diff --git a/onelab.html b/onelab.html index d187e820eaab2b7eb5188e9d18048c16054cf404..8bc405a9946913ff9f1ccc8f2a1c95bb4414cc17 100644 --- a/onelab.html +++ b/onelab.html @@ -85,33 +85,29 @@ or not) can be easily interfaced as well. <p> ONELAB can interface finite element and related software (<em>ONELAB - clients</em>) in two ways: + clients</em>) in several ways: </p> <ol> - <li>By directly embedding the ONELAB C++ library or the ONELAB Python - module. This is what <a href="https://getdp.info">GetDP</a> (a finite element - solver for electromagnetism, heat transfer, acoustics and generic - PDEs), <a href="https://gmsh.info">Gmsh</a> (a mesh generator with built-in - CAD engine and post-processor) and the ONELAB mobile app do. Any C++ and - Python code can do the same. - <li>By preprocessing the input files of any software. The different steps of a - simulation (meshing, solving, post-processing) are then controlled by a - python script, which dynamically regenerates the input - files. <a href="https://www.csc.fi/web/elmer">Elmer</a>, + <li>By using the ONELAB C++ library or the ONELAB Python module to communicate + with the Gmsh ONELAB server over TCP/IP or Unix sockets. This is what is + done by <a href="https://getdp.info">GetDP</a>; any C++ and Python code can + do the same with minimal code modifications. + <li>By using the Gmsh API in C++, C, Python or Julia to comunicate with the + ONELAB server over TCP/IP or Unix sockets, or directly in-memory. This + allows complete flexibility over how the client interacts with ONELAB + (e.g. by pre-processing its input files) and has been successfully used with + e.g. <a href="https://www.csc.fi/web/elmer">Elmer</a>, <a href="https://www.openfoam.com/">OpenFOAM</a>, <a href="https://www.code-aster.org/">Code_Aster</a>, <a href="https://www.3ds.com/fr/produits-et-services/simulia/produits/abaqus">Abaqus</a> - or <a href="http://www.calculix.de">CalculiX</a> can for example be readily - interfaced this way. + <a href="http://www.calculix.de">CalculiX</a>, + <a href="https://www.uee.uliege.be/cms/c_6331644/fr/uee-safir">Safir</a>, ... </ol> <p> - The ONELAB interface allows to call such clients and have them share - parameters and modeling information. The implementation is based on a - client-server model, with a server-side database, an (optional) graphical - front-end, and local or remote clients communicating in-memory or through - TCP/IP sockets. Contrary to most solver interfaces, the ONELAB - server has no <em>a priori</em> knowledge about any specifics (input file - format, syntax, ...) of the clients. This is made possible by having any + The ONELAB interface allows to interact with clients and have them share + parameters and modeling information. Contrary to most solver interfaces, the + ONELAB server has no <em>a priori</em> knowledge about any specifics (input + file format, syntax, ...) of the clients. This is made possible by having any simulation preceded by an analysis phase, during which the clients are asked to upload their parameter set to the server. The issues of completeness and consistency of the parameter sets are completely dealt with on the client @@ -119,8 +115,10 @@ or not) can be easily interfaced as well. re-dispatching. </p> <p> - See the <a href="https://gitlab.onelab.info/doc/tutorials/wikis">tutorials</a> - for examples. + See this <a href="slides/onelab.pdf">general presentation</a> for more + information and + the <a href="https://gitlab.onelab.info/doc/tutorials/wikis">tutorials</a> for + examples. </p> <h2>Sponsors</h2> diff --git a/slides/data_common/uclouvain.png b/slides/data_common/uclouvain.png new file mode 100644 index 0000000000000000000000000000000000000000..3fb4a88a3faa7a301617d7258854f12dc8acf00b Binary files /dev/null and b/slides/data_common/uclouvain.png differ diff --git a/slides/data_common/uliege.png b/slides/data_common/uliege.png new file mode 100644 index 0000000000000000000000000000000000000000..db7066fe7ca8433507ed88e7abdaafdc8727ed29 Binary files /dev/null and b/slides/data_common/uliege.png 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Geuzaine} +\institute{Universit\'e de Li\`ege} +\date{\today} + +\begin{document} + +\begin{frame} + \titlepage +\end{frame} + +\begin{frame}[plain] + \tableofcontents +\end{frame} + +\section{Some background} + +\begin{frame}{Some background} + \begin{tikzpicture}[remember picture,overlay] + \node[xshift=-1.2cm,yshift=-1.4cm] at (current page.north east) + {\hspace*{-2cm}\textcolor{white}{\rule{2cm}{2.5cm}}% + \hspace*{-2px}\includegraphics[width=2cm]{geuzaine.png}}; + \end{tikzpicture} + \begin{itemize} + \item<1-> I am a professor at the University of Li\`ege in Belgium, where I + lead a team of about 15 people in the Montefiore Institute (EECS Dept.), at + the intersection of applied math, scientific computing and engineering + physics + \item<2-> Our research interests include modeling, analysis, algorithm + development, and simulation for problems arising in various areas of + engineering and science + \item<2-> Current applications: low- and high-frequency electromagnetics, + geophysics, biomedical problems + \item<3-> We write quite a lot of codes, some released as open source + software: \url{https://gmsh.info}, \url{https://getdp.info}, + \url{https://onelab.info} + \end{itemize} +\end{frame} + +\begin{frame}{Gmsh, GetDP \& ONELAB} + \begin{itemize} + \item<1-> Gmsh (\url{https://gmsh.info}) is a 3D finite element mesh generator + with a built-in CAD engine and post-processor + \begin{itemize} + \item Joint work with J.-F. Remacle at UCLouvain, with important + contributions from J. Lambrechts, K. Hillewaert, M. Pellikka, A. Johnen, + H. Si, A. Royer, C. Marot, I. Badia, T. Toulorge, M. Reberol, ... + \end{itemize} + \medskip + \item<2-> GetDP (\url{https://getdp.info}) is a general finite element solver + using mixed finite elements + \begin{itemize} + \item Joint work with P. Dular at ULi\`ege, with important contributions from + J. Gyselinck, R. Sabariego, M. Asam, B. Thierry, K. Jacques, + F. Henrotte, G. Dem\'esy, ... + \end{itemize} + \medskip + \item<3-> ONELAB (\url{https://onelab.info}) is an abstract interface for + sharing information between codes + \end{itemize} +\end{frame} + +\begin{frame}{Some numbers} + Today, Gmsh, GetDP and ONELAB represent about 500k lines of C++ code + \begin{itemize} + \item still only 3 core developers; about 100 with $\geq$ 1 commit + \item about 1,200 registered users on the development site + \url{https://gitlab.onelab.info} + \item about 20,000 downloads per month (70\% Windows) + \item about 800 citations per year -- the Gmsh paper is cited about 5000 times + \item Gmsh has probably become one of the most popular (open source) finite + element mesh generators? + \end{itemize} +\end{frame} + +\begin{frame}{Short demo} + \begin{figure} + \includegraphics[width=0.75\textwidth]{data_onelab/helix_alpha.png}\\[1ex] + Download the ONELAB software bundle from \url{https://onelab.info}\\ + Open \href{https://gitlab.onelab.info/doc/models/-/wikis/Superconductors} + {\texttt{models/Superconductors/helix.pro}} with Gmsh + \end{figure} +\end{frame} + +\section{An overview of Gmsh} + +\begin{frame} + \begin{center} + \textbf{\Large An overview of Gmsh} + \end{center} +\end{frame} + +\subsection{Introduction} + +\begin{frame}{What is Gmsh?} + \begin{tikzpicture}[remember picture,overlay] + \node[xshift=-1.7cm,yshift=-4.7cm] at (current page.north east) + {\includegraphics[width=1.25cm]{gmsh.png}}; + \end{tikzpicture} + \begin{itemize} + \item<1-> Gmsh (\url{https://gmsh.info}) is a 3D finite element mesh + generator with a built-in CAD engine and post-processor + \item<1-> Open source (GNU GPL v2+) + \item<2-> Includes a graphical user interface (GUI) + \item<3-> Can be used as a standalone software or as a library (C++, C, Python + or Julia) + \item<4-> Can drive any simulation code interactively through ONELAB + \end{itemize} +\end{frame} + +{ + \setbeamercolor{background canvas}{bg=black} % change bg for this frame + \begin{frame}[plain] + \begin{tikzpicture}[remember picture,overlay] + \mode<handout>{ % simple image for handout version + \node at (current page.center) + {\includegraphics[keepaspectratio, width=\paperwidth, height=\paperheight] + {gource.png}}; + } + \mode<beamer>{ % requires Flash player and Adobe Reader for presentation + % we don't scale to full width/height so that one can click on any + % border to regain mouse control (e.g. to skip the slide) + \node at (current page.center) + {\includemedia[playbutton=none, addresource=data_general_overview/gource_faster.mp4, + flashvars={src=gource_faster.mp4&autoPlay=true}] + {\includegraphics[keepaspectratio, width=0.95\paperwidth, height=0.95\paperheight] + {gource.png}} + {StrobeMediaPlayback.swf}}; + } + \node[above, yshift=2.5em] at (current page.south) + {\href{https://gmsh.info/doc/gource_faster.mp4} + {\textcolor{white}{\underline{$\sim$ 20 years of Gmsh development in 1 minute}}}}; + \node[above, yshift=1em] at (current page.south) + {\href{https://gmsh.info/CREDITS.txt} + {\textcolor{white}{\underline{A warm thank you to all the contributors!}}}}; + \end{tikzpicture} + \end{frame} +} + +\begin{frame}{Gmsh - A little bit of history} + \begin{itemize} + \item Gmsh was started in 1996, as a side project + \item 1998: First public release + \item 2003: Open sourced under GNU GPL + \item 2006: OpenCASCADE integration (Gmsh 2) + \item 2009: IJNME paper and switch to CMake + \item 2012: Curvilinear meshing and quad meshing + \item 2013: Homology and ONELAB solver interface + \item 2015: Multi-threaded 1D and 2D meshing (coarse-grained) + \item 2017: Boolean operations and switch to Git (Gmsh 3) + \item 2018: C++, C, Python and Julia API (Gmsh 4) + \item 2019: Multi-threaded 3D meshing (fine-grained), robust STL remeshing + \item 2021: GmshFEM, Quasi-structured quad meshing + \end{itemize} +\end{frame} + +\begin{frame}{Gmsh - Strategic choices} + \begin{itemize} + \item<1-> Design goals: fast, light and user-friendly + \begin{itemize} + \item Written in simple C++ + \item GUIs: FLTK (desktop), UIKit (iOS), Android + \item OpenGL graphics + \item Highly portable (OSes \& compilers) + \item Easy to distribute \& install: zero dependencies on installation + \end{itemize} + \item<2-> Handling of numerous third party libraries + \begin{itemize} + \item Build system based on CMake -- everything is optional + \item Some libs integrated and redistributed directly in gmsh/contrib + (HXT, BAMG, Metis, Concorde, ...) + \end{itemize} + \item<3-> Funding + \begin{itemize} + \item Hobby until 2006, then industry, Wallonia, Belgium \& EU + \end{itemize} + \end{itemize} +\end{frame} + +\begin{frame}{Gmsh - Strategic choices} + \begin{itemize} + \item<1->Community infrastructure + \begin{itemize} + \item Our own (using GitLab) to enable public/private parts + (\url{https://gitlab.onelab.info/gmsh/gmsh}) + \item Continuous integration and delivery (CI/CD) of Gmsh app and Gmsh SDK + on Windows, Linux and macOS + \item Web site (\url{https://gmsh.info}) with documentation, tutorials, etc. + \item Scientific aspects of algorithms detailed in journal papers + \end{itemize} + \item<2-> Licensing + \begin{itemize} + \item Gmsh is distributed under the GNU General Public License v2 or later, + with exceptions to allow for easier linking with external libraries + \item We double-license to enable embedding in commercial codes + \end{itemize} + \end{itemize} +\end{frame} + +\begin{frame}{Gmsh - Basic concepts} + \begin{itemize} + \item<1-> Gmsh is based around four modules: Geometry, Mesh, Solver and + Post-processing + \item<1-> Gmsh can be used at 3 levels + \begin{itemize} + \item Through the GUI + \item Through the dedicated \texttt{.geo} language + \item Through the C++, C, Python and Julia API + \end{itemize} + \item<2-> Main characteristics + \begin{itemize} + \item All algorithms are written in terms of abstract model entities, using a + Boundary REPresentation (BREP) approach + \item Gmsh never translates from one CAD format to another; it directly + accesses each CAD kernel API (OpenCASCADE, Built-in, ...) + \end{itemize} + \end{itemize} +\end{frame} + +\begin{frame}{Gmsh - Basic concepts} + \begin{center} + The goal is to deal with very different underlying data representations in a + transparent manner + \end{center} + \begin{adjustwidth}{-1em}{-1em} + \only<1-3>{\includegraphics[height=0.66\textheight]{train.png}} + \only<2-3>{\hspace{-1em}\includegraphics[height=0.66\textheight]{ocean.png}} + \only<3>{\includegraphics[height=0.66\textheight]{bio.png}} + \end{adjustwidth} +\end{frame} + +\subsection{Geometry module} + +\begin{frame}{Gmsh - Geometry module} + Under the hood, 4 types of model entities are defined: + \begin{enumerate} + \item Model points $G^0_i$ that are topological entities of dimension 0 + \item Model curves $G^1_i$ that are topological entities of dimension 1 + \item Model surfaces $G^2_i$ that are topological entities of dimension 2 + \item Model volumes $G^3_i$ that are topological entities of dimension 3 + \end{enumerate} +\end{frame} + +\begin{frame}{Gmsh - Geometry module} + \begin{itemize} + \item<1-> Model entities are topological entities, i.e., they only deal with + adjacencies in the model; a bi-directional data structure represents the + graph of adjacencies + \begin{equation*} + G^0_i \rightleftharpoons G^1_i \rightleftharpoons G^2_i \rightleftharpoons G^3_i + \end{equation*} + \item<1-> Any model is able to build its list of adjacencies of any dimension + using local operations + \item<1-> The BRep is extended with non-manifold features: adjacent entities, + and \emph{embedded} (internal) entities + \item<2-> Model entities can be either CAD entities (e.g. from the + built-in or OpenCASCADE kernel) or \emph{discrete} entities + (defined by a mesh, e.g. STL) + \end{itemize} +\end{frame} + +\begin{frame}{Gmsh - Geometry module} + The geometry of a CAD model entity depends on the solid modeler kernel + for its underlying representation. Solid modelers usually provide a + parametrization of the shapes, i.e., a mapping: + \begin{equation*} + \mathbf{p}\in R^d \mapsto \mathbf{x} \in R^3 + \end{equation*} + \begin{enumerate} + \item The geometry of a model point $G^0_i$ is simply its 3-D location + $\mathbf{x}_i = (x_i,y_i,z_i)$ + \item The geometry of a model curve $G^1_i$ is its underlying curve + $\mathcal{C}_i$ with its parametrization $\mathbf{p}(t)\in\mathcal{C}_i$, + $t\in[t_1,t_2]$ + \item The geometry of a model surface $G^2_i$ is its underlying surface + $\mathcal{S}_i$ with its parametrization $\mathbf{p}(u,v)\in\mathcal{S}_i$ + \item The geometry associated to a model volume is $R^3$ + \end{enumerate} +\end{frame} + +\begin{frame}{Gmsh - Geometry module} + \begin{figure} + \includegraphics[width=0.9\textwidth]{mappings.png}\\ + Point $\mathbf{p}$ located on a curve $\mathcal{C}$ that is itself embedded + in a surface $\mathcal{S}$ + \end{figure} +\end{frame} + +\begin{frame}{Gmsh - Geometry module} + Operations on CAD model entities are performed directly within their + respective CAD kernels: + \begin{itemize} + \item There is no common internal geometrical representation + \item Rather, Gmsh directly performs the operations (translation, rotation, + intersection, union, fragments, ...) on the native geometrical + representation using each CAD kernel's own API + \end{itemize} + \begin{adjustwidth}{-2em}{-2em} + \includegraphics[width=0.37\textwidth]{engine.png}% + \includegraphics[width=0.37\textwidth]{airplane.png}% + \includegraphics[width=0.37\textwidth]{ellipses.png} + \end{adjustwidth} +\end{frame} + +\begin{frame}{Gmsh - Geometry module} + Discrete model entities are defined by a mesh (e.g. STL): + \begin{itemize} + \item They can be equipped with a geometry through a \emph{reparametrization} + procedure + \item The parametrization is then used for meshing, in exactly the same way as + for CAD entities + \end{itemize} + \includegraphics[width=0.5\textwidth]{reparam_falcon_atlas.png}% + \includegraphics[width=0.5\textwidth]{reparam_falcon.png}% +\end{frame} + +\subsection{Mesh module} + +\begin{frame}{Gmsh - Mesh module} + \begin{itemize} + \item Gmsh implements several meshing algorithms with specific characteristics + \begin{itemize} + \item 1D, 2D and 3D + \item Structured, unstructured and hybrid + \item Isotropic and anisotropic + \item Straight-sided and curved + \item From standard CAD data or from STL through reparametrization + \end{itemize} + \item Built-in interfaces to external mesh generators (BAMG, MMG3D, Netgen) + \end{itemize} +\end{frame} + +\begin{frame}{Gmsh - Mesh module} + \begin{figure} + \only<1|handout:0>{\includegraphics[width=0.8\textwidth]{seam_geo.png}}% + \only<2>{\includegraphics[width=0.9\textwidth]{seam_mesh.png}}\\ + Typical CAD kernel idiosyncrasies: seam edges and degenerated edges + \end{figure} +\end{frame} + +\begin{frame}{Gmsh - Mesh module} + \begin{itemize} + \item<1-> Mesh data is made of \emph{elements} (points, lines, triangles, + quadrangles, tetrahedra, hexahedra, ...) defined by an ordered list of their + \emph{nodes} + \item<2-> Elements and nodes are stored (\emph{classified}) in the model entity + they discretize: + \begin{itemize} + \item<3-> A model point will thus contain a mesh element of type point, as well + as a mesh node + \item<4-> A model curve will contain line elements as well as its interior + nodes, while its boundary nodes will be stored in the bounding model + points + \item<5-> A model surface will contain triangular and/or quadrangular elements + and all the nodes not classified on its boundary or on its embedded + entities (curves and points) + \item<6-> A model volume will contain tetrahedra, hexahedra, etc. and all the + nodes not classified on its boundary or on its embedded entities + (surfaces, curves and points) + \end{itemize} + \end{itemize} +\end{frame} + +\begin{frame}{Gmsh - Mesh module} + \begin{columns}[c] + \begin{column}{0.5\textwidth} + This mesh data structure allows to easily and efficiently handle the + creation, modification and destruction of conformal finite element meshes + \end{column} + \begin{column}{0.5\textwidth} + \includegraphics[width=\textwidth]{classification.png} + \end{column} + \end{columns} +\end{frame} + +\subsection{Solver module} + +\begin{frame}{Gmsh - Solver module} + \begin{itemize} + \item Gmsh implements a ONELAB (\url{https://onelab.info}) server to pilot + external solvers, called ``clients'' + \item Example client: GetDP finite element solver (\url{https://getdp.info}) + \begin{columns}[T] + \begin{column}{0.35\textwidth} + \begin{itemize} + \item The ONELAB interface allows to call such clients and have them + share parameters and modeling information + \item Parameters are directly controllable from the GUI + \end{itemize} + \end{column} + \begin{column}{0.45\textwidth} + \vspace{1em} + \includegraphics[width=\textwidth]{onelab.png} + \end{column} + \end{columns} + \end{itemize} +\end{frame} + +\begin{frame}{Gmsh - Solver module} + \begin{itemize} + \item<1-> The implementation is based on a client-server model, with a + server-side database and local or remote clients communicating in-memory + or through TCP/IP sockets + \begin{itemize} + \item<2-> Contrary to most solver interfaces, the ONELAB server has no a + priori knowledge about any specifics (input file format, syntax, ...) of + the clients + \item<2-> This is made possible by having any simulation preceded by an + analysis phase, during which the clients are asked to upload their + parameter set to the server + \item<2-> The issues of completeness and consistency of the parameter sets + are completely dealt with on the client side: the role of ONELAB is + limited to data centralization, modification and re-dispatching + \end{itemize} + \end{itemize} +\end{frame} + +\subsection{Post-processing module} + +\begin{frame}{Gmsh - Post-processing module} + \begin{itemize} + \item<1-> Post-processing data is made of \emph{views} + \item<1-> A view stores both display \emph{options} and \emph{data} (unless + the view is an \emph{alias} of another view) + \item<2-> View data can contain several \emph{steps} (e.g. to store time + series) and can be either linked to one or more models (\emph{mesh-based} + data, as stored in \texttt{.msh} or \texttt{.med} files) or independent from + any model (\emph{list-based} data, as stored in parsed \texttt{.pos} files) + \item<2-> Data is interpolated through arbitrary polynomial interpolation + schemes; automatic mesh refinement is used for adaptive visualization of + high-order views + \item<2-> Various \emph{plugins} exist to create and modify views + \end{itemize} +\end{frame} + +\begin{frame}{Gmsh - Post-processing module} + \begin{columns}[c] + \begin{column}{0.36\textwidth} + \includegraphics[width=\textwidth]{transformer.png} + \end{column} + \begin{column}{0.5\textwidth} + \begin{itemize} + \item Cuts, iso-curves and vectors + \item Elevation maps + \item Streamlines + \item Adaptive high-order visualization + \end{itemize} + \end{column} + \end{columns} + \begin{figure} + \includegraphics[width=0.28\textwidth]{streamlines.png} + \includegraphics[width=0.28\textwidth]{neutron.png} + \includegraphics[width=0.28\textwidth]{ho_visu.png} + \end{figure} +\end{frame} + +\subsection{Recent developments} + +\begin{frame}{Gmsh - Recent developments} + \begin{itemize} + \item Constructive Solid Geometry + \item Application Programming Interface (API) + \item Multi-threaded meshing + \item Robust STL remeshing based on parametrizations + \item Quasi-structured quad meshing + \end{itemize} +\end{frame} + +\begin{frame}{Gmsh - Constructive Solid Geometry} + \begin{figure} + \includegraphics[width=0.8\textheight]{csg.png}\\ + \url{https://en.wikipedia.org/wiki/Constructive_solid_geometry} + \end{figure} +\end{frame} + +\begin{frame}[fragile]{Gmsh - Constructive Solid Geometry} + \begin{adjustbox}{max totalheight=0.75\textheight} + \begin{lstlisting}[language=geo] +SetFactory("OpenCASCADE"); // use OpenCASCADE kernel + +R = DefineNumber[ 1.4 , Min 0.1, Max 2, Step 0.01, + Name "Parameters/Box dimension" ]; +Rs = DefineNumber[ R*.7 , Min 0.1, Max 2, Step 0.01, + Name "Parameters/Cylinder radius" ]; +Rt = DefineNumber[ R*1.25, Min 0.1, Max 2, Step 0.01, + Name "Parameters/Sphere radius" ]; + +Box(1) = {-R,-R,-R, 2*R,2*R,2*R}; // explicit entity tag + +Sphere(2) = {0,0,0, Rt}; + +BooleanIntersection(3) = { Volume{1}; Delete; }{ Volume{2}; Delete; }; + // delete object and tool +Cylinder(4) = {-2*R,0,0, 4*R,0,0, Rs}; +Cylinder(5) = {0,-2*R,0, 0,4*R,0, Rs}; +Cylinder(6) = {0,0,-2*R, 0,0,4*R, Rs}; + +BooleanUnion(7) = { Volume{4}; Delete; }{ Volume{5,6}; Delete; }; +BooleanDifference(8) = { Volume{3}; Delete; }{ Volume{7}; Delete; }; + \end{lstlisting} + \end{adjustbox} +\end{frame} + +\begin{frame}{Gmsh - Constructive Solid Geometry} + \begin{figure} + \includegraphics[width=0.9\textwidth]{boolean.png}\\ + \href{https://gitlab.onelab.info/gmsh/gmsh/blob/master/demos/boolean/boolean.geo} + {\texttt{demos/boolean/boolean.geo}} + \end{figure} +\end{frame} + +\begin{frame}[fragile]{Gmsh - Constructive Solid Geometry} + \begin{adjustbox}{max totalheight=0.75\textheight} + \begin{lstlisting}[language=geo] +SetFactory("OpenCASCADE"); + +DefineConstant[ + z = {16, Name "Parameters/z position of box"} + sph = {0, Choices{0,1}, Name "Parameters/Add sphere?"} +]; + +a() = ShapeFromFile("component8.step"); // import STEP shape +b() = 2; +Box(b(0)) = {0,156,z, 10,170,z+10}; + +If(sph) + b() += 3; + Sphere(b(1)) = {0,150,0, 20}; +EndIf + +// fragmentation intersects everything +r() = BooleanFragments{ Volume{a()}; Delete; }{ Volume{b()}; Delete; }; +Save "merged.brep"; // save into native OpenCASCADE format + +Physical Volume("Combined volume", 1) = {r()}; +Physical Surface("Combined boundary", 2) = CombinedBoundary{ Volume{r()}; } + \end{lstlisting} + \end{adjustbox} +\end{frame} + +\begin{frame}{Gmsh - Constructive Solid Geometry} + \begin{figure} + \includegraphics[width=0.9\textwidth]{import.png}\\ + \href{https://gitlab.onelab.info/gmsh/gmsh/blob/master/demos/boolean/import.geo} + {\texttt{demos/boolean/import.geo}} + \end{figure} +\end{frame} + +% \begin{frame}{Gmsh - Constructive Solid Geometry} +% \begin{itemize} +% \item All existing \texttt{.geo} commands are conserved +% \item New or modified \texttt{.geo} commands: +% \begin{itemize} +% \item Shapes (with explicit numbering): \texttt{Circle}, \texttt{Ellipse}, +% \texttt{Wire}, \texttt{Surface}, \texttt{Sphere}, \texttt{Box}, +% \texttt{Torus}, \texttt{Rectangle}, \texttt{Disk}, \texttt{Cylinder}, +% \texttt{Cone}, \texttt{Wedge}, \texttt{ThickSolid}, \texttt{ThruSections}, +% \texttt{Ruled ThruSections} +% \item Operations (implicit numbering): \texttt{ThruSections}, \texttt{Ruled +% ThruSections}, \texttt{Fillet}, \texttt{Extrude} +% \item Boolean operations (explicit or implicit numbering): +% \texttt{BooleanUnion}, \texttt{BooleanIntersection}, +% \texttt{BooleanDifference}, \texttt{BooleanFragments} +% \item Other: \texttt{ShapeFromFile}, \texttt{Recursive Delete} +% \end{itemize} +% \end{itemize} +% \end{frame} + +\begin{frame}{Gmsh - API} + Gmsh 4 introduces a new stable Application Programming Interface (API) + for C++, C, Python and Julia, with the following design goals: + \begin{itemize} + \item Allow to do everything that can be done in \texttt{.geo} files + \begin{itemize} + \item ... and then much more! + \end{itemize} + \item Be robust, in particular to wrong input data (i.e. ``never crash'') + \item Be efficient; but still allow to do simple things, simply + \item Be maintainable over the long run + \end{itemize} +\end{frame} + +\begin{frame}{Gmsh - API} + To achieve these goals the Gmsh API + \begin{itemize} + \item is purely functional + \item only uses basic types from the target language (C++, C, Python or Julia) + \item is automatically generated from a master API description file + \item is fully documented + \end{itemize} +\end{frame} + +\begin{frame}[fragile]{Gmsh - API} + \begin{center} + Same boolean example as before, but using the Python API: + \end{center} + \begin{columns}[c] + \begin{column}{0.55\textwidth} + \begin{adjustbox}{max totalheight=0.65\textheight} + \begin{lstlisting}[language=py] +import gmsh + +gmsh.initialize() +gmsh.model.add("boolean") + +R = 1.4; Rs = R*.7; Rt = R*1.25 + +gmsh.model.occ.addBox(-R,-R,-R, 2*R,2*R,2*R, 1) +gmsh.model.occ.addSphere(0,0,0,Rt, 2) +gmsh.model.occ.intersect([(3, 1)], [(3, 2)], 3) +gmsh.model.occ.addCylinder(-2*R,0,0, 4*R,0,0, Rs, 4) +gmsh.model.occ.addCylinder(0,-2*R,0, 0,4*R,0, Rs, 5) +gmsh.model.occ.addCylinder(0,0,-2*R, 0,0,4*R, Rs, 6) +gmsh.model.occ.fuse([(3, 4), (3, 5)], [(3, 6)], 7) +gmsh.model.occ.cut([(3, 3)], [(3, 7)], 8) + +gmsh.model.occ.synchronize() +gmsh.model.mesh.generate(3) +gmsh.fltk.run() +gmsh.finalize() + \end{lstlisting} + \end{adjustbox} + \end{column} + \begin{column}{0.35\textwidth} + \includegraphics[width=\textwidth]{boolean.png} + \end{column} + \end{columns} + \begin{center} + \href{https://gitlab.onelab.info/gmsh/gmsh/blob/master/demos/api/boolean.py} + {\texttt{demos/api/boolean.py}} + \end{center} +\end{frame} + +\begin{frame}[fragile]{Gmsh - API} + \begin{center} + ... or using the C++ API: + \end{center} + \begin{columns}[c] + \begin{column}{0.55\textwidth} + \begin{adjustbox}{max totalheight=0.65\textheight} + \begin{lstlisting}[language=cpp] +#include <gmsh.h> + +int main(int argc, char **argv) +{ + gmsh::initialize(argc, argv); + gmsh::model::add("boolean"); + + double R = 1.4, Rs = R*.7, Rt = R*1.25; + + std::vector<std::pair<int, int> > ov; + std::vector<std::vector<std::pair<int, int> > > ovv; + gmsh::model::occ::addBox(-R,-R,-R, 2*R,2*R,2*R, 1); + gmsh::model::occ::addSphere(0,0,0,Rt, 2); + gmsh::model::occ::intersect({{3, 1}}, {{3, 2}}, ov, ovv, 3); + gmsh::model::occ::addCylinder(-2*R,0,0, 4*R,0,0, Rs, 4); + gmsh::model::occ::addCylinder(0,-2*R,0, 0,4*R,0, Rs, 5); + gmsh::model::occ::addCylinder(0,0,-2*R, 0,0,4*R, Rs, 6); + gmsh::model::occ::fuse({{3, 4}, {3, 5}}, {{3, 6}}, ov, ovv, 7); + gmsh::model::occ::cut({{3, 3}}, {{3, 7}}, ov, ovv, 8); + + gmsh::model::occ::synchronize(); + + gmsh::model::mesh::generate(3); + gmsh::fltk::run(); + gmsh::finalize(); + return 0; +} + \end{lstlisting} + \end{adjustbox} + \end{column} + \begin{column}{0.35\textwidth} + \includegraphics[width=\textwidth]{boolean.png} + \end{column} + \end{columns} + \begin{center} + \href{https://gitlab.onelab.info/gmsh/gmsh/blob/master/demos/api/boolean.cpp} + {\texttt{demos/api/boolean.cpp}} + \end{center} +\end{frame} + +\begin{frame}{Gmsh - API} + In addition to CAD creation and meshing, the API can be used to + \begin{itemize} + \item Access mesh data (\texttt{getNodes}, \texttt{getElements}) + \item Generate interpolation (\texttt{getBasisFunctions}) and integration + (\texttt{getJacobians}) data to build Finite Element and related solvers + (see e.g. + \href{https://gitlab.onelab.info/gmsh/gmsh/blob/master/demos/api/poisson.py} + {\texttt{demos/api/poisson.py}}) + \item Create post-processing views + \item Run the graphical user-interface + \item Build custom graphical user-interfaces, e.g. for domain-specific codes + (see + \href{https://gitlab.onelab.info/gmsh/gmsh/blob/master/demos/api/prepro.py} + {\texttt{demos/api/prepro.py}} + or + \href{https://gitlab.onelab.info/gmsh/gmsh/blob/master/demos/api/custom_gui.py} + {\texttt{demos/api/custom\_gui.py}}) or co-post-processing via ONELAB + \end{itemize} +\end{frame} + +\begin{frame}{Gmsh - API} + \bigskip + In order to make this API easy to use, we publish a binary Software + Development Toolkit (SDK): + \begin{itemize} + \item Continuously delivered (for each commit in master), like the Gmsh app + \item Contains the dynamic Gmsh library together with the corresponding C++/C + header files, and Python and Julia modules + \end{itemize} + \begin{figure} + \includegraphics[width=0.9\textwidth]{sdk.png} + \end{figure} +\end{frame} + +\begin{frame}{Gmsh - Multi-threaded meshing} + Most meshing algorithms are now multi-threaded using OpenMP: + \begin{itemize} + \item 1D and 2D algorithms are multithreaded using coarse-grained approach, + i.e. several curves/surfaces are meshed concurrently + \item The new 3D Delaunay-based algorithm is multi-threaded using a + fine-grained approach. It currently lacks several features (embedded + entities, hybrid meshes, ...), which will eventually be supported + \end{itemize} + \bigskip\pause + You need to recompile Gmsh with \texttt{-DENABLE\_OPENMP=1} to enable this; + then e.g. \texttt{gmsh file.geo -3 -nt 8 -algo hxt} +\end{frame} + +\begin{frame}{Gmsh - Multi-threaded meshing} + \begin{figure} + \includegraphics[width=0.75\textwidth]{parallel1.png} + \end{figure} + {\hfill\footnotesize [C. Marot et al., IJNME 2019]} +\end{frame} + +\begin{frame}{Gmsh - Multi-threaded meshing} + \begin{figure} + \includegraphics[width=0.9\textwidth]{parallel2.png}\\ + \includegraphics[width=0.9\textwidth]{parallel3.png}\\ + {\footnotesize AMD EPYC 2x 64-core} + \end{figure} +\end{frame} + +\begin{frame}{Gmsh - Multi-threaded meshing} + \begin{figure} + \includegraphics[width=0.55\textwidth]{parallel4.png} + \includegraphics[width=0.35\textwidth]{parallel5.png}\\ + {\footnotesize AMD EPYC 2x 64-core} + \end{figure} +\end{frame} + +\begin{frame}{Gmsh - Robust STL remeshing} + New pipeline to remesh discrete surfaces (represented by triangulations): + \begin{itemize} + \item Automatic construction of a set of parametrizations that form an atlas + of the model + \item Each parametrization is guaranteed to be one-to-one, amenable to meshing + using existing algorithms + \item New nodes are guaranteed to be on the input triangulation (``no + modelling'') + \item Optional pre-processing (i.e. edge detection) to color sub-patches if + sharp features need to be preserved + \end{itemize} + {\vfill\hfill\footnotesize [P. A. Beaufort et al., JCP 2020]} +\end{frame} + +\begin{frame}{Gmsh - Robust STL remeshing} + \begin{figure} + \includegraphics[width=0.9\textwidth]{batman1.png}\\ + Batman STL mesh + \end{figure} +\end{frame} + +\begin{frame}{Gmsh - Robust STL remeshing} + \begin{figure} + \includegraphics[width=0.9\textwidth]{batman2.png}\\ + Automatic atlas creation: each patch is provably parametrizable by solving a + linear PDE, using mean value coordinates + \end{figure} +\end{frame} + +\begin{frame}{Gmsh - Robust STL remeshing} + \begin{figure} + \includegraphics[width=0.9\textwidth]{batman3.png}\\ + Remeshing + \end{figure} +\end{frame} + +\begin{frame}{Gmsh - Robust STL remeshing} + \begin{figure} + \includegraphics[width=0.9\textwidth]{batman4.png}\\ + Automatic atlas creation, this time with feature edge detection + \end{figure} +\end{frame} + +\begin{frame}{Gmsh - Robust STL remeshing} + \begin{figure} + \includegraphics[width=0.9\textwidth]{batman5.png}\\ + Remeshing with feature edge detection + \end{figure} +\end{frame} + +\begin{frame}{Gmsh - Robust STL remeshing} + \begin{figure} + \includegraphics[width=\textwidth]{artery.png}\\ + CT scan of an artery: 101 patches created, most because of the large aspect + ratio + \end{figure} +\end{frame} + +\begin{frame}{Gmsh - Robust STL remeshing} + \begin{figure} + \includegraphics[width=0.9\textwidth]{skull.png}\\ + Remeshing of a skull: 715 patches created for reparametrization; mesh + adapted to curvature + \end{figure} +\end{frame} + +\begin{frame}{Gmsh - Robust STL remeshing} + \begin{figure} + \includegraphics[width=0.5\textwidth]{tomography1.png} + \includegraphics[width=0.5\textwidth]{tomography2.png}\\ + Remeshing of an X-ray tomography image of a silicon carbide foam by P. Duru, + F. Muller and L. Selle (IMFT, ERC Advanced Grant SCIROCCO): 1,802 patches + created for reparametrization + \end{figure} +\end{frame} + +\begin{frame}{Gmsh - Quasi-structured quad meshing} + \begin{figure} + New experimental algorithm by [M. Reberol et al. 2021] that has just + landed in the development version\\ + \includegraphics[width=0.7\textwidth]{quadqs_a.png}\\ + Compute a (scaled) cross-field with multilevel diffusion + \end{figure} +\end{frame} + +\begin{frame}{Gmsh - Quasi-structured quad meshing} + \begin{figure} + \includegraphics[width=0.75\textwidth]{quadqs_2b.png}\\ + Build a unstructured quadrilateral mesh with a frontal approach guided by + the scaled cross field + \end{figure} +\end{frame} + +\begin{frame}{Gmsh - Quasi-structured quad meshing} + \begin{figure} + \includegraphics[width=0.75\textwidth]{quadqs_2c.png}\\ + Pattern-based quadrilateral meshing and cavity remeshing to eliminate + unnecessary irregular vertices while preserving the cross field + singularities + \end{figure} +\end{frame} + +\begin{frame}{Gmsh - Quasi-structured quad meshing} + \begin{figure} + \includegraphics[width=0.75\textwidth]{quadqs_2d.png}\\ + The final quad mesh is very similar to the one obtained with the global + parametrization approach and has the same number of irregular vertices + \end{figure} +\end{frame} + +\begin{frame}{Gmsh - Quasi-structured quad meshing} + \begin{columns}[c] + \begin{column}{0.55\textwidth} + \includegraphics[width=\textwidth]{quadqs_block.png} + \end{column} + \begin{column}{0.45\textwidth} + \begin{itemize} + \item ``Block'' model: 533 surfaces, 1584 curves, 261.5k vertices, 261.6k + quads + \item Average SICN quality: 0.87 (minimum: 0.11) + \item 58 sec. (initial unstructured quad mesh) + 33 sec. (quasi-structured + improvement) on Intel Core i7 4 cores + \item Quasi-structured improvement reduces the number of irregular from + 14.4k to 3.6k + \end{itemize} + \end{column} + \end{columns} +\end{frame} + +\section{An overview of GetDP} + +\begin{frame} + \begin{center} + \textbf{\Large An overview of GetDP} + \end{center} +\end{frame} + +\subsection{Introduction} + +\begin{frame}{What is GetDP?} + \begin{itemize} + \item<1-> GetDP (\url{https://getdp.info}) is a flexible finite element solver + using mixed elements + \item<2-> Open source (GNU GPL v2+); same community infrastructure as Gmsh + \item<3-> Main feature: closeness between + \begin{itemize} + \item the input data defining discrete problems (written in plain text + \texttt{.pro} files), and + \item the symbolic mathematical expressions of these problems + \end{itemize} + \item<4-> New models developed through \texttt{.pro} files --- no compilation + \item<4-> Highly portable: exact same \texttt{.pro} files on iPhone and 10,000 + core supercomputer + \end{itemize} +\end{frame} + +\begin{frame}{GetDP - A little bit of history} + \begin{itemize} + \item GetDP was started at the end of 1996 + \item 1998: First feature-complete release, binary-only; original paper + \item 2002: Socket-based communication with Gmsh + \item 2004: Open sourced under GNU GPL +% \item 2005: Eigensolver using Arpack +% \item 2006: Native Windows version + \item 2010: Major refactoring and move to C++ (GetDP 2) + \item 2011: New default solvers based on PETSc and SLEPc + \item 2012: ONELAB interface +% \item 2013: Switch to CMake and field functions for mesh-to-mesh interpolation + \item 2014: Parallel domain decomposition methods (GetDDM) + \item 2015: Macros, run-time variables, Python and Octave interpreters +% \item 2016: Simple Python API and extensible objects (``Append'') + \item 2017: Polynomial and rational nonlinear eigenvalue problems + \item 2018: Curved meshes and enhanced Gmsh support (GetDP 3) + \item 2020: Auto-similar trees of edges + \end{itemize} +\end{frame} + +\begin{frame}[fragile]{GetDP - Basic concepts} + In a \texttt{.pro} file, the weak formulation: Find $u(x)\in H^1_0(\Omega)$ + such that + \begin{equation*} + - \int_\Omega a(x) \nabla u \cdot \nabla u' \,d\Omega = \int_\Omega + f(x) \, u' \,d\Omega, \quad\forall u' \in H^1_0(\Omega) + \end{equation*} + is transcribed as + \begin{center} + \begin{adjustbox}{max totalheight=0.48\textheight} + \begin{lstlisting}[language=pro] +Formulation{ + { Name MyFirstFormulation; Type FemEquation; + Quantity { + { Name u; Type Local; NameOfSpace H1_0; } + } + Equation { + Integral { [ -a[] * Dof{d u}, {d u} ]; + In Omega; Integration I; Jacobian J; } + Integral { [ -f[], {u} ]; In Omega; Integration I; Jacobian J; } + } + } +} + \end{lstlisting} + \end{adjustbox} + \end{center} +\end{frame} + +\begin{frame}{GetDP - Main features} + \begin{itemize} + \item<1-> $H^1$, $H(\text{curl})$, $H(\text{div})$ and $L^2$ bases in 1D, 2D + and 3D; first and second order for all element types; higher order for some + \item<2-> Natural handling of non-local (global) quantities + \item<2-> Circuit coupling + \item<3-> Static, transient, harmonic, multi-harmonic resolutions + \item<3-> Linear and nonlinear eigenvalue problems + \item<4-> Easy coupling of fields and formulations, staggered or monolithic, + e.g. for explicit Jacobian matrices of strongly coupled nonlinear problems + \item<5-> Linear algebra through PETSc/SLEPc + \item<5-> Built-in Python and Octave interpreters + \item<6-> Flexible templating mechanism, allowing one to build a library of + generic formulations + \end{itemize} +\end{frame} + +\subsection{The 10 GetDP objects} + +\begin{frame}{GetDP - Ten objects} + \begin{figure} + \scalebox{0.625}{\input{data_onelab/getdp-struct-box-dash.tex}}\\ + On top, over the blue background, the ``user'' objects that are sufficient to + parameterize a problem once it has been templated + \end{figure} +\end{frame} + +\begin{frame}[fragile]{GetDP - \code{Group}} + \mybox{colbox}{\textwidth}{ + \begin{itemize} + \item Link with the (physical groups) in a mesh + \item Functions on groups: nodes, edges, tree of edges, ... + \end{itemize} + } + \begin{center} + \begin{adjustbox}{max totalheight=0.4\textheight} + \begin{lstlisting}[language=pro] +Group{ + Air = Region[1]; // link with physical group 1 in the mesh + Core = Region[2]; + Gamma = Region[{3, 4}]; + + Omega = Region[{Air, Core}]; // combining groups + + nodes = NodesOf[Omega]; // nodes of the elements in Omega + edgesOfSpanningTree = EdgesOfTreeIn[Omega, StartingOn Gamma]; +} + \end{lstlisting} + \end{adjustbox} + \end{center} +\end{frame} + +\begin{frame}[fragile]{GetDP - \code{Function}} + \mybox{colbox}{\textwidth}{ + \begin{itemize} + \item Piecewise definitions + \item Space-time dependent + \item Physical characteristics, sources, constraints, ... + \end{itemize} + } + \begin{center} + \begin{adjustbox}{max totalheight=0.45\textheight} + \begin{lstlisting}[language=pro] +Function{ + // constants + f = 50; mu0 = 4.e-7 * Pi; + + // piecewise functions + mu[Air] = mu0; + mu[Core] = mu0 + 1/(100 + 100 * ($1)^6); // argument ($1) + + // using a runtime variable + TimeFct[] = Cos[2*Pi*f*$Time] * Exp[-$Time]; +} + \end{lstlisting} + \end{adjustbox} + \end{center} +\end{frame} + +\begin{frame}[fragile]{GetDP - \code{FunctionSpace}} + \mybox{colbox}{\textwidth}{ + \begin{itemize}\itemsep 0.5ex + \item Basis functions (associated with nodes, edges, faces, ...) of various + orders + \item Coupling of fields and potentials % ($\vec{t}$-$\omega$, + % $\vec{h}$-$\phi$, $\vec{a}$-$v$, ...) + \item Definition of global quantities (fluxes, circulations, ...) + \item Essential constraints (boundary and gauge conditions, ...) + \end{itemize} + } + \begin{center} + \begin{adjustbox}{max totalheight=0.43\textheight} + \begin{lstlisting}[language=pro] +FunctionSpace{ + { Name H1; Type Form0; // discrete function space for H1_h + BasisFunction { + { Name wi; NameOfCoef fi; Function BF_Node; // P1 finite elements + Support Omega; Entity NodesOf[All]; } + } + Constraint { + { NameOfCoef fi; EntityType NodesOf; NameOfConstraint Dirichlet; } + } + } +} + \end{lstlisting} + \end{adjustbox} + \end{center} +\end{frame} + +\begin{frame}[fragile]{} + \begin{center} + \includegraphics[height=0.3\textheight]{data_onelab/tri1.png} + \includegraphics[height=0.3\textheight]{data_onelab/tri2.png}\hspace{2em} + \includegraphics[height=0.3\textheight]{data_onelab/qua1.png} + \includegraphics[height=0.3\textheight]{data_onelab/qua2.png}\\[1em] + \begin{adjustbox}{max totalheight=0.55\textheight} + \begin{lstlisting}[language=pro] +// second-order version, using hierarchical functions +FunctionSpace{ + { Name H1; Type Form0; + BasisFunction { + { Name wi; NameOfCoef fi; Function BF_Node; // order 1 + Support Omega; Entity NodesOf[All]; } + { Name wi2; NameOfCoef fi2; Function BF_Node_2E; // order 2 + Support Omega; Entity EdgesOf[All]; } + } + Constraint { + { NameOfCoef fi; EntityType NodesOf; NameOfConstraint Dirichlet; } + { NameOfCoef fi2; EntityType EdgesOf; NameOfConstraint Dirichlet2; } + } + } +} + \end{lstlisting} + \end{adjustbox} + \end{center} +\end{frame} + +\begin{frame}[fragile]{} + \begin{center} + Exact sequence of the de Rham Complex + \begin{equation*} + \xymatrix{ + \Hone[_h]{\Omega} \ar@{->}[r]^-{\GradSymb_h} & + \Hcurl[_h]{\Omega} \ar@{->}[r]^-{\CurlSymb_h} & + \Hdiv[_h]{\Omega} \ar@{->}[r]^-{\DivSymb_h} & + \Ltwo{\Omega} + } + \end{equation*} + preserved at the discrete level using Whitney elements. E.g. for + $\Hcurl[_h]{\Omega}$: + \end{center} + \begin{center} + \begin{adjustbox}{max totalheight=0.45\textheight} + \begin{lstlisting}[language=pro] +FunctionSpace { + { Name Hcurl_h; Type Form1; // discrete Hcurl_h + BasisFunction { + { Name se; NameOfCoef he; Function BF_Edge; + Support Omega; Entity EdgesOf[All]; } + } + Constraint { + { NameOfCoef he; EntityType EdgesOf; NameOfConstraint Dirichlet; } + } + } +} + \end{lstlisting} + \end{adjustbox} + \end{center} + \begin{equation*} + {\bf h} = \sum_{e\in \mathcal{E}(\Omega)} h_e {\bf s}_e \quad{\bf h}\in W^1(\Omega) + \end{equation*} +\end{frame} + +\begin{frame}[fragile]{} + \begin{center} + Coupled Field-Potential + \begin{equation*} + {\bf h} = \sum_{e\in \mathcal{E}({\Omega_c})} h_e {\bf s}_e + \sum_{n\in + \mathcal{N}(\Omega-\Omega_c)} \phi_n {\bf v}_n \quad{\bf h}\in W^1(\Omega) + \end{equation*} + \begin{adjustbox}{max totalheight=0.6\textheight} + \begin{lstlisting}[language=pro] +FunctionSpace { + { Name Hcurl_hphi; Type Form1; + BasisFunction { + { Name se; NameOfCoef he; Function BF_Edge; + Support OmegaC; Entity EdgesOf[All, Not SkinOmegaC]; } + { Name vn; NameOfCoef phin; Function BF_GradNode; + Support OmegaCC; Entity NodesOf[All]; } + { Name vn; NameOfCoef phic; Function BF_GroupOfEdges; + Support OmegaC; Entity GroupsOfEdgesOnNodesOf[SkinOmegaC];} + } + Constraint { + { NameOfCoef he; EntityType EdgesOf; NameOfConstraint h; } + { NameOfCoef phin; EntityType NodesOf; NameOfConstraint phi; } + { NameOfCoef phic; EntityType NodesOf; NameOfConstraint phi; } + } + } +} + \end{lstlisting} + \end{adjustbox} + \end{center} +\end{frame} + +\begin{frame}[fragile]{} + \begin{center} + Topologically Non-Trivial Domains + \end{center} + \begin{center} + \begin{adjustbox}{max totalheight=0.8\textheight} + \begin{lstlisting}[language=pro] +FunctionSpace { + { Name Hcurl_hphi; Type Form1; + BasisFunction { + ... // same as above + { Name sc; NameOfCoef Ic; Function BF_GradGroupOfNodes; + Support ElementsOf[DomainCC, OnOneSideOf SurfaceCut]; + Entity GroupsOfNodesOf[SurfaceCut]; } + { Name sc; NameOfCoef Icc; Function BF_GroupOfEdges; + Support DomainC; Entity GroupsOfEdgesOf[SurfaceCut, + InSupport ElementsOf[SkinDomainC, OnOneSideOf SurfaceCut]]; } + } + GlobalQuantity { + { Name I; Type AliasOf ; NameOfCoef Ic; } + { Name U; Type AssociatedWith; NameOfCoef Ic; } + } + Constraint { + ...// same as above + { NameOfCoef Ic; EntityType GroupsOfNodesOf; NameOfConstraint I; } + { NameOfCoef Icc; EntityType GroupsOfNodesOf; NameOfConstraint I; } + { NameOfCoef U; EntityType GroupsOfNodesOf; NameOfConstraint V; } + } + } + \end{lstlisting} + \end{adjustbox} + \end{center} +\end{frame} + +\begin{frame}[fragile]{} + \begin{center} + Global Quantities + \begin{equation*} + v = \sum_{n\in N_v} v_n s_n + v_f \left (\sum_{n\in N_f} s_n \right) + = \sum_{n\in N_v} v_n s_n + v_f s_f + \end{equation*} + \end{center} + \begin{center} + \begin{adjustbox}{max totalheight=0.55\textheight} + \begin{lstlisting}[language=pro] +FunctionSpace { + { Name Hgrad_v_floating; Type Form0; + BasisFunction { + { Name sn; NameOfCoef vn; Function BF_Node; + Support Domain; Entity NodesOf[All, Not SkinDomainC]; } + { Name sf; NameOfCoef vf; Function BF_GroupOfNodes; + Support Domain; Entity GroupsOfNodesOf[SkinDomainC]; } + } + GlobalQuantity { + { Name GlobalElectricPotential; Type AliasOf; NameOfCoef vf; } + { Name GlobalElectricCharge; Type AssociatedWith; NameOfCoef vf; } + } + } +} + \end{lstlisting} + \end{adjustbox} + \end{center} +\end{frame} + +\begin{frame}[fragile]{GetDP - \code{Constraint}} + \mybox{colbox}{\textwidth}{ + \begin{itemize} + \item Boundary conditions (Dirichlet, periodic) + \item Initial conditions + \item Topology of circuits with lumped elements + \item Other constraints on local and global quantities + \end{itemize} + } + \begin{center} + \begin{adjustbox}{max totalheight=0.35\textheight} + \begin{lstlisting}[language=pro] +Constraint{ + { Name Dirichlet; Type Assign; // boundary conditions + Case { + { Region Surface0; Value 0; } + { Region Surface1; Value 1; } + } + } +} + \end{lstlisting} + \end{adjustbox} + \end{center} +\end{frame} + +\begin{frame}[fragile]{} + \begin{center} + Network constraints and circuit coupling + \end{center} + \begin{center} + \begin{adjustbox}{max totalheight=0.4\textheight} + \begin{lstlisting}[language=pro] +Constraint{ + { Name ElectricalCircuit; Type Network; + Case Circuit { + { Region E1; Branch {1, 2}; } + { Region R1; Branch {1, 3}; } + { Region L1; Branch {3, 2}; } + { Region C1; Branch {1, 2}; } + } + } +} + \end{lstlisting} + \end{adjustbox} + \end{center} + \begin{center} + \scalebox{0.75}{\input{data_onelab/getdp-rlccircuit.tex}} + \end{center} +\end{frame} + + +\begin{frame}[fragile]{GetDP - \code{Formulation}} + \bigskip + \mybox{colbox}{\textwidth}{ + \begin{itemize}\itemsep 0.ex + \item Equation builder, with symbolic expression of weak forms + \item Involves local, global and integral quantities based on function + spaces + \end{itemize} + } + \begin{center} + \begin{adjustbox}{max totalheight=0.5\textheight} + \begin{lstlisting}[language=pro] +Formulation{ + { Name Maxwell_e; Type FemEquation; + Quantity { + { Name e; Type Local; NameOfSpace Hcurl_h; } + } + Equation { + Integral { [ 1/mu[] * Dof{Curl e}, {Curl e} ]; + In Omega; Jacobian Jac1; Integration Int1; } + Integral { DtDt [ epsilon[] * Dof{e}, {e} ]; + In Omega; Jacobian Jac1; Integration Int1; } + } + } +} + \end{lstlisting} + \end{adjustbox}\\ + Find $\vec{e}\in\Hcurl[_h]{\Omega}$ such that\\ + $\ivol{\mu^{-1}\Curl{\vec{e}}}{\Curl{\vec{e}'}} + + \partial_t^2\ivol{\epsilon\vec{e}}{\vec{e}'} = 0,\quad + \forall\vec{e'}\in\Hcurl[_h]{\Omega}$ + \end{center} +\end{frame} + +\begin{frame}[fragile,plain]{} + \begin{center} + \begin{adjustbox}{max totalheight=0.9\textheight} + \begin{lstlisting}[language=pro] +Formulation { // handle complexity with loops, etc. + { Name OSRC; Type FemEquation; + Quantity { + { Name psi; Type Local; NameOfSpace Hdiv_psi; } + { Name w; Type Local; NameOfSpace Hdiv_w; } + For j In{1:N} + { Name phi~{j}; Type Local; NameOfSpace Hdiv_phi~{j}; } + EndFor + { Name nxh; Type Local; NameOfSpace Hdiv_nxh; } + } + Equation { + Integral { [ Z0 * OSRC_C0[]{N, th} * Dof{nxh}, {nxh} ]; + In Gama; Jacobian JSur; Integration I1; } + Integral { [ -{psi}, {nxh} ]; + In Gama; Jacobian JSur; Integration I1; } + For j In{1:N} + Integral { [ Z0 * OSRC_Aj[]{j, N, th} * Dof{phi~{j}}, {nxh} ]; + In Gama; Jacobian JSur; Integration I1; } + Integral { [ Dof{phi~{j}}, {phi~{j}} ]; + In Gama; Jacobian JSur; Integration I1; } + Integral { [ -OSRC_Bj[]{j, N, th} / keps[]^2 * Dof{d phi~{j}}, {d phi~{j}} ]; + In Gama; Jacobian JSur; Integration I1; } + Integral { [ 1 / keps[]^2 * Dof{d nxh}, {d phi~{j}} ]; + In Gama; Jacobian JSur; Integration I1; } + EndFor + } + } +} + \end{lstlisting} + \end{adjustbox} + \end{center} +\end{frame} + +\begin{frame}[fragile]{GetDP - \code{Jacobian}} + \mybox{colbox}{\textwidth}{ + \begin{itemize} + \item Mapping from reference to real space + \item Geometrical transformations (axisymmetry, infinite domains, ...) + \end{itemize} + } + \begin{center} + \begin{adjustbox}{max totalheight=0.35\textheight} + \begin{lstlisting}[language=pro] +Jacobian{ + { Name Jac1; + Case { // piecewise defined on groups + { Region OmegaInf; Jacobian VolSphShell{Rint, Rext}; } + { Region OmegaAxi; Jacobian VolAxi; } + { Region All; Jacobian Vol; } + } + } +} + \end{lstlisting} + \end{adjustbox} + \end{center} +\end{frame} + +\begin{frame}[fragile]{GetDP - \code{Integration}} + \mybox{colbox}{\textwidth}{ + \begin{itemize} + \item Various numeric and analytic integration methods + \item Criterion-based selection + \end{itemize} + } + \begin{center} + \begin{adjustbox}{max totalheight=0.5\textheight} + \begin{lstlisting}[language=pro] +Integration { + { Name Int1; Criterion Test[]; + Case { + { Type Gauss; + Case { + { GeoElement Triangle; NumberOfPoints 3; } + { GeoElement Tetrahedron; NumberOfPoints 3; } + } + } + { Type Analytic; } + } + } +} + \end{lstlisting} + \end{adjustbox} + \end{center} +\end{frame} + +\begin{frame}[fragile]{GetDP - \code{Resolution}} + \bigskip + \mybox{colbox}{\textwidth}{ + \begin{itemize}\itemsep 0ex + \item Description of the sequence of operations to solve the problem + \item Time stepping, nonlinear iterations, ... + \item Coupled problems (e.g.\ magneto-thermal coupling) + \item Link various resolution steps (e.g.\ pre-computation of source fields) + \end{itemize} + } + \begin{center} + \begin{adjustbox}{max totalheight=0.5\textheight} + \begin{lstlisting}[language=pro] +Resolution{ + { Name Parabolic; + System { + { Name A; NameOfFormulation Parabolic; } + } + Operation{ + InitSolution[A]; + TimeLoopTheta[tmin, tmax, dt, 1]{ + Generate[A]; Solve[A]; If[Save[]]{ SaveSolution[A]; } + } + } + } + \end{lstlisting} + \end{adjustbox} + \end{center} +\end{frame} + +\begin{frame}[fragile]{GetDP - \code{PostProcessing}} + \mybox{colbox}{\textwidth}{ + \begin{itemize} + \item ``Front-end'' to computational data + \item Piecewise definition of any post-processing quantity of interest + \item Local or integral evaluation + \end{itemize} + } + \begin{center} + \begin{adjustbox}{max totalheight=0.5\textheight} + \begin{lstlisting}[language=pro] +PostProcessing { + { Name magfields; NameOfFormulation Dynamic; + Quantity { + { Name b; + Value { + Local { [ -mu[] * {Grad phi} ]; In OmegaCC; } + Local { [ mu[] * {h} ]; In OmegaC; } + } + } + } +} + \end{lstlisting} + \end{adjustbox} + \end{center} +\end{frame} + +\begin{frame}[fragile]{GetDP - \code{PostOperation}} + \mybox{colbox}{\textwidth}{ + \begin{itemize} + \item Evaluation of post-processing quantities (e.g.\ maps, sections, local + or global evaluation, ...) + \item Various output formats (e.g.\ space or time oriented, text, binary, + ...) + \item Output to disk or to memory as ONELAB parameters or Gmsh + post-processing views + \end{itemize} + } + \begin{center} + \begin{adjustbox}{max totalheight=0.35\textheight} + \begin{lstlisting}[language=pro] +PostOperation { + { Name Map_b; NameOfPostProcessing magfields; + Operation { + Print[ b, OnElementsOf Omega, File "b.pos", Format Gmsh ]; + Print[ b, OnLine {{0, 0, 0} {1, 0, 0}} {100}, File "b.txt" ]; + } + } +} + \end{lstlisting} + \end{adjustbox} + \end{center} +\end{frame} + +\subsection{Recent developments} + +\begin{frame}{GetDP - Recent developments} + \begin{itemize} +% \item Support for curved meshes + \item Optimized Schwarz domain decomposition methods + \item Vector energy-based hysteresis models + \item Sensitivity calculations for shape and topology optimization + \item Computational homogenization + \item 3D moving band with symmetries + \item Nonlinear eigenvalue problems + \end{itemize} +\end{frame} + +\begin{frame}{GetDP - Optimized Schwarz DDM} + \begin{figure} + \includegraphics[width=0.42\textwidth]{data_onelab/submarine.png} + \includegraphics[width=0.45\textwidth]{data_onelab/cobraSol_a0.pdf}\\[-0.5ex] + \includegraphics[width=0.32\textwidth]{data_onelab/falcon_field.png} + \includegraphics[width=0.55\textwidth]{data_onelab/marmousi_u.pdf}\\ + Massively parallel, distributed (MPI) optimized Schwarz domain decomposition + methods for high-frequency wave scattering + \end{figure} + {\hfill\footnotesize [B. Thierry et al., CPC 2016]} +\end{frame} + +\begin{frame}{GetDP - Energy-based hysteresis models} + \begin{figure} + \begin{columns}[c] + \begin{column}{0.5\textwidth} + \includegraphics[width=\textwidth]{hysteresis_1.png} + \end{column} + \begin{column}{0.35\textwidth} + \begin{center} + \includegraphics[width=0.8\textwidth]{hysteresis_3.png}\\ + \includegraphics[width=\textwidth]{hysteresis_2.png} + \end{center} + \end{column} + \end{columns} + \end{figure} + {\hfill\footnotesize [K. Jacques et al., 2018]} +\end{frame} + +\begin{frame}{GetDP - Sensitivities and optimization} + \begin{figure} + \includegraphics[width=0.5\textwidth]{data_onelab/opti_1.png} + \includegraphics[width=0.45\textwidth]{data_onelab/opti_2.png}\\[1ex] + Design sensitivity analysis for combined topology and shape optimization, + based on the Lie derivative\\ + \end{figure} + {\hfill\footnotesize [E. Kuci et al., SMO 2019]} +\end{frame} + +\begin{frame}{GetDP - Computational homogenization} + \begin{figure} + \begin{columns}[c] + \begin{column}{0.5\textwidth} + \begin{center} + \includegraphics[width=\textwidth]{hmm_1.png}\\ + \includegraphics[width=0.8\textwidth]{hmm_3.png} + \end{center} + \end{column} + \begin{column}{0.5\textwidth} + \includegraphics[width=\textwidth]{hmm_2.png} + \end{column} + \end{columns} + \bigskip + Massively parallel (MPI) Heterogeneous Multi-scale Method (HMM) for 3D + lamination stacks + \end{figure} + {\hfill\footnotesize [I. Niyonzima et al, 2021]} +\end{frame} + +\begin{frame}{GetDP - 3D moving band} + \begin{figure} + \includegraphics[width=0.45\textwidth]{sliding_1.png} + \includegraphics[width=0.45\textwidth]{sliding_2.png}\\ + Auto-similar trees for efficient and accurate 3D sliding surfaces + \end{figure} +\end{frame} + +\begin{frame}{GetDP - Nonlinear eigenvalue problems} + \begin{figure} + \includegraphics[width=0.6\textwidth]{nleig.png}\\ + General polynomial and rational eigenvalue problems for the analysis of + frequency-dispersive photonic open structures + \end{figure} + {\hfill\footnotesize [G. Dem\'esy et al, CPC 2020]} +\end{frame} + +\section{Tying it all together with ONELAB} + +\begin{frame} + \begin{center} + \textbf{\Large Tying it all together with ONELAB} + \end{center} +\end{frame} + +\begin{frame}{ONELAB - Context} + \begin{itemize} + \item Economic + \begin{itemize} + \item Growing importance of numerical simulation in education and industry + \item Prohibitive cost of commercial packages for a significant subset of + potential users (SMEs, education, occasional use) + \end{itemize} + \item Scientific + \begin{itemize} + \item High quality of free/open-source software developed in universities and + research centers + \item Sometimes ahead of commercial equivalents + \end{itemize} + \item Practical + \begin{itemize} + \item No user-friendly interface and/or sparse documentation (e.g. missing + complete examples) for many (most?) open source Finite Element Analysis + (FEA) codes + \end{itemize} + \end{itemize} +\end{frame} + +\begin{frame}{ONELAB - Objective} + Develop an interface for integrating FEA software: + \begin{itemize} + \item allowing to share parameters between any code + \item with an intuitive GUI allowing new users to get started and guided into + the world of FE modeling---but with the possibility to construct + sophisticated, upgradable, multi-code, multi-platform scripts for the + specialized user + \item and with the possibility to construct application-specific tools for + both education and industry + \end{itemize} +\end{frame} + +\begin{frame}{ONELAB - Design} + \begin{itemize} + \item Don't reimplement, interface the existing + \item Make it as small, lightweight and as easy to maintain as possible (no + solver-dependent code in the interface) + \item Make it easy to provide templates, with interactive parameter + modification + \item ONELAB role $=$ data centralization, modification and redispatching + \item Issues of completeness and consistency of the parameter set are + completely dealt with on the client (e.g. FEA software) side + \end{itemize} +\end{frame} + +\begin{frame}{ONELAB - Design} + \begin{itemize} + \item Client-server: + \begin{itemize} + \item Clients: CAD kernels, meshers, solvers, post-processors + \item Server: Gmsh + database + \end{itemize} + \item Abstract interface: + \begin{itemize} + \item The server has no a priori knowledge of the clients (no meta-language + or exchange file format) + \item The client communicates with the server to define what information + should be exchanged + \item Information is exchanged either directly in-memory, or through TCP/IP + or Unix sockets + \end{itemize} + \end{itemize} +\end{frame} + +% \begin{frame}{ONELAB - Implementation} +% \begin{itemize} +% \item Abstract interface to physical properties, constraints \& code drivers: +% \begin{itemize} +% \item Reference server in C++, clients in C++ or Python +% \item Exchange of parameters through TCP/IP, Unix sockets or in-memory +% \end{itemize} +% \item ``Native'' clients use C++ or Python directly +% \begin{itemize} +% \item Gmsh, GetDP, Octave +% \end{itemize} +% \item ``Non-native'' clients use Python, by instrumenting their input files +% \begin{itemize} +% \item Elmer, OpenFOAM, Code_Aster, Abaqus, Gnuplot, ... +% \end{itemize} +% \end{itemize} +% \end{frame} + +\begin{frame}[fragile]{ONELAB - Sharing parameters} + Sharing parameter through ONELAB in \texttt{.geo} and \texttt{.pro} files is + as simple as: + \begin{lstlisting}[language=geo,basicstyle=\ttfamily\bfseries\footnotesize] + DefineConstant[ N = { 50, Name "Input/Number of steps"} ]; + \end{lstlisting} + + \pause + In Python one can use the \texttt{onelab.py} module: + \begin{lstlisting}[language=py,basicstyle=\ttfamily\bfseries\footnotesize] + c = onelab.client() + N = c.defineNumber('Input/Number of steps', value=50) + \end{lstlisting} + \pause + Or one can directly use the Gmsh API, with JSON encoded data: + \begin{lstlisting}[language=py,basicstyle=\ttfamily\bfseries\footnotesize] + gmsh.onelab.set("""[ + { + "type":"number", + "name":"Input/Number of steps", + "values":[50] + } + ]""") + N = gmsh.onelab.getNumber('Input/Number of steps') + \end{lstlisting} +\end{frame} + +\begin{frame}{ONELAB - Tutorial} + \bigskip + The best way to get started is the + \href{https://gitlab.onelab.info/doc/models/-/wikis/home}{ONELAB tutorial}: + \begin{itemize} + \item Examples of increasing complexity using both Gmsh and GetDP + \item Used for teaching the ``Modeling and design of electromagnetic + systems'' class at ULi\`ege since 2018 + \end{itemize} + \begin{figure} + \includegraphics[width=0.9\textwidth]{data_onelab/onelab_tutorial.png} + \end{figure} +\end{frame} + +\begin{frame}[fragile]{ONELAB - Laplace example} + \begin{figure} + \includegraphics[width=0.75\textwidth]{data_onelab/onelab_microstrip.png}\\[1ex] + Open \href{https://gitlab.onelab.info/doc/tutorials/-/wikis/Electrostatics} + {\texttt{tutorials/Electrostatics/microstrip.pro}} with Gmsh + \end{figure} +\end{frame} + +\begin{frame}[fragile]{ONELAB - Multiphysics example} + \begin{figure} + \includegraphics[width=0.75\textwidth]{data_onelab/onelab_magnetometer.png}\\[1ex] + Open \href{https://gitlab.onelab.info/doc/models/-/wikis/Magnetometer} + {\texttt{models/Magmetomater/magnetometer.pro}} with Gmsh + \end{figure} +\end{frame} + +\begin{frame}{ONELAB - Going further} + \begin{itemize} + \item<1-> In addition to the tutorial, various models are available on + \url{https://gitlab.onelab.info/doc/models} + \item<2-> Shape and topology optimization examples are also available on + \url{https://gitlab.onelab.info/conveks/tutorials} + \item<3-> ONELAB has proved to be very useful in building application-specific + codes for industry + \begin{itemize} + \item<3-> Transformer design (Gmsh+GetDP+LTSpice), filter design + (Gmsh+GetDP), busbar design (Gmsh+GetDP), behavior of structures subjected + to fire (Gmsh+Safir), thermal laser skin treatment (Gmsh+GetDP+Elmer), + building resistance (Gmsh+Code\_Aster), ... + \item<4-> Using the Gmsh API allows one to create dedicated graphical user + interfaces, with advanced interactivity for the selection of boundary + conditions, specification of material properties, etc. + \end{itemize} + \end{itemize} +\end{frame} + +\section{Conclusions and perspectives} + +\begin{frame} + \begin{center} + \textbf{\Large Conclusions and perspectives} + \end{center} +\end{frame} + +\begin{frame}{Conclusions and perspectives} + \begin{itemize} + \item<1-> Overview of Gmsh, GetDP and ONELAB + \begin{itemize} + \item<2-> Modelling freedom (but some coding is necessary) + \item<2-> Accessibility, reproducibility and interoperability (free and open source) + \item<2-> Easy installation (binary distribution) + \item<2-> Encapsulated and scriptable + \item<3-> Successfully used both in academia and in industry + \item<3-> More ``Swiss Army knife'' than ``bazooka'' + \item<4-> Some open source alternatives: deal.II, dune-fem, FEMM, FEniCS, + FreeFEM, NGSolve, Elmer, MFEM, ... + \end{itemize} + \item<5-> Many exciting developments in the pipeline: + \begin{itemize} + \item<5-> Meshing: improved curved mesh generation, hex-dominant meshes, + boundary layers, ... + \item<6-> Solver: next-generation assembler GmshFEM, domain decomposition + framework GmshDDM and full wave inversion code GmshFWI; GPU acceleration, + ... + \end{itemize} + \end{itemize} +\end{frame} + +\begin{frame}{Post-Scriptum} + \begin{columns}[b] + \begin{column}{0.8\textwidth} + \begin{itemize} + \item<1-> To download the ONELAB software bundle, including Gmsh and + GetDP: \url{https://onelab.info} \vspace{2em} + \item<2-> For fun, go to the + \begin{itemize} + \item \href{https://play.google.com/store/apps/details?id=org.geuz.onelab} + {Google Play Store} (if you are on Android) + \item \href{https://itunes.apple.com/us/app/onelab/id845930897}{Apple + AppStore} (if you are on iOS) + \end{itemize} + and download the \textbf{ONELAB app}: it contains a full-featured + version of Gmsh \& GetDP\\[1ex] + ... so you can impress your friends by solving finite element problems + on your smartphone! + \end{itemize} + \end{column} + \begin{column}{0.17\textwidth} + \only<2>{\includegraphics[width=\textwidth]{data_onelab/ios_onelab.png}} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{} + \begin{center} + \vspace{5em} + {\Large Thanks for your attention}\\[4em] + {\small \url{https://people.montefiore.ulg.ac.be/geuzaine}}\\[2em] + {\small \Letter \hspace{.5em} cgeuzaine@uliege.be} + \end{center} +\end{frame} + +\end{document}