diff --git a/doc/manual/manual-gettingstarted.tex b/doc/manual/manual-gettingstarted.tex index c2912282a..383b48e38 100644 --- a/doc/manual/manual-gettingstarted.tex +++ b/doc/manual/manual-gettingstarted.tex @@ -1,462 +1,466 @@ \chapter{Getting Started} \section{Downloading the Code} The \akantu source code can be requested using the form accessible at the URL \url{http://lsms.epfl.ch/akantu}. There, you will be asked to accept the LGPL license terms. \section{Compiling \akantu} \akantu is a \code{cmake} project, so to configure it, you can either follow the usual way: \begin{command} > cd akantu > mkdir build > cd build > ccmake .. [ Set the options that you need ] > make > make install \end{command} \noindent Or, use the \code{Makefile} we added for your convenience to handle the \code{cmake} configuration \begin{command} > cd akantu > make config > make > make install \end{command} \noindent All the \akantu options are documented in Appendix \ref{app:package-dependencies}. \section{Writing a \texttt{main} Function\label{sect:common:main}} \label{sec:writing_main} First of all, \akantu needs to be initialized. The memory management included in the core library handles the correct allocation and de-allocation of vectors, structures and/or objects. Moreover, in parallel computations, the initialization procedure performs the communication setup. This is achieved by a pair of functions (\code{initialize} and \code{finalize}) that are used as follows: \begin{cpp} #include "aka_common.hh" #include "..." using namespace akantu; int main(int argc, char *argv[]) { initialize("input_file.dat", argc, argv); // your code ... finalize(); } \end{cpp} The \code{initialize} function takes the text inpute file and the program parameters which can be parsed by \akantu in due form (see \ref{sect:parser}). Obviously it is necessary to include all files needed in main. In this manual all provided code implies the usage of \code{akantu} as namespace. \section{Creating and Loading a Mesh\label{sect:common:mesh}} In its current state, \akantu supports three types of meshes: Gmsh~\cite{gmsh}, Abaqus~\cite{abaqus} and Diana~\cite{diana}. Once a \code{Mesh} object is created with a given spatial dimension, it can be filled by reading a mesh input file. The method \code{read} of the class \code{Mesh} infers the mesh type from the file extension. If a non-standard file extension is used, the mesh type has to be specified. \begin{cpp} UInt spatial_dimension = 2; Mesh mesh(spatial_dimension); // Reading Gmsh files mesh.read("my_gmsh_mesh.msh"); mesh.read("my_gmsh_mesh", _miot_gmsh); // Reading Abaqus files mesh.read("my_abaqus_mesh.inp"); mesh.read("my_abaqus_mesh", _miot_abaqus); // Reading Diana files mesh.read("my_diana_mesh.dat"); mesh.read("my_diana_mesh", _miot_diana); \end{cpp} The Gmsh reader adds the geometrical and physical tags as mesh data. The physical values are stored as a \code{UInt} data called \code{tag\_0}, if a string name is provided it is stored as a \code{std::string} data named \code{physical\_names}. The geometrical tag is stored as a \code{UInt} data named \code{tag\_1}. The Abaqus reader stores the \code{ELSET} in ElementGroups and the \code{NSET} in NodeGroups. The material assignment can be retrieved from the \code{std::string} mesh data named \code{abaqus\_material}. % \akantu supports meshes generated with Gmsh~\cite{gmsh}, a free % software available at \url{http://geuz.org/gmsh/} where a detailed % documentation can be found. Consequently, this manual will not provide % Gmsh usage directions. Gmsh outputs meshes in \code{.msh} format that can be read % by \akantu. In order to import a mesh, it is necessary to create % a \code{Mesh} object through the following function calls: % \begin{cpp} % UInt spatial_dimension = 2; % Mesh mesh(spatial_dimension); % \end{cpp} % The only parameter that has to be specified by the user is the spatial % dimension of the problem. Now it is possible to read a \code{.msh} file with % a \code{MeshIOMSH} object that takes care of loading a mesh to memory. % This step is carried out by: % \begin{cpp} % mesh.read("square.msh"); % \end{cpp} % where the \code{MeshIOMSH} object is first created before being % used to read the \code{.msh} file. The mesh file name as well as the \code{Mesh} % object must be specified by the user. % The \code{MeshIOMSH} object can also write mesh files. This feature % is useful to save a mesh that has been modified during a % simulation. The \code{write} method takes care of it: % \begin{cpp} % mesh_io.write("square_modified.msh", mesh); % \end{cpp} % which works exactly like the \code{read} method. % \akantu supports also meshes generated by % DIANA (\url{http://tnodiana.com}), but only in reading mode. A similar % procedure applies where the only % difference is that the \code{MeshIODiana} object should be used % instead of the \code{MeshIOMSH} one. Additional mesh readers can be % introduced into \akantu by coding new \code{MeshIO} classes. \section{Using \texttt{Arrays}} Data in \akantu can be stored in data containers implemented by the \code{Array} class. In its most basic usage, the \code{Array} class implemented in \akantu is similar to the \code{vector} class of the Standard Template Library (STL) for C++. A simple \code{Array} containing a sequence of \code{nb\_element} values (of a given type) can be generated with: \begin{cpp} Array example_array(nb_element); \end{cpp} where \code{type} usually is \code{Real}, \code{Int}, \code{UInt} or \code{bool}. Each value is associated to an index, so that data can be accessed by typing: \begin{cpp} auto & val = example_array(index) \end{cpp} \code{Arrays} can also contain tuples of values for each index. In that case, the number of components per tuple must be specified at the \code{Array} creation. For example, if we want to create an \code{Array} to store the coordinates (sequences of three values) of ten nodes, the appropriate code is the following: \begin{cpp} UInt nb_nodes = 10; UInt spatial_dimension = 3; Array position(nb_nodes, spatial_dimension); \end{cpp} In this case the $x$ position of the eighth node number will be given by \code{position(7, 0)} (in C++, numbering starts at 0 and not 1). If the number of components for the sequences is not specified, the default value of 1 is used. Here is a list of some basic operations that can be performed on \code{Array}: \begin{itemize} \item \code{resize(size)} change the size of the \code{Array}. \item \code{clear()} set all entries of the \code{Array} to zero. \item \code{set(t)} set all entries of the \code{Array} to \code{t}. \item \code{copy(const Array $\&$ other)} copy another \code{Array} into the current one. The two \code{Array} should have the same number of components. \item \code{push$\_$back(tuple)} append a tuple with the correct number of components at the end of the \code{Array}. \item \code{erase(i) erase the value at the i-th position.} \item \code{find(value)} search \code{value} in the current \code{Array}. Return position index of the first occurence or $-1$ if not found. \item \code{storage()} Return the address of the allocated memory of the \code{Array}. \end{itemize} \subsection{\texttt{Arrays} iterators} It is very common in \akantu to loop over arrays to perform a specific treatment. This ranges from geometric calculation on nodal quantities to tensor algebra (in constitutive laws for example). The \code{Array} object has the possibility to request iterators in order to make the writing of loops easier and enhance readability. For instance, a loop over the nodal coordinates can be performed like: \begin{cpp} //accessing the nodal coordinates Array (spatial_dimension components) const auto & nodes = mesh.getNodes(); //creating the iterators auto it = nodes.begin(spatial_dimension); auto end = nodes.end(spatial_dimension); for (; it != end; ++it){ const auto & coords = (*it); //do what you need .... } \end{cpp} In that example, each \code{coords} is a \code{Vector} containing geometrical array of size \code{spatial\_dimension} and the iteration is conveniently performed by the \code{Array} iterator. With the switch to \code{c++14} this can be also written as \begin{cpp} //accessing the nodal coordinates Array (spatial_dimension components) const auto & nodes = mesh.getNodes(); for (const auto & coords : make_view(nodes, spatial_dimension) { //do what you need .... } \end{cpp} The \code{Array} object is intensively used to store second order tensor values. In that case, it should be specified that the returned object type is a matrix when constructing the iterator. This is done when calling the \code{begin} function. For instance, assuming that we have a \code{Array} storing stresses, we can loop over the stored tensors by: \begin{cpp} //creating the iterators auto it = stresses.begin(spatial_dimension, spatial_dimension); auto end = stresses.end(spatial_dimension, spatial_dimension); for (; it != end; ++it){ Matrix & stress = (*it); //do what you need .... } \end{cpp} In that last example, the \code{Matrix} objects are \code{spatial\_dimension} $\times$ \code{spatial\_dimension} matrices. The light objects \code{Matrix} and \code{Vector} can be used and combined to do most common linear algebra. If the number of component is 1, it is possible to use a scalar\_iterator rather than the vector/matrix one. In general, a mesh consists of several kinds of elements. Consequently, the amount of data to be stored can differ for each element type. The straightforward example is the connectivity array, namely the sequences of nodes belonging to each element (linear triangular elements have fewer nodes than, say, rectangular quadratic elements etc.). A particular data structure called \code{ElementTypeMapArray} is provided to easily manage this kind of data. It consists of a group of \code{Arrays}, each associated to an element type. The following code can retrieve the \code{ElementTypeMapArray} which stores the connectivity arrays for a mesh: \begin{cpp} const ElementTypeMapArray & connectivities = mesh.getConnectivities(); \end{cpp} Then, the specific array associated to a given element type can be obtained by \begin{cpp} const Array & connectivity_triangle = connectivities(_triangle_3); \end{cpp} where the first order 3-node triangular element was used in the presented piece of code. \subsection{Vector \& Matrix} The \code{Array} iterators as presented in the previous section can be shaped as \code{Vector} or \code{Matrix}. This objects represent $1^{st}$ and $2^{nd}$ order tensors. As such they come with some functionalities that we will present a bit more into detail in this here. \subsubsection{\texttt{Vector}} \begin{enumerate} \item Accessors: \begin{itemize} \item \code{v(i)} gives the $i^{th}$ component of the vector \code{v} \item \code{v[i]} gives the $i^{th}$ component of the vector \code{v} \item \code{v.size()} gives the number of component \end{itemize} \item Level 1: (results are scalars) \begin{itemize} \item \code{v.norm()} returns the geometrical norm ($L_2$) \item \code{v.norm()} returns the $L_N$ norm defined as $\left(\sum_i |\code{v(i)}|^N\right)^{1/N}$. N can take any positive integer value. There are also some particular values for the most commonly used norms, \code{L\_1} for the Manhattan norm, \code{L\_2} for the geometrical norm and \code{L\_inf} for the norm infinity. \item \code{v.dot(x)} return the dot product of \code{v} and \code{x} \item \code{v.distance(x)} return the geometrical norm of $\code{v} - \code{x}$ \end{itemize} \item Level 2: (results are vectors) \begin{itemize} \item \code{v += s}, \code{v -= s}, \code{v *= s}, \code{v /= s} those are element-wise operators that sum, substract, multiply or divide all the component of \code{v} by the scalar \code{s} \item \code{v += x}, \code{v -= x} sums or substracts the vector \code{x} to/from \code{v} \item \code{v.mul(A, x, alpha)} stores the result of $\alpha \mat{A} \vec{x}$ in \code{v}, $\alpha$ is equal to 1 by default \item \code{v.solve(A, b)} stores the result of the resolution of the system $\mat{A} \vec{x} = \vec{b}$ in \code{v} \item \code{v.crossProduct(v1, v2)} computes the cross product of \code{v1} and \code{v2} and stores the result in \code{v} \end{itemize} \end{enumerate} \subsubsection{\texttt{Matrix}} \begin{enumerate} \item Accessors: \begin{itemize} \item \code{A(i, j)} gives the component $A_{ij}$ of the matrix \code{A} \item \code{A(i)} gives the $i^{th}$ column of the matrix as a \code{Vector} \item \code{A[k]} gives the $k^{th}$ component of the matrix, matrices are stored in a column major way, which means that to access $A_{ij}$, $k = i + j M$ \item \code{A.rows()} gives the number of rows of \code{A} ($M$) \item \code{A.cols()} gives the number of columns of \code{A} ($N$) \item \code{A.size()} gives the number of component in the matrix ($M \times N$) \end{itemize} \item Level 1: (results are scalars) \begin{itemize} \item \code{A.norm()} is equivalent to \code{A.norm()} \item \code{A.norm()} returns the $L_N$ norm defined as $\left(\sum_i\sum_j |\code{A(i,j)}|^N\right)^{1/N}$. N can take any positive integer value. There are also some particular values for the most commonly used norms, \code{L\_1} for the Manhattan norm, \code{L\_2} for the geometrical norm and \code{L\_inf} for the norm infinity. \item \code{A.trace()} return the trace of \code{A} \item \code{A.det()} return the determinant of \code{A} \item \code{A.doubleDot(B)} return the double dot product of \code{A} and \code{B}, $\mat{A}:\mat{B}$ \end{itemize} \item Level 3: (results are matrices) \begin{itemize} \item \code{A.eye(s)}, \code{Matrix::eye(s)} fills/creates a matrix with the $s\mat{I}$ with $\mat{I}$ the identity matrix \item \code{A.inverse(B)} stores $\mat{B}^{-1}$ in \code{A} \item \code{A.transpose()} returns $\mat{A}^{t}$ \item \code{A.outerProduct(v1, v2)} stores $\vec{v_1} \vec{v_2}^{t}$ in \code{A} \item \code{C.mul(A, B, alpha)}: stores the result of the product of \code{A} and code{B} time the scalar \code{alpha} in \code{C}. \code{t\_A} and \code{t\_B} are boolean defining if \code{A} and \code{B} should be transposed or not. \begin{tabular}{ccl} \toprule \code{t\_A} & \code{t\_B} & result \\ \midrule false & false & $\mat{C} = \alpha \mat{A} \mat{B}$\\ false & true & $\mat{C} = \alpha \mat{A} \mat{B}^t$\\ true & false & $\mat{C} = \alpha \mat{A}^t \mat{B}$\\ true & true & $\mat{C} = \alpha \mat{A}^t \mat{B}^t$\\ \bottomrule \end{tabular} \item \code{A.eigs(d, V)} this method computes the eigenvalues and eigenvectors of \code{A} and store the results in \code{d} and \code{V} such that $\code{d(i)} = \lambda_i$ and $\code{V(i)} = \vec{v_i}$ with $\mat{A}\vec{v_i} = \lambda_i\vec{v_i}$ and $\lambda_1 > ... > \lambda_i > ... > \lambda_N$ \end{itemize} \end{enumerate} \subsubsection{\texttt{Tensor3}} Accessors: \begin{itemize} \item \code{t(i, j, k)} gives the component $T_{ijk}$ of the tensor \code{t} \item \code{t(k)} gives the $k^{th}$ two-dimensional tensor as a \code{Matrix} \item \code{t[k]} gives the $k^{th}$ two-dimensional tensor as a \code{Matrix} \end{itemize} \section{Manipulating group of nodes and/or elements\label{sect:common:groups}} \akantu provides the possibility to manipulate subgroups of elements and nodes. Any \code{ElementGroup} and/or \code{NodeGroup} must be managed by a \code{GroupManager}. Such a manager has the role to associate group objects to names. This is a useful feature, in particular for the application of the boundary conditions, as will be demonstrated in section \ref{sect:smm:boundary}. To most general group manager is the \code{Mesh} class which inheritates from the \code{GroupManager} class. For instance, the following code shows how to request an element group to a mesh: \begin{cpp} // request creation of a group of nodes NodeGroup & my_node_group = mesh.createNodeGroup("my_node_group"); // request creation of a group of elements ElementGroup & my_element_group = mesh.createElementGroup("my_element_group"); /* fill and use the groups */ \end{cpp} \subsection{The \texttt{NodeGroup} object} A group of nodes is stored in \code{NodeGroup} objects. They are quite simple objects which store the indexes of the selected nodes in a \code{Array}. Nodes are selected by adding them when calling \code{NodeGroup::add}. For instance you can select nodes having a positive $X$ coordinate with the following code: \begin{cpp} const auto & nodes = mesh.getNodes(); auto & group = mesh.createNodeGroup("XpositiveNode"); for (auto && data : enumerate(make_view(nodes, spatial_dimension))){ auto node = std::get<0>(data); const auto & position = std::get<1>(data); if (position(0) > 0) group.add(node); } \end{cpp} \subsection{The \texttt{ElementGroup} object} A group of elements is stored in \code{ElementGroup} objects. Since a group can contain elements of various types the \code{ElementGroup} object stores indexes in a \code{ElementTypeMapArray} object. Then elements can be added to the group by calling \code{addElement}. For instance, selecting the elements for which the barycenter of the nodes has a positive $X$ coordinate can be made with: \begin{cpp} auto & group = mesh.createElementGroup("XpositiveElement"); Vector barycenter(spatial_dimension); for(auto type : mesh.elementTypes()){ UInt nb_element = mesh.getNbElement(type); for(UInt e = 0; e < nb_element; ++e) { Element element{type, e, _not_ghost}; mesh.getBarycenter(element, barycenter); if (barycenter(_x) > 0.) group.add(element); } } \end{cpp} \section{Compiling your simulation} -The easiest way it to create a \code{cmake} project. The minimum \code{CMakeLists.txt} file would look like +The easiest way to compile your simulation is to create a \code{cmake} project by putting all your code in some directory of your choosing. Then, make sure that you have \code{cmake} installed and create a \code{CMakeLists.txt} file. An example of a minimal \code{CMakeLists.txt} file would look like this: \begin{cmake} project(my_simu) cmake_minimum_required(VERSION 3.0.0) find_package(Akantu REQUIRED) - + add_akantu_simulation(my_simu my_simu.cc) \end{cmake} +% +Then create a directory called \code{build} and inside it execute \code{ccmake ..} which opens a configuration screen. If you installed \akantu in a standard directory such as \code{/usr/local} (using \code{make install}), you should be able to compile by hitting the \code{c} key, setting \code{CMAKE\textunderscore{}BUILD\textunderscore{}TYPE} to \code{Release}, hitting the \code{c} key again a few times and then finishing the configuration with the \code{g} key. After that, you can type \code{make} to build your simulation. If you change your simulation code later on, you only need to type \code{make} again. + +If you get an error that \code{FindAkantu.cmake} was not found, you have to set the \code{Akantu\textunderscore{}DIR} variable, which will appear after dismissing the error message. If you built \akantu without running \code{make install}, the variable should be set to the \code{build} subdirectory of the \akantu source code. If you installed it in \code{\$PREFIX}, set the variable to \code{\$PREFIX/share/cmake/Akantu} instead. %%% Local Variables: %%% mode: latex %%% TeX-master: "manual" %%% End: