FEMG library (Finite Element Methods on Graphs)

Coding a library to define, analyze and solve differential problems on graphs.

This work is the final project for the course in Advanced Programming for Scientific Computing (a.y. 2018/19) held at Politecnico di Milano (Milan, Italy).

The repository contains a report with some detailed theoretical and numerical analysis made by the two authors on differential problem on graphs. Particular attention is given to eigenvalue problems.

Authors:
Stefano Abbate ([email protected])
Andrea Di Primio ([email protected])

Dependencies

The library depends on several external libraries.

GetFEM++ (ver. 5.3 or higher)

The GetFEM++ library can be downloaded here.
For export routines, the GetFEM++-MATLAB interface is necessary.

Boost Graph Library (ver. 1.63 or higher)

The Boost Graph Library (BGL) can be downloaded here.

LAPACK

The Linear Algebra PACKage (LAPACK) can be downloaded here.
On Linux, it can be installed using the Package Manager executing
$ sudo apt-get install liblapack-dev
on the terminal.

BGLgeom

The BGLgeom library is not strictly necessary to build the project, although it is used to create data files (denoted by the format .pts). In all test cases, .pts files are pre-generated and read at runtime. To handle custom graphs data files refer to the README.md in the folder data_builder/graph_maker. The BGLgeom repository can be found here.

Installation

To build the library, firstly fill the files Makefile.inc and data_builder/graph_maker/Makefile.inc as indicated therein. Only empty fields have to be modified. Then, open the terminal and run
$ make all
to compile the whole project in the specified installation folder. Partial compilations can be made, type
$ make help
for the list of possible keywords.

To compile the code in verbose mode, use
$ make CPPFLAGS+=-DFEMG_VERBOSE_ all

Code documentation will be generated in both html and LaTeX format (LaTeX compiler eventually needed). To this end, alongside doxygen, the graphviz package is also needed.

Installation issues

A known installation issue in Linux involves BGL library linking. A workaround is to modify the Linux environment variable LD_LIBRARY_PATH, so to include the path to the Boost lib folder. This can be achieved through the command
$ export LD_LIBRARY_PATH=path/to/boost/lib:$LD_LIBRARY_PATH
every time the project is compiled from a new terminal session. To modify the variable once and for all, execute from the terminal
$ sudo nano ~/.bashrc
and add the export command above (without the initial $ sign) as the last line of the file.

A known issue involves setting up the Makefile of the BGLgeom library. First, modify the following in Makefile.inc:

1. libvtk*.so.1 in place of libvtk*.so.5.10.1 at line 69 (if not using VTK 5.10);
2. $(basename $(basename $(VTK_LIBS2))) in place of $(basename $(basename $(basename $(basename $(VTK_LIBS2))))) at line 70 (if not using VTK 5.10);

Then, in libBGLgeom/Makefile:

3. -soname in place of -$(SONAME) at line 62.

A known issue involves the installation of the GetFEM++-MATLAB interface. In the file getfem-5.3/interface/src/matlab/gfm_commmon.c comment lines 45 and 107, both referring to mxSPARSE_CLASS. This only concerns the execution of the MATLAB routines provided in this repository.

A known issue involves the usage of modules to load libraries. The code has been tested installing the external dependencies locally.

Execution and postprocessing

For details on how to execute the code and postprocess the results, refer to the README.md in the test_problem folder.

Dev settings

The code has been tested on Linux Ubuntu 18.04.