# FreeFem++

## Category

Mathematics, Physics

## Description

FreeFem++ is a partial differential equation solver. It has its own language. freefem scripts can solve multiphysics non linear systems in 2D and 3D. Problems involving PDE (2d, 3d) from several branches of physics such as fluid-structure interactions require interpolations of data on several meshes and their manipulation within one program. FreeFem++ includes a fast 2^d-tree-based interpolation algorithm and a language for the manipulation of data on multiple meshes (as a follow up of bamg (now a part of FreeFem++ ).

## Available versions (Euler, old software stack)

Legacy versions Supported versions New versions
3.34

## Environment modules (Euler, old software stack)

3.34 module load new gcc/4.8.2 hdf5/1.8.12 open_mpi/1.6.5 fftw/3.3.3 openblas/0.2.8_seq gsl/1.16 scalapack/2.0.2 freefem/3.34 szip/2.1 legacy centos_cruft/6

## How to submit a job

You can submit a FreeFem++ job (using the input file test.epd) in batch mode with the following command:
bsub [LSF options] "FreeFem++ test.epd"

Here you need to replace [LSF options] with LSF parameters for the resource requirements of the job. Please find a documentation about the parameters of bsub on the wiki page about the batch system.

## Example

As an example for using FreeFem++, we are going to solve a Poisson equation. For a given function $f(x, y)$, find a function $u(x, y)$ satisfying \begin{align} -\Delta u(x,y) & = & f(x,y) & \quad\forall & (x,y) & \in \Omega \\ u(x,y) & = & 0 & \quad\forall & (x,y) & \,\text{on}\, \partial\Omega \\ \end{align}

Here $\partial\Omega$ is the boundary of the bounded open set $\Omega \subset R^2 \text{and} \Delta u = \tfrac{\partial^2u}{\partial x^2} + \tfrac{\partial^2u}{\partial y^2}$

The following is a FreeFem++ program which computes $u$ when $f(x, y) = xy$ and $\Omega$ is the unit disk. The boundary $C = \partial\Omega$ is $C = {(x, y)| x = \cos(t)\,, y = \sin(t), 0 \le t \le 2\Pi}$

[leonhard@euler06 ~]$ls -ltr test.edp -rw-r--r-- 1 leonhard T0000 283 Dec 6 12:56 test.edp [leonhard@euler06 ~]$ cat test.edp
border C(t=0,2*pi){x=cos(t); y=sin(t);}
mesh Th = buildmesh (C(50));
fespace Vh(Th,P1);
Vh u,v;
func f= x*y;
real cpu=clock();
solve Poisson(u,v,solver=LU) = int2d(Th)(dx(u)*dx(v) + dy(u)*dy(v)) - int2d(Th)( f*v) + on(C,u=0) ;
cout << " CPU time = " << clock()-cpu << endl;
[leonhard@euler06 ~]$module load new gcc/4.8.2 hdf5/1.8.12 open_mpi/1.6.5 fftw/3.3.3 openblas/0.2.8_seq gsl/1.16 scalapack/2.0.2 freefem/3.34 [leonhard@euler06 ~]$ bsub -n 1 -W 1:00 -R "rusage[mem=2048]" "FreeFem++ test.edp"
Generic job.
Job <33651159> is submitted to queue <normal.4h>.
[leonhard@euler06 ~]$bjobs JOBID USER STAT QUEUE FROM_HOST EXEC_HOST JOB_NAME SUBMIT_TIME 33651159 leonhard PEND normal.4h euler06 * test.edp Dec 6 13:17 [leonhard@euler06 ~]$ bjobs
JOBID      USER        STAT  QUEUE      FROM_HOST   EXEC_HOST   JOB_NAME   SUBMIT_TIME
33651159   leonhard    RUN   normal.4h  euler06     e3011       * test.edp Dec  6 13:17
[leonhard@euler06 ~]$bjobs No unfinished job found [leonhard@euler06 ~]$ grep -A1 Solve lsf.o33651159
-- Solve :
min -0.0103244  max 0.0102905
[leonhard@euler06 ~]\$

You can find the resource usage summary in the LSF log file.