the cut is the profile. +The profile is oriented by the (local) y-direction $\bar{y} := d - (d \cdot t) t$ and the (local) x-direction $\bar{x} := t \times \bar{y}$. The +syntax is: +\begin{quote} + \tt + extrusion ( ; ; $d_x$, $d_y$, $d_z$ ) +\end{quote} +The following points have to be noticed: +\begin{itemize} +\item If the path is not closed, then also the body is NOT closed. In this case e.g.\ planes or orthobricks have to be used to construct +a closed body. +\item The path has to be smooth, i.e.\ the tangents at the end- resp.\ startpoint of two consecutive spline or line patches have +to have the same directions. +\end{itemize} + +\item A body of revolution is given by two points, defining the axis of revolution, and the 2D curve which is rotated: +\begin{quote} + \tt + revolution ( $p_{1,x}$, $p_{1,y}$, $p_{1,z}$; $p_{2,x}$, $p_{2,y}$, $p_{2,z}$; ) +\end{quote} +The first point defines the origin of the local 2D coordinate system of the curve. It is assumed, that the curve lies above the +(local) x-axis, and that it is described \textit{clockwise}. + +If the curve is not closed, then the start point and the end point have to lie on the x-axis, and the tangents at those points +have to be orthogonal to the x-axis. +\end{enumerate} + + +\section{Surface Identification} +In Netgen it is possible to construct prismatic meshes between two surfaces, where these surfaces +have to be specified explicitely in the .geo file with the command +\begin{quote} + \tt + identify closesurfaces ; +\end{quote} +(this feature originally was intented for close surface, which is the reason for the command name). +\paragraph{Optional parameters:} (selection) +\begin{itemize} +\item \texttt{-tlo=}\\ +the prisms are only constructed between two faces of a tlo. +\item \texttt{-direction=[,,]}\\ +This parameter has to be used if \textbf{skew prisms} should be built. In this case netgen ``needs help'' by the user, +it needs to know the direction of identification. + +\textit{Example:} We start with a cylinder with the axis given by the points $(-1,0,4)$ and $(4,10,1)$. This cylinder +is cut by the planes \texttt{p1} and \texttt{p2} (which are not necessarily normal to the axis and not necessarily parallel) +and we want to build prisms between +these planes. Then the command would, e.g., look like +\begin{quote} +\tt identify closesurfaces p1 p2 -direction=[5,10,-3] +\end{quote} +\end{itemize} + + + + + + + +\section{Known problems and work-arounds} +\subsection{Interfaces} +A airdomain with two connected interior parts may be described by +\begin{quote} +\begin{verbatim} +algebraic3d + +solid cube = orthobrick (0, 0, 0; 1, 1, 1); +solid part1 = orthobrick (0.2, 0.2, 0.2; 0.5, 0.8, 0.8); +solid part2 = orthobrick (0.5, 0.2, 0.2; 0.8, 0.8, 0.8); +solid air = cube and not part1 and not part2; + +tlo air; +tlo part1; +tlo part2; +\end{verbatim} +\end{quote} +The problem is, that a domain is an open domain. Thus, the domain +{\it air} is not only the outer part, but also the interface between +{\it part1} and {\it part2}. The result is unspecified. To fix this +problem, one can define the {\it air}-domain by cutting out one big +brick: +\begin{quote} +\begin{verbatim} +solid air = cube and not othrobrick (0.2, 0.2, 0.2; 0.8, 0.8, 0.8); +\end{verbatim} +\end{quote} + +\subsection{Degenerated edges} +Degenerated edges are found sometimes, but some still cause troubles. +A sphere on top of a cylinder my be described by: +\begin{quote} +\begin{verbatim} +solid cyl = cylinder (0, 0, 0; 1, 0, 0; 0.5) + and plane (0, 0, 0; -1, 0, 0) + and plane (1, 0, 0; 1, 0, 0); +solid main = cyl or sphere (1, 0, 0; 0.5); +tlo main; +\end{verbatim} +\end{quote} +The edge is a degenerated one. A work-around is to split the +domain (artificially) into two non-degenerated parts: +\begin{quote} +\begin{verbatim} +solid cyl = cylinder (0, 0, 0; 1, 0, 0; 0.5) + and plane (0, 0, 0; -1, 0, 0) + and plane (1, 0, 0; 1, 0, 0); +solid hemisphere = sphere (1, 0, 0; 0.5) and not plane (1, 0, 0; -1, 0, 0); +tlo cyl; +tlo hemisphere; +\end{verbatim} +\end{quote} + + + + + +\chapter{Other Geometry Formats} + +\section{Using IGES/STEP Geometries} +% +IGES and STEP are standard exchange formats for CAD files. Contrary to the STL format, IGES and STEP deliver an exact representation of the geometry and do not approximate it. In order to use IGES/STEP geometries you have to install NETGEN with the OpenCascade Geometry Kernel as described in \ref{subsec_occ}. Most solid modellers can export IGES or STEP files. However, often these files are not as exact as a mesher needs them to be. So is meshing fails, try repairing the model via {\bf IGES/STEP Topology Explorer/Doctor}. + +\section{Using STL Geometries} +% +STL is a standardized file format to describe (approximate) geometies +by triangulated surfaces. It is useful to describe complicated parts +which are modeled with some CAD programmes. Also, some users have written +their own (C) programmes to define STL geometries, where was not so easy +to use the CSG format. The syntac of STL files is as follos +\begin{quote} +(not available yet. please figure out the syntax from the examples) +\end{quote} + +We found that many STL geometries have some difficulties. Some of them +can be corrected (removed) by the {\bf STL - Doctor}. Please see the +corresponding manual pages (not available yet). + + +\section{2D Spline Geometry} +% +The extension for 2D spline geometry is ``.in2d''. + +The boundary is given in terms of straight lines and of quadratic rational +spline patches. +A line is given by the two endpoints, a spline patch by 3 d'Boor +points. The patch is an elliptic arc from point 1 to point 3, such that +the lines 1-2 and 2-3 are tangents. + +It is possible to use different subdomains with this format. + +This file format also supports a priori mesh grading. To the spline +point i one adds a local refinement factor {\tt rp}$_i$ . Close to +this point the mesh-size $h(x)$ is {\tt h}$_{Glob}$ / {\tt rp}$_i$ . +The global parameter {\tt grading} describes how fast the mesh-size decreases. +The gradient of the local mesh-size function $h(x)$ is bounded by +$| \nabla_x h(x)| \leq \mbox{grading}^{-1}$ +Also a refinement by a factor {\tt rs}$_i$ > 1 along the whole +segment i is possible. +The file looks like: +% +\begin{quote} +\samepage +\tt +splinecurves2d \\ +grading \\ +np \\ +x$_1$ y$_1$ rp$_1$ \\ +... \\ +x$_{np}$ y$_{np}$ rp$_{np}$ \\ +ns \\ +dil$_1$ dir$_1$ [ 2 | 3 ] pi$_{1,1}$ pi$_{1,2}$ [ pi$_{1,3}$ ] rs$_1$ \\ +... \\ +dil$_{nl}$ dir$_{nl}$ [ 2 | 3 ] pi$_{nl,1}$ pi$_{nl,2}$ [ pi$_{nl,3}$ ] rs$_{nl}$ \\ +\end{quote} +% +{\tt np} is the number of points, {\tt ns} the number of spline segments. +Every segment starts with the domain numbers at the left and at the +right sides of the segment. Domain number 0 is reserved for the exterior. +Then the number of points and two or three point indices follow. +Finally, the refinement factor along the line follows. + + +\chapter{Mesh and Solution Formats} + +You can export meshes to a couple of file formats. Some are self-defined, +some other are standard formats. The self-defined are the followings: + +\section{Mesh Size File} +By means of a mesh size file you can provide a local mesh size density. The file extension must be {\it .msz}. If you want to use the mesh size file, you specify it in the ``Meshing Options'', doalog box, page ``Mesh Size''. + +The syntay is: +\begin{verbatim} +np +x1 y1 z1 h1 +x2 y2 z2 h2 +.... +xnp ynp znp hnp +nl +xs1 ys1 zs1 xe1 ye1 ze1 h1 +xs2 ys2 zs2 xe2 ye2 ze2 h2 +.... +xsnl ysnl zsnl xenl yenl zenl hnl +\end{verbatim} +You specify {\tt np} points, given by the $(x_i,y_i,z_i)$-coordinates, +where the mesh size will be reduced at least to $h_i$. You specify +also {\tt nl} line-segments by the start-point and end-point +coordinates. The mesh-size along the whole line will be reduced to the given $h_i$. + +\section{Neutral Format} +The neutral volume mesh format contains the following sections: + +\begin{enumerate} +\item +nodes \\ +After the number of nodes there follows a list of $x$, $y$, +and $z$-coordinates of the mesh-nodes. +\item +volume elements \\ +After the number of volume elements there follows the list of tetrahedra. +Each element is specified by the sub-domain number, and 4 node indices. The +node indices start with 1. +\item +surface elements \\ +After the number of surface elements there follows +the list of triangles. Each element is specified by the boundary +condition number, and 3 node indices. The node indices start with 1. +\end{enumerate} + + + +\section{Fepp Format 2D} +The Fepp 2D format contains the following sections: + +\begin{enumerate} +\item +boundary segmetns \\ +After the number of boundary segments there follows a list of +segments. Each segment is specified by the spline - patch number, +and the two node indices. Counting starts with 1 +\item +domain elements \\ +After the number of domain elements there follows the list of elements. +Each element is specified by the sub-domain number, the number of nodes (3 or 4) and the node indices. Counting starts with 1 +\item +nodes \\ +After the number of nodes there follows a list of $x$ and $y$ +-coordinates of the mesh-nodes. +\item +geometric information \\ +After the number of spline patches there follows a list of spline specifications. Each spline patch is given by the 6 coefficients of the descibing +quadratic polynomial equation +$$ +c_1 x^2 + c_2 y^2 + c_3 xy + c_4 x + c_5 y + c_6 = 0 +$$ +\end{enumerate} + +\section{Surface triangulaton file} +One can export to and import from a surface mesh file. It´s structure +is as follows: +\begin{enumerate} +\item + {\tt surfacemesh} \\ + starts with that keyword +\item + number of points \\ + point coordinates $(x,y,z)$. +\item + number of surface triangles, \\ + surface triangles oriented counter-clock wise when looking at the + object, index starts from 1. +\end{enumerate} + + + +\section{Solution File Format} +The Netgen software includes also a simple visualizer for finite +element gridfunctions. It supports scalar fields (e.g. temperature), +and vector valued fields (flow velocities, mechanical deformations). +The solution field is imported by the menu item File $->$ Import Solution. +It is important to load the corresponding mesh in advance. + +The format of the solution file is as follows. It consists of an +arbitrary number of blocks of this structure: + +\begin{enumerate} +\item + {\tt solution} {\it function-name} flags + + {\tt solution} is the keyword, {\it function-name} is a string to + refer to that functions. The supported flags are + \begin{enumerate} + \item -size=s \\ + number of entries (default: number of mesh-points) + \item -components=c \\ + number of components (default: 1). Mechanical deformations have 3 components. + \item -type=[nodal,element,surfaceelement] \\ + the grid-funciton has nodal values, or one value per volume element, + or one value per surface element (default: nodal) + \end{enumerate} +\item + block of $size \times components$ values +\end{enumerate} + +Please try out to import the solution file 'tutorials/cube.sol' fitting +to the mesh 'tutorials/cube.vol'. + + +\chapter{Netgen operations} +You can use netgen in interactive mode using its menus, or, you +can run netgen in batch-mode using command line arguments. + +\section{Command line arguments} +Command line arguments are specified as {\it -flag=value}. +\begin{itemize} +\item -help \newline +Prints the availabel command line arguments +\item -geofile=filename \newline +Specifies geometry file. Is equivalent to {\it filename}, i.e., you can +scip {\it -geofile=}. +\item -meshfile=filename \newline +Mesh file will be stored in file {\it filename}. +\item -batchmode \newline +Exit after mesh generation. Otherwise, the GUI will be started +\item -V \newline +Verbose mode. Prints some additional information +\item -verycoarse, -coarse, -moderate, -fine, -veryfine \newline +Mesh size control +\end{itemize} + +\chapter{Using the Graphical User Interface} +The Netgen main window looks like: +\begin{center} +\includegraphics[width=12cm]{pictures/screenshot} +\end{center} +It consists of the menuline and the button line at the top, the status line at +the bottom, and the large drawing window. The menu items will be explained in +\ref{sec_menuitems}. The button line provides shot-cuts for common opteration: +\begin{itemize} +\item Quit \newline +Terminate Netgen +\item Generate mesh \newline +Performe mesh generation +\item Stop Meshing \newline +Stop mesh generation +\item Geometry/Edges/Mesh/Solution \newline +Switch between operation modes of visualization. +\item Zoom all \newline +Zooms such that the whole visualization scene fits into the window. +\item Center \newline +Center rotation and scaling at marked point, available only in mesh - visuailzation mode. +\item Rotate/Move/Zoom +Left mouse drag rotates/moves/zooms object. +\end{itemize} + +The status line shows information, namely +\begin{itemize} +\item Points \newline +Number of points in the mesh +\item Elements \newline +Number of volume elements (3D) in the mesh +\item Surf Elements \newline +Number of surface elements (3D) or inner elements (2d) in the mesh. +\item Mem \newline +Used memory in the large memory arena +\item Meshing Job, percentage +Douriing mesh generation, the current job as well as the progress is displayed on the +right side of the statu line. +\end{itemize} + +The drawing window displays the geometry or the mesh. The view +can be changed with the mouse: +\begin{itemize} +\item drag with left button pressed rotates the object, +\item drag with middle button pressed moves the object, +\item drag with right button pressed zooms the object. +\end{itemize} +The view can also be changed with the keyboard: +\begin{itemize} +\item cursor keys rotate the object +\item shift + cursor keys move the object +\item control + cursor keys zoom the object +\end{itemize} + +When in Mesh - visualization scene, double clicking on triangles mark the +surface. The point cursor is set. + +\section{The Netgen menu items} +\label{sec_menuitems} +\subsection{The menu item {\em File}} +\includegraphics[height=7.8cm]{pictures/menufile} + +\subsection{The menu item {\em Geometry}} +\includegraphics[height=2.7cm]{pictures/menugeometry} + +\subsection{The menu item {\em Mesh}} +\includegraphics[height=9.8cm]{pictures/menumesh} + +\subsection{The menu item {\em View}} +\includegraphics[height=6.0cm]{pictures/menuview} + +\subsection{The menu item {\em Refinement}} +\includegraphics[width=3.2cm]{pictures/menurefinement} + + +\section{Meshing Options} + +\includegraphics[width=10cm]{pictures/meshingoptions_1} + +\includegraphics[width=10cm]{pictures/meshingoptions_2} + +\includegraphics[width=10cm]{pictures/meshingoptions_3} + +\includegraphics[width=10cm]{pictures/meshingoptions_4} + +\includegraphics[width=10cm]{pictures/meshingoptions_5} + +\includegraphics[width=10cm]{pictures/meshingoptions_6} + + +\section{Visualization Options} + + + +% \chapter{The Algorithms of Netgen} +% +% Netgen follows a top down strategy. It starts from computing the +% corner points (CSG only). Then, the edges are defined and meshed into +% segments (CSG and STL). Next, the faces are meshed by an advancing front +% surface mesh generator. After meshing, the faces meshes are optimized. +% Finally, the individual sub-domains are filled with tets. Therefore, +% a fast Delaunay algorithm generates most of the elements (about 98 percent). +% But often it fails for mesh the whole domain, then the slower back-tracking +% rule-base algorithm takes over. Finally, the volume is optimized by the +% usual node - movement, element swapping and splitting algorithms. + + +\chapter{Programming Interfaces} +% +\section{The nginterface} +By means of the nginterface one's own simulation code can be +included into the netgen environment. This is particular useful +for FEM (FVM,BEM) code developers, since they may profit from the +netgen preprocessing and postprocessing possibilities. + +Please download the example Netgen-add-on module {\it demoapp} and +follow the instructions therein + +\section{The nglib} + + +\subsection{Introduction} +The NETGEN mesh generation library {\it nglib} is available in C++ +source code and can be compiled for Unix/Linux as well as Win95/98/NT +and linked to one library file. The interface to the application +programme is by the C language header file {\it nglib.h}. + +The functionality of nglib is volume mesh generation by a domain given +by a surface triangulation, and surface mesh generation from a domain +described by an STL file (standard file format for geometries defined by +triangle approximation). It can do mesh optimization as well as mesh +refinement. It can generate 4 node tetrahedra and 10 node tetrahedrons +(with quadratic shape functions). The local mesh size can be defined +automatically by geometric features and/or by user specification. + + +\subsection{The Header File} + +The interface file contains the following type definitions and function +calls. All Netgen types and functions start with {\tt Ng}. Types and +functions have capital initial letters, constants are in capital letters. + +\subsection{Types and Constants} +\begin{verbatim} + +/// Data type for NETGEN mesh +typedef void * Ng_Mesh; + +/// Data type for NETGEN STL geomty +typedef void * Ng_STL_Geometry; + + +// max number of nodes per element +#define NG_VOLUME_ELEMENT_MAXPOINTS 10 + +// implemented element types: +enum Ng_Volume_Element_Type { NG_TET = 1, NG_PYRAMID = 2, NG_PRISM = 3, + NG_TET10 = 4 }; + +// max number of nodes per surface element +#define NG_SURFACE_ELEMENT_MAXPOINTS 6 + +// implemented element types: +enum Ng_Surface_Element_Type { NG_TRIG = 1, NG_QUAD = 2, + NG_TRIG6 = 3 }; + + +struct Ng_Meshing_Parameters +{ + double maxh; + double fineness; // 0 .. coarse, 1 .. fine + int secondorder; +}; + +enum Ng_Result { NG_OK = 0, + NG_SURFACE_INPUT_ERROR = 1, + NG_VOLUME_FAILURE = 2, + NG_STL_INPUT_ERROR = 3, + NG_SURFACE_FAILURE = 4 }; +\end{verbatim} + + +{\tt Ng\_Mesh} is a data type representing a Netgen mesh. {\tt Ng\_STL\_Geometry} +represents an STL geometry. One can operate on these data structures by +the functions defined below. Netgen can (now and/or in future) work with +various element types defined by generic constants. Several parameters +can be specified in the {\tt Ng\_Meshing\_Parameters} structure for +volume and/or surface mesh generation. The result of Netgen functions +is of type {\tt Ng\_Result}. + + + +\subsection{Initialization} +Please call these functions before using netgen functions and after +using netgen functions, respectively: +\begin{verbatim} + // initialize, deconstruct Netgen library: + void Ng_Init (); + void Ng_Exit (); +\end{verbatim} + + +\subsection{Mesh access} +Netgen meshes can be processed by the means of the following functions. +A mesh contains nodes, surface elements and volume elements. Counting +starts from 1. + +\begin{verbatim} + // Generates new mesh structure + Ng_Mesh * Ng_NewMesh (); + void Ng_DeleteMesh (Ng_Mesh * mesh); + + // feeds points, surface elements and volume elements to the mesh + void Ng_AddPoint (Ng_Mesh * mesh, double * x); + void Ng_AddSurfaceElement (Ng_Mesh * mesh, Ng_Surface_Element_Type et, + int * pi); + void Ng_AddVolumeElement (Ng_Mesh * mesh, Ng_Volume_Element_Type et, + int * pi); + + // ask for number of points, surface and volume elements + int Ng_GetNP (Ng_Mesh * mesh); + int Ng_GetNSE (Ng_Mesh * mesh); + int Ng_GetNE (Ng_Mesh * mesh); + + + // return point coordinates + void Ng_GetPoint (Ng_Mesh * mesh, int num, double * x); + + // return surface and volume element in pi + Ng_Surface_Element_Type + Ng_GetSurfaceElement (Ng_Mesh * mesh, int num, int * pi); + + Ng_Volume_Element_Type + Ng_GetVolumeElement (Ng_Mesh * mesh, int num, int * pi); +\end{verbatim} + + +\subsubsection{Mesh Generation} +The user can specify the mesh size function by the global parameter +maximal mesh size, and can additionally restrict the mesh size in +points or cubes. The function {\tt Ng\_GenerateVolumeMesh} generates +the volume mesh starting from the surface. + +\begin{verbatim} + // Defines MeshSize Functions + void Ng_RestrictMeshSizeGlobal (Ng_Mesh * mesh, double h); + void Ng_RestrictMeshSizePoint (Ng_Mesh * mesh, double * p, double h); + void Ng_RestrictMeshSizeBox (Ng_Mesh * mesh, double * pmin, double * pmax, double h); + + // generates volume mesh from surface mesh + Ng_Result Ng_GenerateVolumeMesh (Ng_Mesh * mesh, Ng_Meshing_Parameters * mp); +\end{verbatim} + + +\subsection{STL Geometry} +A STL geometry can be read from a STL file (ASCII or binary), or can +be assembled by providing triangle by triangle. Either, the user +can specify the edges of the geometry, or netgen can define edges +by {\tt Ng\_STL\_MakeEdges} by using an angle criterium. + +\begin{verbatim} + // loads geometry from STL file + Ng_STL_Geometry * Ng_STL_LoadGeometry (char * filename, int binary = 0); + + // generate new STL Geometry + Ng_STL_Geometry * Ng_STL_NewGeometry (); + + // fills STL Geometry + // positive orientation + // normal vector may be null-pointer + void Ng_STL_AddTriangle (Ng_STL_Geometry * geom, + double * p1, double * p2, double * p3, double * nv); + + // add (optional) edges: + void Ng_STL_AddEdge (Ng_STL_Geometry * geom, + double * p1, double * p2); + + + // after adding triangles (and edges) initialize + Ng_Result Ng_STL_InitSTLGeometry (Ng_STL_Geometry * geom); + + // automatically generates edges: + void Ng_STL_MakeEdges (Ng_STL_Geometry * geom); + + // generates mesh, empty mesh be already created. + Ng_Result Ng_STL_GenerateSurfaceMesh (Ng_STL_Geometry * geom, + Ng_Mesh * mesh, + Ng_Meshing_Parameters * mp); +\end{verbatim} + +\subsection{Programming Example} + +The File {\it ngcore.cc}, see Appendix A, is a simple application +using the netgen volume mesh generator. First, the surface mesh +is read from a file containing point coordinates and surface triangles +(see e.g. file {\it cube.surf}). 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