4 CDMATH is a geometrical and numerical toolbox designed for numerical analysts who work on the discretisation of partial differential equations on general shapes and meshes and would rather focus on high-level scripting. The library originates from [CDMATH](http://cdmath.jimdo.com), a collaborative workgroup with the same name. It is based on the [MEDcoupling](https://docs.salome-platform.org/latest/dev/MEDCoupling/tutorial/index.html) C++/python library of the [SALOME](http://www.salome-platform.org/) project for the handling of meshes and fields, and on the C++ library [PETSC](https://www.mcs.anl.gov/petsc/) for the handling of matrices and linear solvers. The library is currently developed for linux distributions and is maintained on Ubuntu 14.04 LTS, 16.04 LTS and 18.04 LTS, as well as on Fedora 24, 26, 28 and 29.
8 - [Examples of stable numerical methods for the 1D linear transport equation](tests/doc/1DTransportEquation/RegularGrid/TransportEquation1D_RegularGrid.ipynb)
9 - [Example of stable numerical scheme for the 1D heat equation](tests/doc/1DHeatEquation/HeatEquation1D_RegularGrid.ipynb)
10 - [Examples of unstable numerical methods for the 1D linear transport equation](tests/doc/1DTransportEquation/UnstableSchemes/TransportEquation1D_UnstableSchemes.ipynb)
11 - [Shock formation and numerical capture issues for the 1D Burgers' equations](tests/doc/1DBurgersEquation/BurgersEquation1D.ipynb)
12 - [Numerical convergence and maximum principle analysis for the linear finite element method applied to the 2D Poisson equation](tests/doc/2DPoissonEF/Convergence_Poisson_FE_SQUARE.ipynb)
13 - [Numerical convergence analysis for the FV5 finite volume method applied to the 2D Poisson equation](tests/doc/2DPoissonVF/Convergence_Poisson_FV5_SQUARE.ipynb)
14 - [Numerical convergence analysis for the linear finite element and FV5 finite volume methods applied to the 2D Poisson equation with discontinuous boundary conditions](tests/doc/2DPoisson_StiffBC_DISK/2DPoisson_StiffBC_DISK.ipynb)
15 - [Numerical convergence analysis for the FV5 finite volume method applied to a 2D anisotropic diffusion equation](tests/doc/2DDiffusionVF/Convergence_Diffusion_FV5_SQUARE.ipynb)
16 - [Influence of the mesh on the convergence and low Mach precision for the UPWIND finite volume method applied to the 2D wave system](tests/doc/2DWaveSystemVF_stationary/Convergence_WaveSystem_Upwind_SQUARE.ipynb)
17 - [Influence of the mesh on the convergence and low Mach precision for the CENTERED finite volume method applied to the 2D wave system](tests/doc/2DWaveSystemVF_stationary/Convergence_WaveSystem_Centered_SQUARE.ipynb)
18 - [Influence of the mesh on the convergence and low Mach precision for the STAGGERED finite volume method applied to the 2D wave system](tests/doc/2DWaveSystemVF_stationary/Convergence_WaveSystem_Staggered_SQUARE_squares.ipynb)
19 - [Influence of the mesh on the convergence and low Mach precision for the PSEUDO-STAGGERED (colocated) finite volume method applied to the 2D wave system](tests/doc/2DWaveSystemVF_stationary/Convergence_WaveSystem_PStag_SQUARE.ipynb)
20 - [Finite elements for the Poisson problem on a cube in 3D (by S. Kameni Ngwamou, PhD student)](tests/doc/3DPoissonEF/FiniteElements3DPoisson_CUBE.ipynb)
21 - [Finite elements for the stationary diffusion of the temperature in a 3D room. Influence of the radiator position (by S. Kameni Ngwamou, PhD student)](tests/doc/3DRoomCoolingEF/3DRoomCoolingEF.ipynb)
22 - [Surface Finite elements for the Poisson-Beltrami problem on a sphere in 3D (by M. Nguemfouo, PhD student)](tests/doc/3DPoissonSphereEF/SynthesisConvergenceFESphere.pdf)
23 - [Surface Finite elements for the Poisson-Beltrami problem on a torus in 3D (by M. Nguemfouo, PhD student)](tests/doc/3DPoissonTorusEF/SynthesisConvergenceFETorus.pdf)
25 Download CDMATH sources to compile
26 ----------------------------------
28 Create your source directory. For instance:
29 * `mkdir ~/workspace/cdmath`
30 * `cd ~/workspace/cdmath`
33 * click on the following link : `https://github.com/ndjinga/CDMATH/archive/master.zip` then unzip the file in a directory cdmath-master
34 * or type the following in a terminal : `wget https://github.com/ndjinga/CDMATH/archive/master.zip` then unzip the file in a directory cdmath-master
35 * or clone the git repository to a folder cdmath-master: `git clone https://github.com/ndjinga/CDMATH.git cdmath-master`
38 Set environment for the compilation of CDMATH
39 ---------------------------------------------
40 Dependencies. The following packages list is sufficient on Ubuntu 14.04, Ubuntu 16.04, Ubuntu 18.04 :
42 - `cmake3` (mandatory)
43 - `g++` or another C++ compiler (mandatory)
44 - `libhdf5-dev` (mandatory)
45 - `python-dev`, `python-numpy` and `swig`, if you want to use CDMATH commands in Python scripts. Use the compilation option `-DCDMATH_WITH_PYTHON=ON`. (highly recommended)
46 - `python-matplotlib` and `paraview` for postprocessing tools such as plotting curves (matplotlib) or generating 3D view images (paraview). Use the compilation option `-DCDMATH_WITH_POSTPRO=ON` (recommended).
47 - `petsc` if you want to solve large spase linear systems. Typically required for implicit methods. Use the compilation option `-DCDMATH_WITH_PETSC=ON` (recommended).
48 - `jupyter`, in order to generate and visualise nice reports from test case simulations (optional)
49 - `doxygen`, `graphviz` and `mscgen`, if you want to generate a nice source code documentation in `~/workspace/cdmath/cdmath_install/doc/`. Use the compilation option `-DCDMATH_WITH_DOCUMENTATION=ON` (optional).
50 - `libcppunit-dev`, if you want to generate unit tests. Use the compilation option `-DCDMATH_WITH_TESTS=ON` (optional).
51 - `rpm`, if you want to generate RPM installation packages. Use the compilation option `-DCDMATH_WITH_PACKAGE=ON` (optional).
53 Directories. Create the suggested build and installation folders:
54 * `cd ~/workspace/cdmath`
55 * `mkdir cdmath_build`
56 * `mkdir cdmath_install`
60 Compile and install CDMATH
61 --------------------------
62 Generate makefiles for a minimum version:
63 * `cmake ../cdmath-master/ -DCMAKE_INSTALL_PREFIX=../cdmath_install -DCMAKE_BUILD_TYPE=Release`
65 Or generate makefiles for an all-options version:
66 * `cmake ../cdmath-master -DCMAKE_INSTALL_PREFIX=../cdmath_install -DCMAKE_BUILD_TYPE=Release -G"Eclipse CDT4 - Unix Makefiles" -D_ECLIPSE_VERSION=4.3 -DCDMATH_WITH_PETSC=ON -DCDMATH_WITH_PYTHON=ON -DCDMATH_WITH_POSTPRO=ON -DCDMATH_WITH_TESTS=ON -DCDMATH_WITH_DOCUMENTATION=ON`
72 Run unit and example tests:
78 Notes for compilation options:
79 * Eclipse: The Cmake options `-G"Eclipse CDT4 - Unix Makefiles" -D_ECLIPSE_VERSION=4.3` create project files if you want to develop CDMATH with Eclipse Kepler or higher.
80 * HDF5: On some systems (not Ubuntu 14.04 nor Ubuntu 16.04), you may have to use the compilation option `-DHDF5_ROOT_DIR=/path/to/hdf5/library` too.
81 * PETSc: If the library Petsc is already installed in your system (packages libpetsc-dev for ubuntu and petsc-devel for fedora 25 and 26), you may save time and disk space by using the installed library instead of installing a new one. In order to do so use the compilation options `-DPETSC_DIR=/path/to/petsc/installation/petsc -DPETSC_ARCH=arch-linux2-c-opt`. If you prefer to compile PETSc yourself from the sources you may follow the instructions given in [the official documentation](http://www.mcs.anl.gov/petsc/documentation/installation.html).
85 We recommend using CDMATH in python scripts which avoids the hassle of having to edit Makefile files and compiling every C++ scripts.
87 To use CDMATH with your Python code, you can load the CDMATH environment in your terminal using the command
88 * source `~/workspace/cdmath/cdmath_install/env_CDMATH.sh`
89 Then in your terminal simply type
92 If performance or parallelism is an issue for your simulations, you can use CDMATH librairies with your C++ code :
93 * C++ libraries: `export LD_LIBRARY_PATH=~/workspace/cdmath/cdmath_install/lib`
94 * To know how to include the right libraries for compilation, see the makefiles of the examples. They include the list `-linterpkernel -lmedC -lmedloader -lmedcoupling -lbase -lmesh -llinearsolver`.
96 The CDMATH environment variables consist in :
97 * C++ libraries: `export LD_LIBRARY_PATH=~/workspace/cdmath/cdmath_install/lib`
98 * Python libraries: `export PYTHONPATH=~/workspace/cdmath/cdmath_install/lib/cdmath:~/workspace/cdmath/cdmath_install/bin/cdmath`
100 Create Linux installation packages for CDMATH
101 ---------------------------------------------
102 After popular request, here is how you can create packages for Debian and Red Hat-based Linux distributions:
104 1. Download CDMATH as explained hereabove.
105 2. Set the environment as explained hereabove (in particular, make sure you have `rpm` installed).
106 3. Generate a makefile with `cmake -DCMAKE_INSTALL_PREFIX=../cdmath_install -DCMAKE_BUILD_TYPE=Release -DCDMATH_WITH_PACKAGE=ON ../cdmath-master/` and eventually other options (documentation, tests, swig, etc).
107 4. Compile with `make package`.
109 You will then find a Debian package in the build directory; you may install it on Ubuntu 14.04 or Ubuntu 16.04. You will also find an RPM package, which you may install on Red Hat-based distributions. This way, the packages you generate may include all the compilation options you want.
111 Unfortunately, the Debian package may be said to be of “bad quality” for Debian standards as far as ownership is concerned. This is true and due to limitations in CMake/CPack. The package should still install nonetheless.
