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FreeFem++ v 4.7-1 (November 06 2020 15:18:22.)
Introduction

 
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++ ).

FreeFem++ is written in C++ and the FreeFem++ language is a C++ idiom. It runs on Macs, Windows, Unix machines. FreeFem++ replaces the older freefem and freefem+.

If you use Freefem++ please cite the following reference in your work (books, articles, reports, etc.): Hecht, F. New development in FreeFem++. J. Numer. Math. 20 (2012), no. 3-4, 251–265. 65Y15

the bibtex is: 
@article {MR3043640,
    AUTHOR = {Hecht, F.}, TITLE = {New development in FreeFem++},
   JOURNAL = {J. Numer. Math.},  FJOURNAL = {Journal of Numerical Mathematics},
    VOLUME = {20}, YEAR = {2012},
    NUMBER = {3-4}, PAGES = {251--265},
      ISSN = {1570-2820}, MRCLASS = {65Y15}, MRNUMBER = {3043640},
}


HPC and FreeFem++
Some FreeFem++ presentation (with useful information):
Related software:


Examples 2d
  • A small movie (340Kb) : Cool air (green) comes from the lower left and mix with hot air (magenta), the right boundary is free. This is Navier-Stokes-Boussinesq integrated with P1-bubble P1 mixte finite element.
  • A very small example 2d of how to solve the Poisson equation on a L shape : 
border aaa(t=0,1){x=t;y=0;};
border bbb(t=0,0.5){x=1;y=t;};
border ccc(t=0,0.5){x=1-t;y=0.5;};
border ddd(t=0.5,1){x=0.5;y=t;};
border eee(t=0.5,1){x=1-t;y=1;};
border fff(t=0,1){x=0;y=1-t;};
mesh Th = buildmesh (aaa(6) + bbb(4) + ccc(4) +ddd(4) + eee(4) + fff(6));
fespace Vh(Th,P1);   //  to change P1 in P2 to make P2 finite element.
Vh u=0,v;
func f= 1;
func g= 0;
int i=0;
real error=0.1, coef= 0.1^(1./5.);
problem Probem1(u,v,solver=CG,eps=-1.0e-6) =
    int2d(Th)(  dx(u)*dx(v) + dy(u)*dy(v)) 
  + int2d(Th) ( v*f ) 
  + on(aaa,bbb,ccc,ddd,eee,fff,u=g)  ;
  
for (i=0;i< 10;i++)
{   
  real d = clock();
  Probem1; //  solve the problem 
  plot(u,Th,wait=1);
  Th=adaptmesh(Th,u,inquire=1,err=error);
  error = error * coef;
} ;

Solution on adapted mesh and associated mesh.

Examples 3d
  • A very small example of how to solve the Stokes equation 3d on cube shape : 
    
load "msh3" load "medit"  // dynamics load tools for 3d.
int nn=8;
mesh Th2=square(nn,nn);
fespace Vh2(Th2,P2);  Vh2 ux,uz,p2;
int[int] rup=[0,2],  rdown=[0,1], rmid=[1,1,2,1,3,1,4,1];
real zmin=0,zmax=1;
mesh3 Th=buildlayers(Th2,nn,
  zbound=[zmin,zmax],  reffacemid=rmid, 
  reffaceup = rup,     reffacelow = rdown);
  
medit("c10x10x10",Th);  // see the 3d mesh with medit software
fespace VVh(Th,[P2,P2,P2,P1]);

 macro Grad(u) [dx(u),dy(u),dz(u)] // EOM
 macro div(u1,u2,u3) (dx(u1)+dy(u2)+dz(u3))  //EOM

VVh [u1,u2,u3,p];
VVh [v1,v2,v3,q];
  
solve vStokes([u1,u2,u3,p],[v1,v2,v3,q]) = 
  int3d(Th,qforder=3)( Grad(u1)'*Grad(v1) +  Grad(u2)'*Grad(v2) +  Grad(u3)'*Grad(v3)
                  - div(u1,u2,u3)*q - div(v1,v2,v3)*p + 1e-10*q*p ) 
  + on(2,u1=1.,u2=0,u3=0) + on(1,u1=0,u2=0,u3=0) ;
 plot(p,wait=1, nbiso=5);  // a 3d plot of iso  pressure. in progress... march 2009
 //  to see the 10 cut plan in 2d 
for(int i=1;i<10;i++)
{
 real yy=i/10.; // compute yy.
  // do 3d -> 2d interpolation.
 ux= u1(x,yy,y); uz= u3(x,yy,y);  p2= p(x,yy,y);
 plot([ux,uz],p2,cmm=" cut y = "+yy,wait= 1);
}

    Solution on cup plan y=0.5 and mesh 10x10x10 and associated mesh.

Ongoing Work
  • FreeVol: Finite Vol technics in FreeFem++ for hyperbolic PDEs
  • 3D implementation: new solver, new mesh tools, new kind of finite element
  • Stabilize and test all parallel linear solver interface
Download, The current version of FreeFem++ is 4.7-1
Coloring Syntax FreeFem++
Last modified: 2 juin 2014