mFEM by aeslaughter

Welcome to mFEM.

mFEM is a parallel, object-oriented, open-source finite element library that includes automatic assembly routines. The project was started to serve as a means for methods testing and comparison against advanced, massively parallel frameworks such as libMesh.

This project is currently inactive. I am no longer working on the projected that supported the development of this code and no longer have access to MATLAB. The master branch is a relatively complete implementation and th parallel branch is a work in progress to imporve the efficiency. The later is working to some extent but requires quite a bit of work and some re-implementation before it is in a stable state. I honestly hope to return to this project some day and create a valuable educational tool, but it will likely not be for some years.

Installation

Installation is trival, since mFEM relies soley on MATLAB's built in functionality. To install mFEM:

Download the zipped source code: mFEM zipped source .
Unzipped the source code in a directory of your choice (e.g., ../MATLAB/mFEM).
Start MATLAB and naviate to the directory of the mFEM source code.
Run the install function from the MATLAB command line.
```
 >> install; 
```

The install functions simply adds the necessary directories to the path and adds the documentation to the help browser. Once installed an mFEM section should be added to MATLAB's help, which may be found by opening the help browser and searching for mFEM.

Demo Problem

The following code solves a simple displacement problem using 13 lines of code, with a few extra for plotting the results. This is demo was extracted from Example 7 of the mFEM source code, which contains dozens of example problems, with and without the automatic solvers and assembly functionality.

Generate a rectangular, 2D grid. This grid rangs from 0 to 10 in the x-direction and -0.5 to 0.5 in the y-direction. It is discritized into 30 and 20 elements in the x- and y-direction, respectively.

mesh = mFEM.Mesh('Space','vector');
mesh.grid('Quad4',0,10,-0.5,0.5,30,20);

Add boundary tags to the left and right side.

mesh.addBoundary(1, 'right'); 
mesh.addBoundary(2, 'left');
mesh.update();

Add the finite element equations.

sys = mFEM.System(mesh);
sys.addConstant('E', 1e7, 'v', 0.3, 'P', [0;100]);
sys.addConstant('D', 'E / (1-v^2) * [1, v, 0; v, 1, 0; 0, 0, (1-v)/2]');
sys.addMatrix('K', 'B''*D*B');
sys.addVector('f', 'N''*P', 'Tag', 2);

Assemble and solve the equations.

solver = mFEM.solvers.LinearSolver(sys);
solver.addEssential('tag',1,'value',0);
u = solver.solve();

Plot the results.

mesh.plot(u,'-deform','Patch',{'EdgeColor','k'},'Colorbar','y-disp. (m)','Component', 2);
title('FEM Solution');
xlabel('x (m)'); ylabel([]);

Acknowledments

Funding for this project was provided by the National Science Foundation Earth Sciences Postdoctoral Fellowship Program.