mfem 4.3.0.0

MFEM + PyMFEM (finite element method library)

MFEM + PyMFEM (FEM library)

This package provides MFEM and its Python wrapper (PyMFEM). MFEM is a high performance parallel finite element method (FEM) library (http://mfem.org/).

Installer downloads a couple of external libraries and build them. By default, "pip install mfem" downloads and builds the serial version of MFEM and PyMFEM. See more detail below for other configurations

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 /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

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()

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