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#  MFEM + PyMFEM (FEM library)

This repository provides Python binding for MFEM. MFEM is a high performance parallel finite element method (FEM) library (http://mfem.org/). 

Installer (setup.py) builds both MFEM and binding together. 
By default, "pip install mfem" downloads and builds the serial version of MFEM and PyMFEM.
Additionally, the installer supports building MFEM with specific options together with other external libraries, including MPI version.

## Install
```
pip install mfem                    # binary install is available only on linux platforms (Py36-39) 
pip install mfem --no-binary mfem   # install serial MFEM + wrapper
```
The setup script accept various options. TO use it, please download
the package and run the script manually. For example, this below download
and build parallel version of MFEM library (linked with Metis and Hypre)
and install under <prefix>/mfem
```
$ pip3 download mfem
(expand tar.gz file and move to the downloaded directory)
$ python setup.py install --with-parallel # it download and build metis/hypre/mfem
```
Choosing compiler
```
$ python setup.py install --with-parallel --CC=icc --CXX=icpc --MPICC=mpiicc --MPICXX=mpiicpc
```
For other configurations, see docs/install.txt or help
```
$ python setup.py install --help
```
## Install from github master
```
git clone https://github.com/mfem/PyMFEM.git
cd PyMFEM
python setup.py install --mfem-branch=master  # build both MFEM and PyMFEM
  
cd test
python test_examples.py -serial
```  
## Usage
Here is an example to solve div(grad(f)) = 1 in a square and to plot the result
with matplotlib (modified from ex1.cpp). Use the badge above to open this in Binder.
```
import mfem.ser as mfem

# create sample mesh for square shape
mesh = mfem.Mesh(10, 10, "TRIANGLE")

# create finite element function space
fec = mfem.H1_FECollection(1, mesh.Dimension())   # H1 order=1
fespace = mfem.FiniteElementSpace(mesh, fec)      

# 
ess_tdof_list = mfem.intArray()
ess_bdr = mfem.intArray([1]*mesh.bdr_attributes.Size())
fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list)

# constant coefficient 
one = mfem.ConstantCoefficient(1.0)

# define Bilinear and Linear operator
a = mfem.BilinearForm(fespace)
a.AddDomainIntegrator(mfem.DiffusionIntegrator(one))
a.Assemble()
b = mfem.LinearForm(fespace)
b.AddDomainIntegrator(mfem.DomainLFIntegrator(one))
b.Assemble()

# create gridfunction, which is where the solution vector is stored
x = mfem.GridFunction(fespace);
x.Assign(0.0)

# form linear equation (AX=B)
A = mfem.OperatorPtr()
B = mfem.Vector()
X = mfem.Vector()
a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
print("Size of linear system: " + str(A.Height()))

# solve it using PCG solver and store the solution to x
AA = mfem.OperatorHandle2SparseMatrix(A)
M = mfem.GSSmoother(AA)
mfem.PCG(AA, M, B, X, 1, 200, 1e-12, 0.0)
a.RecoverFEMSolution(X, b, x)

# extract vertices and solution as numpy array
verts = mesh.GetVertexArray()
sol = x.GetDataArray()

# plot solution using Matplotlib

import matplotlib.pyplot as plt
import matplotlib.tri as tri

triang = tri.Triangulation(verts[:,0], verts[:,1])

fig1, ax1 = plt.subplots()
ax1.set_aspect('equal')
tpc = ax1.tripcolor(triang, sol, shading='gouraud')
fig1.colorbar(tpc)
plt.show()
```
![](https://raw.githubusercontent.com/mfem/PyMFEM/pip_install_dev/docs/example_image.png)


## License
PyMFEM is licensed under BSD-3.
Please refer the developers' web sites for the external libraries
* MFEM: https://mfem.org/
* Hypre: https://computing.llnl.gov/projects/hypre-scalable-linear-solvers-multigrid-methods
* METIS: http://glaros.dtc.umn.edu/gkhome/metis/metis/overview
