load "msh3"

// Parameters
int nn = 20; // Mesh quality

// Mesh
int[int] labs = [1, 2, 2, 1, 1, 2]; // Label numbering
mesh3 Th = cube(nn, nn, nn, label=labs);
// Remove the ]0.5,1[^3 domain of the cube
Th = trunc(Th, (x < 0.5) | (y < 0.5) | (z < 0.5), label=1);

// Fespace
fespace Vh(Th, P1);
Vh u, v;

// Macro
macro Grad(u) [dx(u), dy(u), dz(u)] //

// Define the weak form and solve
solve Poisson(u, v, solver=CG)
    = int3d(Th)(
          Grad(u)' * Grad(v)
          1 * v
    + on(1, u=0)

// Plot
plot(u, nbiso=15);

A high level multiphysics finite element software

FreeFEM offers a fast interpolation algorithm and a language for the manipulation of data on multiple meshes.

Easy to use PDE solver

FreeFEM is a popular 2D and 3D partial differential equations (PDE) solver used by thousands of researchers across the world. It allows you to easily implement your own physics modules using the provided FreeFEM language. FreeFEM offers a large list of finite elements, like the Lagrange, Taylor-Hood, etc., usable in the continuous and discontinuous Galerkin method framework.

Numerous physics are pre-built :

  • Incompressible Navier-Stokes (using the P1-P2 Taylor Hood element)
  • Lamé equations (linear elasticity)
  • Neo-Hookean, Mooney-Rivlin (nonlinear elasticity)
  • Thermal diffusion
  • Thermal convection
  • Thermal radiation
  • Magnetostatics
  • Electrostatics
  • Fluid-structure interaction (FSI)

Strong mesh and parallel capabilities

FreeFEM has it own internal mesher, called BAMG, and is compatible with the best open-source mesh and visualization software like Tetgen, Gmsh, Mmg and ParaView. Written in C++ to optimize for speed, FreeFEM is interfaced with the popular mumps, PETSc and HPDDM solvers.

Latest Articles

September 05, 2019 | S.Ye. Donets, V.F. Klepikov, V.V. Lytvynenko, E.M. Prokhorenko, O.A. Startsev, Yu.F. Lonin, A.G. Ponomarev, V.T. Uvarov, R.I. Starovoytov

Modification Effects of Microsecond High Current Electron Beam Exposure on Titanium VT22 Alloy

Titanium VT22 alloy was irradiated in the TEMP-A accelerator with the high current electron beam with the en-ergy of 350 keV, beam current of 2 kA, pulse length around 5μs, and beam diameter of 45 mm. The irradiation was performed for three samples with 1 to 3 pulses separately. Numeric simulations of the temperature distributions in the targets were conducted using the thermoelastic ablation model. The microstructural and mechanical properties of the irradiated alloy were studied using microhardness testing, metallography and fractography analysis.

September 05, 2019 | M.I. Bazaleev, V.V. Bryukhovetsky, S.Ye. Donets, V.F. Klepikov, V.V. Lytvynenko, E.M. Prokhorenko, O.A. Startsev, Yu.F. Lonin, A.G. Ponomarev, V.T. Uvarov

Application of radiation processes for testing of gas turbine blades

Structural integrity of the gas turbine blades is of great concern. A set of methods and instruments is proposed to study the problems of the test loading of the industrial turbine blades. The approach aims to model the possible high-temperature, shock and irradiation impacts. The test loading is performed using the high-current relativistic electron beam. The developed methodology can be used for test and identification trails of the turbine blades. The experi-mental bench is designed to assist the thermographic measurements of the temperature dynamics in the blades. It also comprises the corresponding algorithms and software to perform the necessary calculations with.

September 02, 2019 | J Li, H Zheng, Q Zou

A priori and a posteriori estimates of the stabilized finite element methods for the incompressible flow with slip boundary conditions arising in arteriosclerosis

In this paper, we develop the lower order stabilized finite element methods for the incompressible flow with the slip boundary conditions of friction type whose weak solution satisfies a variational inequality. The 𝐻1-norm for the velocity and the 𝐿2-norm for the pressure decrease with optimal convergence order. The reliable and efficient a posteriori error estimates are also derived. Finally, numerical experiments are presented to validate the theoretical results.


17-19 DECEMBER 2019

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16-20 SEPTEMBER 2019

CIRM - Marseille, France

Workshop - Parallel Solution Methods for Systems Arising from PDEs

03-13 JULY 2019

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Scientific calculation in the context of household waste management

19-21 JUNE 2019

Rencontre Mathématiques de Rouen

Introduction to FreeFEM version 4

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