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        "author": "Roman Poya",
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        "description": "[![Build Status](https://travis-ci.com/romeric/florence.svg?token=HFW6d19YsYpKDNwvtqDr&branch=master)](https://travis-ci.com/romeric/florence)\n[![Coverage Status](https://coveralls.io/repos/github/romeric/florence/badge.svg?branch=master&service=github)](https://coveralls.io/github/romeric/florence?branch=master)\n\n**Florence** is a Python-based computational framework for multi-physics simulations using the finite element and boundary element methods.\n\n# Features\nA non-exhaustive list of core features:\n- High order planar and curved finite and boundary elements (line, tri, quad, tet, hex)\n- In-built CAD-conformal curvilinear mesh generator\n- Powerful in-built pre and post processor with the ability to visualise high order curved meshes\n- Poisson, electrostatic and heat transfer solvers\n- Linear, geometrically linearised and fully nonlinear solid/structural mechanics solvers\n- Linear, geometrically linearised and fully nonlinear electromechanics solvers\n- Implicit and explicit dynamic solver with contact formulation\n- Generic monolithic, staggered and multigrid solvers for coupled multiphysics driven problems\n- Strain gradient and micropolar elasticity and electro-elasticty solvers\n- A suite of advanced hyperelastic, electrostatic and electro-hyperelastic material models\n- Ability to read/write mesh/simulation data to/from gmsh, Salome, GID, Tetgen, obj, FRO, VTK and HDF5\n- Support for heterogeneous computing using SIMD, shared parallelism, cloud-based parallelism and cluster-based parallelism\n- Interfaces to a suite of sparse direct and iterative solvers including MUMPS, Pardiso & Petsc and hypre\n\nIn addition, the framework also provides Python interfaces to many low-level numerical subroutines written in C, C++ and Cython.\n\n# Platform support\nFlorence supports all major operating systems including Linux, macOS and Windows (under Cygwin/MinGW) under\n- Python 2.7\n- Python >= 3.5\n- PyPy >= v5.7.0\n\n\n# Dependencies\nThe following packages are hard dependencies\n- [Fastor](https://github.com/romeric/Fastor):          Data parallel (SIMD) FEM assembler\n- cython\n- numpy\n- scipy\n\nThe following packages are optional (but recommended) dependencies\n- [PostMesh](https://github.com/romeric/PostMesh):      High order curvilinear mesh generator\n- pyevtk\n- matplotlib\n- mayavi\n- scikit-umfpack\n- pyamg\n- psutil\n- h5py\n\nIn addition, it is recommended to have an optimised BLAS library such as OpenBLAS or MKL installed and configured on your machine.\n\n# Installation\n## The easy way\nusing pip\n\n```\npip install Florence\n```\n\nFor pip installation to work you need to have `Fastor` installed. You can achieve this by\n\n```\ncd ~\ngit clone https://github.com/romeric/Fastor\nmv Fastor/ /usr/local/include/Fastor/\n```\n\nIt is also a good practice to set your compilers before pip installing florence\n\n```\nexport CC=/path/to/c/compiler\nexport CXX=/path/to/c++/compiler\n```\n\n## Building from source\nHave a look at `travis.yml` file for directions on installing florence's core library. First install `cython`, `numpy` and `scipy`. Download `Fastor` headers and place them under their default location `/usr/local/include/Fastor`\n\n```\ncd ~\ngit clone https://github.com/romeric/Fastor\nmv Fastor/ /usr/local/include/Fastor/\n```\n\nThen installation of the core library is as easy as\n\n```\ngit clone https://github.com/romeric/florence\ncd florence\npython setup.py build\nexport PYTHONPATH=\"/path/to/florence:$PYTHONPATH\"\n```\n\nThis builds many low-level cython modules, ahead of time. Options can be given to `setup.py` for instance\n\n```\npython setup.py build BLAS=mkl CXX=/usr/local/bin/g++ CC=~/LLVM/clang\n```\n\nBy default, florence builds in parallel using all the machine's CPU cores. To limit the build process to a specific number of cores, use the `np` flag for instance, for serial build one can trigger the build process as\n\n```\npython setup.py build np=1\n```\n\n## Configuring MUMPS direct sparse solver\nFlorence can automatically switch to `MUMPS` sparse direct solver if available. To install `MUMPS`, the easiest way is to use `homebrew` on macOS and `linuxbrew` on linux:\n\n```\nbrew install mumps --without-mpi --with-openblas\ngit clone https://github.com/romeric/MUMPS.py\ncd MUMPS.py\npython setup.py build\npython setup.py install\n```\n\nAnd whenever `MUMPS` solver is needed, just open a new terminal window/tab and do (this is the default setting for linuxbrew)\n```\nexport LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/home/linuxbrew/.linuxbrew/lib\n```\n\n## Configuring Pardiso direct sparse solver\nThe direct sparse solver shipped with `MKL`, `Pardiso` can be used if `MKL` is available. Both Anaconda and Intel distribution for python ship these.\nIf `MKL` is installed, the low-level FEM assembler in florence is also automatically linked to it during compilation, as long as \"`BLAS=mkl`\" flag is issued to `setup.py`.\n\n```shell\nconda install -c haasad pypardiso\n```\nWe typically do not recommed adding `anaconda/bin` to your path. Hence, whenever `MKL` features or `Pardiso` solver is needed, just open a new terminal window/tab and type\n\n```\nexport PATH=\"/path/to/anaconda2/bin:$PATH\"\n```\n\n# Philosophy\nFlorence follows scipy's philosophy of providing a high level pythonic interface to finite element analysis of partial differential equations. It is a light weight library that depends only on the most ubiquitous python packages namely numpy, scipy and cython. Yet it is aimed to deliver high performance numerical computations on a range modern architectures. It is backend is designed to be configurable for plugging new solvers such as Petsc's and hypre's parallel solvers.\n\n# Documentation\nDocumentation is available under [wiki](https://github.com/romeric/florence/wiki) pages. Furthermore, a series of well explained examples are provided in the example folder that cover most of the functionality of florence.\n\nTo get a quick taste of Florence, let us consider the Laplacian for example. Setting up and solving the Laplace equation using fourth order hexahedral Lagrange shape functions over a cube is as simple as\n\n~~~python\nimport numpy as np\nfrom Florence import *\n\n\ndef simple_laplace():\n    \"\"\"An example of solving the Laplace equation using\n        fourth order hexahedral elements on a cube\n    \"\"\"\n\n    # generate a linear hexahedral mesh on a cube\n    mesh = Mesh()\n    mesh.Cube(element_type=\"hex\", nx=6, ny=6, nz=6)\n    # generate the corresponding fourth order mesh\n    mesh.GetHighOrderMesh(p=4)\n\n    # set up boundary conditions\n    def dirichlet_function(mesh):\n        # create boundary flags - nan values would be treated as free boundary\n        boundary_data = np.zeros(mesh.nnode)+np.NAN\n        # potential at left (Y=0)\n        Y_0 = np.isclose(mesh.points[:,1],0)\n        boundary_data[Y_0] = 0.\n        # potential at right (Y=1)\n        Y_1 = np.isclose(mesh.points[:,1],mesh.points[:,1].max())\n        boundary_data[Y_1] = 10.\n\n        return boundary_data\n\n    boundary_condition = BoundaryCondition()\n    boundary_condition.SetDirichletCriteria(dirichlet_function, mesh)\n\n    # set up material\n    material = IdealDielectric(mesh.InferSpatialDimension(), eps=2.35)\n    # set up variational form\n    formulation = LaplacianFormulation(mesh)\n    # set up solver\n    fem_solver = FEMSolver(optimise=True)\n    # solve\n    results = fem_solver.Solve( boundary_condition=boundary_condition,\n                                material=material,\n                                formulation=formulation,\n                                mesh=mesh)\n\n    # write results to vtk file\n    results.WriteVTK(\"laplacian_results\")\n\n\nif __name__ == \"__main__\":\n    simple_laplace()\n~~~",
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